BUS 352 Grand Canyon University Titanic Survival Exploratory Data Analysis Excel Task

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This is a Collaborative Learning Community (CLC) assignment.

Follow the instructions found in the "CLC - Titanic Survival: Exploratory Data Analysis" Excel spreadsheet. 

While APA style is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

You are not required to submit this assignment to LopesWrite.

"I shared the spreadsheet, We each must complete these tasks on our own and we can each do 3 slides with speakers notes for our final powerpoint.

Here is the assignment list for everyone for the final power point. Before this can be completed we each have to complete tasks 1-6 on our own then share the data.

Put it all together:

#1. 1 slide Martha

#2. 2 slides Martha

#3. 2-3 Slide Ulises

#4. 1-2 Slides Banipal

#5 1 Slide Banipal

#5 1 Slides Keaolani

#6 2 Slides Keaolani

 

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129 Chapter 6 Solution: How do you feel when someone ask you to come up with a solution? Angellicia I feel like solutions come very easy to me. I think of all the possible solutions and put them all out there. Then, I brainstorm and prioritize the right or most valuable solution. This is where values come to play. What is valued the most will be prioritize first and presented as a solution, but there is not only one solution to try. Try other solutions until you get the desired outcome. Allow yourself the opportunity to fail and correct. Dr. Leslie At first, when someone asked me to come up with a solution it was overwhelming. I did not think or know that I had the expertise to provide solutions. One day during the summer, I went home to visit my fiancée, Angellicia. I remember when my sister-in-law ask me to teach a math summer class. I did not feel like I could teach anyone anything. As I taught the class, I realized that I was the right person for the job. I had so many skills under my belt to be a solution to kids who needed my help. We have what it takes. 130 Does God care about solutions? Yes! In the beginning, God, created the heavens and the earth. The earth had three main issues or dilemmas. The earth was formless, empty, and is the solution to formlessness, emptiness, and darkness. But did you know that you are also the light of the the light of the world. A town built on a hill cannot be hidden. When we build on the hill of Jesus, we will be set on His hill for all to see. Matthew 5:14-16 Shine Your Light 14 town built on a hill cannot be hidden. 15 Neither do people light a lamp and put it under a bowl. Instead they put it on its stand, and it gives light to everyone in the house. 16 In the same way, let your light shine before others, that they may see your good deeds and glorify your Father in heaven. 131 The solution should be presented as light in your areas of influence so that other may see and give God glory. Presenting the solution must be done in a clear and precise way. The solution is light in formlessness, emptiness, and darkness. 6.1 Solution Approach: The solution approach involves three main ideas. The three main ideas are to go to God in prayer, market the solution, and deliver the solution. We want you to think about the solution as a petition, appeal, or request to cause positive change. Go to God in prayer (ask for His direction) Market the Solution (as best as you can) o Find the right target audience (the best area of influence) o Consider your delivery method Advertisement (1 minute or less video) Presentation (10 15 slides) Video (5 minutes or less) Report (1 page summary page is ideal) Paper o Consider your appearance Casual Simi-professional Professional o Consider the place of delivery Use a familiar location or environment 132 Practice Deliver the Solution (as best as you can) o D Define the dilemma o C Describe how data was collected o O Describe how data was organized o V Visualize the data o A Analyze and explain the facts o S Present the solution Share the petition in one bold sentence Share the disadvantages: Describe a bad outcome of what could happen if no improvements were made. Paint a real-world negative impact of the dilemma. Share the advantages: Provide recommendation(s) based on a positive outcome and describe what could happen if improvements were made (choose one or more) Adding to Removing from Changing to/from Motivating with Educating about Call for Action: Ask your target audience for action 133 6.2 Queen Esther Example: The book of Esther is a good book in the Bible to see many of these concepts in action. We will use specific parts of it to explain the concept of having a good solution approach. You will be able to apply DCOVAS to the story of queen Esther and be able to learn some simple everyday life-hacks. Queen Esther became queen by the hand of God placed there because God was going to use her in a miraculous way to have a solution to a dilemma the Jews would face. 134 Esther 3:8-10 8 Then Haman told King Ahasuerus, and divided among the people throughout the provinces of your kingdom. Their laws are different interest to leave them alone. 9 If the king approves, let it be decreed talents treasury for those who will do the 10 The king removed his signet ring from his hand and gave it to Haman, the enemy of the Jewish people. 135 Now that we have a good starting point of the story of Esther, let us dig a little deeper to find secrets and simple everyday life-hacks. We will use DCOVAS to dig a little deeper. Let us start with defining the dilemma and collecting data. D Defining the Dilemma: What is the dilemma here? There is a plot to kill and destroy the Jews. How would you define all the possible outcomes? Jews killed or Jews freed. C Collecting data or evidence: The decree was published to everyone The decree was public information that can be collected (secondary source of data) Queen Esther was an orphan. Mordecai her cousin adopted her and raised her as his own daughter. Mordecai was a great father to Esther. He provided her with good advice which helped her become queen. When Mordecai heard of this decree, he cried, put on mourning clothes, and told queen Esther about this threat seriously. He sent queen Esther a message with stern advice. 136 Esther 4:13-16 13 Mordecai told them to reply to Esther, pose that because you are in the palace, you will escape any more than the other Jewish people.[l] 14 Indeed, if you are silent at this time, relief and deliverance will come to the Jewish people from another place, but you and rish. Who knows but that you were brought to the 15 16 Then Esther replied to Mordecai, eat or drink for three days, night or day. Both I and my young women will also Mordecai to gather and organize all the Jews living in Susa, pray, and fast. It is important to organize when things seem scary and overwhelming. Queen Esther felt compelled to take it to the Lord in prayer corporately and personally. She needed protection, wisdom, and direction from God. The decision to go talk with the king without being 137 asked by name by the king could mean the death for her. Change needs divine and bold action. How would Would you have organized? Would you be willing to pray and fast? Would you be willing to put yourself in danger to live? Would you be willing to cause waves when everything on your end seems to be good? O Organizing data: Pray and ask God for direction Organize categorical data Organize numerical data Queen Esther ask Mordecai to pray. She asked him to gather and organize in two specific categorical ways. The first way was to gather the Jews living in the city of Susa to pray. The second way was for her to gather and organize her young women to pray. Their plan was to fast for three days. They were not going to eat or drink for those three days. This was serious to them. They were going to give protection, wisdom, and direction. protection, wisdom, and direction? What was the result of such organized sacrifice? 138 Esther 5:1-8 Queen Esther Goes before the King 1 On the third day, Esther put on her royal attire and stood in the inner courtyard of the palace in front of the his royal throne in the throne room, opposite the entrance to the building. 2 When the king saw Queen Esther standing in the courtyard, she won his favor, and the king extended to Esther the gold scepter that he was holding. Esther approached and touched the top of the scepter. 3 want, Queen Esther? What is your 4 let the king and Haman come today to 139 5 quickly so we may do what Esther has went to the banquet that Esther had prepared. 6 While they were drinking wine, the your request? Up to half of the 7 and my request: 8 ve found favor with the king and if it pleases the king to grant my petition and to honor my request, let the king and Haman come Looking at the solution approach, queen Esther, Mordecai, and the Jews living in Susa fasted for 3 days. Prayer is always a good starting point for any solution. It provides divine insight and strategies. The story does not say how queen Esther received insight or a strategy, but it does show us the strategy she implemented. God will guide you in 140 many ways. Your goal is to act on what you believe God is saying and go forward in faith. Ask yourself the question, who does God want me to share the petition, appeal, or request with? It is important to find the right person or target audience to share a request with to cause positive change. Although the king signed the decree, he did not fully understand what he was signing. Sometimes we must market to the source of the hurt or dilemma. Other times we need to market to the largest crowd possible. You want to shine your light where you can get the best outcome. Consider your audience and dress appropriately. The way you dress is important. In some cases, casual wear or semi-casual wear is needed. Most times when you are trying to get a point across, you will need to be professional. Queen Esther put on her royal attire (her best clothes). Sharing your petition is a big deal and it should not be taken lightly. There is a huge risk involved when presenting risk. She was willing to put her life on the line to save her people, the Jews. Many times, we are scared to present because we fear looking bad or appearing stupid. If you prepare well and have quality work, your preparation and quality of work will keep you from failing. 141 The framework DCOVAS is a good process to use to present good quality work. You will be able to define, collect, organize, visualize, analyze, and provide a great solution (recommendation). Completing DCOVAS will give you confidence to face your fears just like queen Esther did. and ask him and Haman to join her at her royal banquet. Be bold in your approach just like queen Esther but do things within your power and strength. The best way for queen Esther to celebrate the king was to invite him and his friend to a banquet made just for them. Consider the venue you have available to you and make the best of it. Enticing, luring, or attracting someone is also a good life-hack. Sometimes, it is good to make someone wait for something or desire something. It builds anticipation and excitement. Queen Esther did just that. She asked the king and Haman to come back the next day to hear her request. 142 Esther 7:1-6 Queen Esther Makes Her Request 1 So the king and Haman went to Queen 2 and as they were drinking wine on the second day, the your petition? It will be given you. What is your request? Even up to half the 3 found favor with you, Your Majesty, and if it pleases you, grant me my life this is my petition. And spare my people this is my request. 4 For I and my people have been sold to be destroyed, killed and annihilated. If we had merely been sold as male and female slaves, I would have kept quiet, because no such distress 5 King Xerxe is he? Where is he the man who has 6 143 When it is the right time to provide a solution or request, try to paint a picture of what could happen if nothing changed. Queen Esther did an amazing job of painting the picture that her life was in danger. Use facts to support the claim. Queen Esther was methodical in the way she laid out the facts in verse four in a quick and precise manner. Do not bore your audience with excessive facts, get to the point. Queen Esther did just enough to get the king ready to act. The king did act. He was furious with Haman. Haman lost his life. 144 Esther 8:3-8 3 Esther again pleaded with the king, falling at his feet and weeping. She begged him to put an end to the evil plan of Haman the Agagite, which he had devised against the Jews. 4 Then the king extended the gold scepter to Esther and she arose and stood before him. 5 he regards me with favor and thinks it the right thing to do, and if he is pleased with me, let an order be written overruling the dispatches that Haman son of Hammedatha, the Agagite, devised and wrote provinces. 6 For how can I bear to see disaster fall on my people? How can I 7 King Xerxes replied to Queen Esther and attacked the Jews, I have given his estate to Esther, and they have impaled him on the pole he set up. 8 Now write another Jews as seems best to you, and seal it with for no document and sealed with 145 Queen Esther went back to the king and provided a solution to the dilemma. Many times, we identify a problem or dilemma but never have a solution. The king agreed with the solution and provided Mordecai and queen Esther with a blank decree to write whatever seemed right to them. The solution should be easy to identify. Do not try to over think it. Based your solution on the desired example, the desired outcome was for the Jews not to be killed. They wrote a decree to fight back against anyone who came against the Jews. There were 75 thousand people who were killed for attacking the Jews. Always have a solution. You did all the work defining, collecting, organizing, visualizing, and analyzing a dilemma. Ensure that you use it all to provide a good solution to any dilemma. 6.3 Creating A Presentation (PowerPoint Slides): Create a presentation that you are proud of and excited about presenting. Think about using a tool like PowerPoint to list the main ideas that you would like to present. Make the presentation based on ideas that you are comfortable talking about. Title Slide Overview Slide (Explain what will be seen) D Define Slide (State the dilemma and outcomes) 146 C Collect Slide (Describe how data was gathered) O Organize Slide(s) (Present a table of data gathered 1 2 slides) V Visualize Slide(s) (Provide some type of display 1 3 slides) A Analyze (Calculate and present the facts 1 4 slides) S Solution Slide(s) (Con/Pro: 1 2 slides) Call for Action Slide (1 slide) Questions Slide (1 slide) Resources Slide (List your sources 1 slide) What are you taking away from finding the right solution? Angellicia Finding the solution is a motivator. It is one of those things that keeps you going. You want to find solutions from God. It is the same feeling as helping someone in need. You walk away feeling good. It will motivate us to keep finding good solutions wherever we go. Dr. Leslie Finding the right solution to me is everything when God is included. The idea of using a framework such as DCOVAS to develop a good solution is simple, detailed, and effective. Anyone relying on a solution that comes from God should feel 147 confident that the solution came from a welldefined process. As I look back at my career, the solutions that were based on well-defined processes were successful. Do not rush your solutions. Ask God for direction. Put in the time and watch it bring about success. 148 Chapter 6 Practice, Test, and Apply (PTA) Chapter 6 Practice: Write in your own words the three main solution approaches (found in Section 6.1). 1. 2. 3. Chapter 6 Quiz: Chapter 6 Apply: Final Project Create a PowerPoint presentation summarizing what you have learn. Your goal is to make an appeal as if you were presenting this information to 20 or more persons at one time. Explain why this course could be beneficial for personal and professional growth. Extra Credit: Create 1 minute video summarizing the course. 149 Appendix A: Glossary A A Analyzing Data: Use well established methods, calculations, and/or life-hacks to interpret and explain the data. Alternative Hypothesis (Ha): The opposite of the NULL hypothesis assumption is called the alternative hypothesis (Ha). This is what the researcher wants to test or prove. The alternative will never include the equals to sign and will always be written usin is where the data is least likely to appear, the outer tail(s). The outer tail(s) is known as the alpha value 0. Appearance Coefficient (b1): This is the slope of the first independent variable. It tells the story of how many x-values will produce a y-value as it relates to the trendline. Area Chart: An Area Chart is a good graphical display for visualizing and displaying trends within the data. Average: It is also called the mean, Mu (µ), or x-bar ( ). It looks at all your data and provides a normal or typical or common point of all the data. The average is used the most in statistics. Note: Every time you see a bar on top of a letter like x-bar, it is calculating the average. Excel Formula: [Population Average ( ) or Sample Average ( ) =AVERAGE(values)]. 150 B Bar Chart: A Bar Chart is a good graphical display for visualizing several categories or sub-categorical amounts. C C Collecting Data: Identify the best way to gather your data. Calculate Probability & x-value to the Right: When calculating areas to the right, you must do equals to 1 minus the equation. Calculate Probability between x-values: A simple life-hack to calculate probability between two x-values if you know the x-value1, x-value2, the population average (µ), and the formula requires that you use the largest x-value first minus the second x-value. Calculate the Probability: The entire probability for all the data collected from the smallest value to the greatest value is 1. Categorical Data: Some type of category or quality Classical Method based on equal possible outcome =1/n. The possible outcomes of the lost sheep (LS) is: 1 lost sheep out of 100 sheep (n), P(LS) =1/100, P(LS) = 0.01 or 1%. Continuous: Anything that is measured such as time, voltage, current, height, weight, and the like. It is a number that we round off to make sense of it. Am I really 4 feet 9 inches or am I 4 feet 8.929844200021... The number continues but we round it off to make sense of it. 151 Critical Values: Are the boundaries that show the beginning and ending point of the area that is known to be true, status quo, or historical data (H0). The left critical value is called the Lower Limit. The right critical value is called the Upper Limit. Cumulative Distribution: Add (cumulate) the running count appearing within groups and then calculate each percentage. D D Defining the Dilemma: Identify the dilemma. Write or describe the dilemma plainly. Describe all possible outcomes. Dataset: All observed data (example: All survey results). DCOVAS: The process or framework in which we will be using throughout this book to help us uncover secrets in hopes of inspiring good solutions. Dependent Variable: Relies on another variable. Descriptive Statistics: It describes and summaries collected information. Discrete: The exact number of something. It is a counted item (example: The number of customers in the donut shop right now). E Elements: A part, section, aspect, or characteristic of a variable. It shows up in rows. (example: Early Morning, 152 Equal Frequency Method based on each probability of a variable that all sum up to 1. Always get the variable total first by adding each number (frequency) together. F F or F-stat (Test Statistic): You can use either the Fstat score or the Significance F (overall p-value) score to determine if to reject or accept the NULL hypothesis. They both provide the same answer. It is the overall test statistic value in a regression analysis. It tells if the variables are independent or dependent on each other. Typically, a large F-stat value(over 7) shows that the variables are dependent of each other. Frequency Distribution: Count how often (how frequent) numbers appear within a group or class and calculate its percentages. H Heart Coefficient: (b2): This is the slope of the second independent variable. It tells the story of how many x-values will produce a y-value as it relates to the trendline. Hypothesis Testing: Is another way to uncover the secrets of the data. Hypothesis testing allows us to test against an assumption, a status quo, or something that is known to be true. It tells us if the sample data is considered true or false 153 I Independent Variable: Does not rely on another variable. Intercept Coefficient (b0): This is the y-intercept value. If all the points of the data were plotted on a scatter plot and a trendline was drawn in the middle of all the dots, where the line hits the y-axis would be considered the y-intercept. M Making Predictions & Forecasting: The line formula allows us to make predictions and forecast. We can only make predictions and forecast within the data values being compared on a scatter plot. Predictions outside those values will not be supported by your data. N Non-probability convenience sample: Participants are selected by the easiest way possible. Non-probability judgment sample: Participants are selected by an expert. Normally Distributed: A sample size (n) of 30 or more data points collected. This means that you have collected the minimum required to do an analysis. If there are many outliers (unusual responses) in your dataset, then 50 or more data points will be considered normally distributed. The shape of the data will look like a bell-shaped curve. NULL Hypothesis (H0): The assumption, status quo, and/or something that is known to be true. The 154 NULL (H0) will always have an equals-to sign: =, u zero (µ0) is equal to the population average. It is also called the Hypothesized value. The NULL hypothesis is written as such: H0: µ = µ0. Numerical Data: Some type of number or quantity. O O Organizing Data: Take the information you have collected and put it in order. Observation: All the measurements for an element. (example: The observations for the element Morning are Plain, $800, and Three). Ordered Array: Always try to organize numbers from your smallest to your largest number or vice-versa. P Pie Chart: A Pie Chart is a good graphical display for visualizing several categories or sub-categorical parts. Pivot Tables (PT): Used to create Frequency Distributions, Cumulative Distributions, and/or convert categorical data to numerical data. Population Data: All the possible data and information relating to the dilemma (example: Every customer at a Donut shop). Population data is extremely hard to get in terms of cost, time, and scope. The population size is symbolized by (N). Primary Sources of Data: The researcher collects the data themselves (example: The shepherd takes inventory of the sheep to find that one is missing). 155 Probability cluster sample: Participants are randomly selected from any group or bunch found within the population. Probability simple random sample: Participants are selected randomly from the entire population where every participant has the same opportunity to be selected. Probability stratified sample: Participants are randomly selected from each group or section within the entire population. Probability systematic sample: Participants are randomly selected based on some type of system or order chosen by the collector (example: Collect data from every third participant). Probability: is the chance or likelihood that something will happen. p-value: Also known as the probability value. You can use either the Z-stat score, F-stat score, or the p- value score to determine if to reject or accept the NULL hypothesis. They both provide the same answer. Here is the rule for the p-value: If the p. Q Qualitative Study: A qualitative study looks to understand the how, the what, and/or the why a trend is happening. It primarily uses non-numeric data from an interview. Quantitative Study: A quantitative study looks to understand numbers to make good decisions. It primarily uses numeric data, but it can also use non-numeric data that is changed (recoded) to numeric data. 156 R Random Variable: All data will have the same opportunity to be selected and used within the study. Regression Analysis: Regression analysis is one of the best analysis tools used to determine the strength of a relationship, make predictions, and make forecast. It looks at a dependent (reliant on) variable and compares it with one or more independent (non-reliant) variable(s). A simple line formula helps us understand the strength, make a prediction, and make forecast. Reject or Do Not Reject the NULL (H0): We can test to see if we need to accept H0 or reject H0. This is done by calculating the test statistics to determine if the test statistic appear in the H0 confidence zone or if it appears in the Ha zone. S S Solution: Provide a good recommendation. Sample Data: A random portion of the population data (example: 16 random customers at a Donut shop). Sample data is much easier to get. The sample size is symbolized by (n). Excel Formula: [Population (N) or Sample Size (n) =COUNT(values)]. Scatter Plot: A Scatter Plot is a good graphical display for visualizing and comparing two variables in columns. Secondary Sources of Data: The researcher uses historical data collected by someone else (example: We are using the story from the Lost Sheep to help us make good decisions). Significance F: Also called the overall p-value (probability value). If the overall p-value is very 157 low and less than the alpha value, then the variables are dependent on each other. Standard Deviation: It provides a good understanding of how far away values are from the average. The variance and the standard deviation are saying the same thing. The standard deviation is a measurement that is easier for the human brain to comprehend. Excel Formula: [Population =STDEV.P(values) Or =SQRT(PopulationVariance); Sample Deviation (s) =STDEV.S(values) Or =SQRT(SampleVariance)]. Statistical Inference: Uses sample data to identify the characteristics of the population (example: What type of donuts will the sample customers purchase to represent what the population might purchase). statistician is to uncover hidden secrets by using a welldefined process in hopes of inspiring good solutions. Subjective Method based on religion, convenience, or judgement (example: A Pastor provides a success probability rating based on their expertise probability for success will be P(John) ~ 75%). T t-stat (Test Statistic): You can use either the t-stat score or the p-value score to determine if to reject or accept the NULL hypothesis. They both provide the same answer. V V Visualizing Data: Use graphs, charts, and displays to tell the story of your data. 158 1 Table of Contents Introduction: DCOVAS 5 Chapter 1 Defining the Dilemma: 11 Chapter 2 Collecting Data: 26 Chapter 3 Organizing Data: Chapter 4 Visualizing Data: 54 68 Chapter 5 Analyzing Data: 82 Chapter 6 Solution: 130 Appendix A: Glossary 150 Appendix B: Installing Data Analysis ToolPak 160 Appendix C: Quiz and Application Answers Acknowledgements 162 169 About Authors 170 Index 171 2 Genesis 1:1 (NIV) In the beginning, God created the heavens and the earth. 3 4 Introduction: DCOVAS The goal of a statistician is to uncover hidden secrets by using a well-defined process in hopes of inspiring good solutions. Think about the beginning of time! The biblical claim from the very beginning of time is that God created our environment in which we live in and know. The statistician in you gets to use what God has created, uncover hidden secrets, and provide good solutions. Let us start uncovering secrets. Can you uncover hidden secrets in the creation story? 5 Boring, right? You may have heard that story hundreds of times. What secrets can be pulled out from this story? Did you know that the earth was all water when it was first created? There is a clear dilemma at the very beginning of the creation story. The earth that God has created was formless, empty, and dark. God had a process of uncovering hidden secrets by using real data and information in which He had created to make good decisions and recommendations. excellent, we often skip over the value of the process. They saw that the earth was formless, empty, and dark. The solution to the dilemma was powerful. formlessness, emptiness, and darkness is light. What is that light? John 8: am the light of the world. Whoever follows me will not walk in darkness, but will have the light of Did you get it? Did you know that the solution and recommendation to formlessness, emptiness, and 6 darkness is the light, Jesus? This is only one of many secrets found in the creation story. What other secrets did you find? This book will help the statistician in you to shed light on darkness. We will show you how to uncover hidden facts by using real-world simple life-hacks in hopes of inspiring good solutions. You might have heard about the creation story many times and never looked closely at the data and information provided. As a statistician, you must take a closer look at data and information to get a better understanding of what is happening. Data and information are there in plain sight, but do we see it? This book will help you to dig deeper and see hidden secrets. The process or framework in which we will be using throughout this book to help us uncover secrets in hopes of inspiring good solutions is called, DCOVAS. The acronym DCOVAS stands for: D Defining the Dilemma: Identify the dilemma. Write or describe the dilemma plainly. Describe all possible outcomes. C Collecting Data: Identify the best way to gather your data. 7 O Organizing Data: Take the information you have collected and put it in order. V Visualizing Data: Use graphs, charts, and displays to tell the story of your data. A Analyzing Data: Use well established methods, calculations, and/or life-hacks to interpret and explain the data. S Solution: Provide a good recommendation. Throughout this book we will be practicing, testing, and asking you to apply (PTA) what you have learn to your everyday life. The statistician in you will learn throughout this book how to use the process of DCOVAS to uncover facts by using data and information to make good decisions and recommendations. You will be able to learn and use simple everyday lifehacks. God has created each and every one of us in His own image and likeness. He has created us in an awesome, unique, and brilliant way. Many of us do not tap into the gifts God has given us. This book will remind you of the statistician in you and show you how to uncover secrets and use simple everyday life-hacks in hopes of inspiring good solutions. 8 Introduction Practice, Test, and Apply (PTA) Introduction Practice: 1. What does V stand for? ___________ 2. What does C stand for? ___________ 3. What does A stand for? ___________ 4. What does S stand for? ___________ 5. What does D stand for? ___________ 6. What does O stand for? ___________ Introduction Quiz: In your own words, how would you describe defining the dilemma? Introduction Apply: How would you apply DCOVAS to the creation story knowing that the earth was formless, empty, and dark? There is no right or wrong answers. Fill in the blanks. How would you: D: _______________________ C: _______________________ O: _______________________ V: _______________________ A: _______________________ S: _______________________ 9 10 Chapter 1 Defining the Dilemma: How do you know when to work on a problem, dilemma, or issue? Angellicia I really start working on a problem when the wheels start falling off the bus. I also know when to work on a problem when it starts to mess with something I value. Dr. Leslie I know when to work on a problem, dilemma, or issue when there is a need or a dire need. How does God work on a problem, dilemma, or issue? He works on it in His timing. His timing is perfect. It all works out for His glory. When all is said and done, there is little doubt than to say that this was done by the hand of the Lord. Let us look at another biblical example. Three men came to visit Abraham and Sarah when they were very old (around 99 years old). One of the men was the Lord. The Lord defined their dilemma directly with a desired outcome. Take a deeper look at the story of Abraham and Sarah and see what facts you can uncover. 11 When defining the dilemma, you should first identify the dilemma, write or describe it plainly, and state the outcome(s). Pay attention to how 12 clear the Lord identified the dilemma and stated the desired outcome. The Lord told Abraham that Sarah will already have a son by the time he returns around the same time the following year. The dilemma was that Sarah was childless. The possible outcomes to their dilemma were to remain childless or to have a child. We all know that it is very unlikely to get a baby after a certain age, but the Lord made a promise. We all also know that it takes about 9 months to carry a baby and give birth to the child. The Lord was informing them that around that very time they were having that conversation that they would become pregnant. Is there anything that is too difficult for God? Whatever God says will come to past. Even if it seems impossible, it will come to past. God created everything. He is in total control. We as use His examples to make good decisions and recommendations. 1.1 Definitions: Here are a few definitions to learn before we can start to define the dilemma. The examples used for the definitions are based on imaginary questions answered by customers at a donut shop. 13 Variables: Something that can be changed, controlled, measured, or used in a trial. It shows up in columns. (example: Best Donut, Purchases, and Customer Rating). Elements: A part, section, aspect, or characteristic of a variable. It shows up in rows. (example: Early Morning, Morning, Observation: All the measurements for an element. (example: The observations for the element Morning are Plain, $800, and Three) Dataset: All observed data (example: All survey results) Random Variable: All data will have the same opportunity to be selected and used within the study. 14 Population Data: All the possible data and information relating to the dilemma (example: Every customer at a Donut shop). Population data is extremely hard to get in terms of cost, time, and scope. The population size is symbolized by (N). Sample Data: A random portion of the population data (example: 16 random customers at a Donut shop). Sample data is much easier to get. The sample size is symbolized by (n) Excel Formula: Population (N) or Sample Size (n) =COUNT(values) Average: It is also called the mean, Mu (µ), or x-bar ( ). It looks at all your data and provides a normal or typical or common 15 point of all the data. The average is used the most in statistics. Note: Every time you see a bar on top of a letter like x-bar, it is calculating the average. Excel Formula: Population Average ( ) or Sample Average ( ) =AVERAGE(values) Standard Deviation: It provides a good understanding of how far away values are from the average. The variance and the standard deviation are saying the same thing. The standard deviation is a measurement that is easier for the human brain to comprehend. Excel Formula: Population Standard Deviation ( ) =STDEV.P(values) Or =SQRT(PopulationVariance) Sample Deviation (s) =STDEV.S(values) Or =SQRT(SampleVariance) 16 Statistical Inference: Uses sample data to identify the characteristics of the population (example: What type of donuts will the sample customers purchase to represent what the population might purchase). 1.2 Type of Variables: There are two main types of variables, categorical and numerical. All data collected can be described as one of these two variables. 17 Categorical Data: Some type of category or quality (example: Hair color, gender, Numerical Data: Some type of number or quantity. o Discrete: The exact number of something. It is a counted item (example: The number of customers in the donut shop right now). o Continuous: Anything that is measured such as time, voltage, current, height, weight, and the like. It is a number that we round off to make sense of it. Am I really 4 feet 9 inches or am I 4 feet 8.929844200021... The number continues but we round it off to make sense of it. 1.3 D Defining the Dilemma Now that we have these definitions, we can define the dilemma. Defining the dilemma is a simple two to three-step life-hack process. First, write the dilemma plainly. Secondly, identify the type of dilemma. This step is optional but good to have and know. Lastly, describe all possible outcomes. Write the dilemma plainly: Within one sentence describe the dilemma! Identify the Type of Dilemma (optional): Data Type? 18 Population Sample What type of variable are you dealing with? Categorical Numerical Discrete Continuous Describe all possible outcomes: List all your possible outcomes. Outcomes A or B (example: Customers like or dislike the service) Outcomes A, B, C, etc (example: When should you close the Donut shop, morning, afternoon, or in the evening) 1.4 Ethical Considerations: Ethical, moral, right, proper, and/or just actions must be considered when defining the dilemma. If the dilemma is not simply defined or has clearly defined outcomes, then the statistician in you and these simple everyday life-hacks will be useless. It is your goal to do it right. Consider Doing It Wrong: Unethical behaviors stating or writing the dilemma: o False wordy definitions o Misleading descriptions o Unclear dilemma Incorrect outcomes 19 o Disconnected results o Unclear effects What are you taking away from defining the dilemma? Angellicia I love the simple life-hacks of defining the dilemma. In my example of knowing when to work on a problem, the wheels had to be falling off the bus before I acted. That would represent a plain way of writing the dilemma. The outcome would be as simple as the wheels are good, still falling off, or have fell off the bus. Now, I have a simple way of defining a problem. 20 Dr. Leslie The biggest take away for me is the definitions section. We get to understand the formation of statistical words and see how God had it all under control from the very beginning. The continuous numerical variable. Time is a describes a discrete numerical variable. The number of sons Sarah will give birth to is one. The word son represents a sub-categorical variable. The main category of son is gender. Knowing these definitions can help us define the dilemma in a simple and easy way. 21 Chapter 1 Practice, Test, and Apply (PTA) Chapter 1 Practice: Chapter 1 Quiz: 22 Chapter 1 Apply: Here is the story about Abraham and Sarah again. Can you define their dilemma? Genesis 18:10-12 10 One of the guests was the LORD, and next year, and when I do, Sarah will Sarah was behind Abraham, listening at the entrance to the tent. 11 Abraham and Sarah were very old, and Sarah was well past the age for having children. 12 So she laughed and said to herself, I am worn out and my husband is old, will I really know such 13 The LORD Sarah laugh? Does she doubt that she can have a child in her old age? 14 I am the LORD! There is nothing too difficult t year at the time I promised, and Sarah will already 23 D Defining the Dilemma Write the dilemma plainly: Within one sentence describe the dilemma! _________________________________________ _________________________________________ _________________________________________ Identify the Type of Dilemma (optional): Data Type? Population Sample What type of variable are you dealing with? Categorical Numerical Discrete Continuous Describe all possible outcome: List all your possible outcomes. _________________________________________ 24 25 Chapter 2 Collecting Data: How would you collect data? Dr. Leslie Collecting data to me comes from a willingness of the collector to observe, gather, and document all the evidence needed. It does take time. It does take skills. It must be done randomly where all participant responses, if more than one, will have an equal opportunity to be selected without bias. Then and only then will the collector have good unbiased collected evidence. Angellicia As a therapist in training, we are taught how to have persons openly share information so that we can have them see the root cause of the problem. It is not easy getting this information. Collecting evidence takes time and skill. Does God collect data? The parable (story) of the lost sheep describes the business of caring for sheep. It is a great example of collecting data and uncovering hidden facts. Pay attention to how the shepherd has a count of the number of sheep (100 sheep, discrete numerical variable). Notice that the shepherd did not know 26 the exact time the one sheep went missing. The shepherd had a process in place to gather and collect information about the sheep. It is very important to keep close attention to the business you have been entrusted to manage. Always have a process in place to collect data to uncover hidden secrets. Never make assumptions that all is well. Always trust but verify! Look at the story of the lost sheep to see what secrets you can uncover. The first step in the process is to define the dilemma. The second step in the process is to collect data. What do you see? 27 The religious persons of that time wanted to know response was spectacular. He told a parable that everyone could relate to and understand while at the same time painting a picture of what happens in heaven. Jesus defines the problem by identifying the dilemma and He also described the desired 28 outcome. One sheep out of 99 was lost. The outcome was to find or not find the lost sheep. There are two simple life-hacks for collecting data. First, the shepherd had a process of observing and gathering information on the things he had. Second, he had to collect and gather information outside of his fold to find the lost sheep. Always be willing to go outside the fold to find the desired outcome. Heaven is tracking and gathering information on lost sinners. The thing that causes a celebration in heaven is when one sinner repents even if it is only one percent. When a sinner is able to see the shepherd again and repent, it causes heaven to rejoice. This is such an encouraging thought. Heaven is excited for us when any of us sees the light. We must collect data internally and/or externally. Note: In many examples, God uses a sample size (n) of one. As a statistician, we should use a sample size (n) of 30 or more. If a sample size (n) of 30 or more data points are collected, the data would be considered normally distributed. This means that you have collected the minimum required to do an analysis. If there are many outliers (unusual responses) in your dataset, then 50 or more data points will be considered normally distributed. The shape of the data will look like a bell-shaped curve. 29 Before collecting data, it is always a good idea to go to God in prayer for direction. The story of the lost sheep did not say that the shepherd prayed for direction, but in Proverbs 3:6 it says that if we acknowledge God, He will direct our path. A simple life-hack is to pray for direction. How many times have you found something by simply praying? God often drops a thought into your brain on where to find that lost thing. It is so exciting to find something by praying. 2.1 Sources of Data: There are two sources of data that the researcher can use to collect data internally and/or externally. The two sources of data collections are: Primary Sources of Data: The researcher collects the data themselves (example: The shepherd takes inventory of the sheep to find that one is missing). Secondary Sources of Data: The researcher uses historical data collected by someone else (example: We are using the story from the Lost Sheep to help us make good decisions). 30 Once the researcher has selected their source of data, they must consider whether they are using population or sample data. Here is a quick recap from Chapter 1: Population Data: All the possible data and information relating to the dilemma (example: Every customer at a Donut shop). Population data is extremely hard to get in terms of cost, time, and scope. Sample Data: A random portion of the population data (example: 16 random customers at a Donut shop). Sample data is much easier to get. 2.2 Probability: Probability is the chance or likelihood that something will happen. When we are collecting data, it is good to understand probability to put a calculated value to the possible chance or likelihood that something will happen. It is not a good idea to do something without knowing the probability. Probability may sound difficult, but it is simple to understand when you understand the concept. Here are some facts about probability: Probability is between 0 and 1. It is a decimal number that can be converted to a percentage. 31 A probability of 0 is fairly unlikely to happen A probability of 1 is nearly certain to happen All combined probabilities related to one variable totals to 1 or 100%. When probability is written, use P(variable) (example: The probability of a lost sheep can be written as P(LS) where LS represents a lost sheep) Probability can also be written using the xvalue (example: Donuts purchased in the early morning is $400. The x-value would be 400). Probability to the Left: -value) Probability to the Right: -value) Probability between 2 points: The final authority if something will happen or not happen belongs to God. Whenever God says something, it will come to past. Probability Methods: We can assign probabilities in 3 main ways: Subjective Method based on religion, convenience, or judgement (example: A Pastor provides a success probability rating 32 based on their expertise Judy probability for success probability for success will be P(John) ~ 75%) Classical Method based on equal possible outcome =1/n. The possible outcomes of the lost sheep (LS) is: 1 lost sheep out of 100 sheep (n) P(LS) =1/100 P(LS) = 0.01 or 1% Equal Frequency Method based on each probability of a variable that all sum up to 1. Always get the variable total first by adding each number (frequency) together. Probabilities can also be found by converting a number to a standard value (Z score). Each standard value (Z) has a probability (P) assigned to it. This can be done in a three-step process as followed: 1. Identify the x-value 2. Convert to a Z-score 33 3. Find the probability value (P) Calculating the Standard Value Z-score: The formula to calculate Z is equal to x minus the population average ( ) divided by the population standard deviation ( ). Excel Formula: x-value convert to z-score x = 350, = 500, = 209.76 z-score = ? =STANDARDIZE(x,µ, ) =STANDARDIZE(350,500,209.76) = -0.72 Create in Excel: Finding Z-score x-value (x) Population Average (µ) Z-score 350 500 209.76 -0.72 Standard values (Z-scores) can quickly identify outliers. If the value is less than -3 or greater than +3, it would be considered an outlier. The average (mean) of any number when converted to a Z-score is zero. 34 -3 0 +3 Each standard value (Z-score) has a probability assigned to it. We can convert any population number to a Z-score in order to find the probability of it. Calculate the Probability: The entire probability for all the data collected from the smallest value to the greatest value is 1. Statisticians say that the probability area under the bell-shaped curve is equal to 1. If the entire probability area was split in half, the probability to the left P(L) is 0.5 or 50% and the probability to the right P(R) is also 0.5 or 50%. To calculate the probability to the right, we did 1 minus 0.5 = 0.5. Every time we need to calculate 35 the area to the right, we must do 1 minus the probability to the left. Example: If the probability to the left is 0.60, what is the probability to the right? P(R) = 1 0.60 P(R) = 0.4 Practice 2.2: If the probability to the left is 0.40, what is the probability to the right? P( _ ) = 1 - ___ = ___ Calculate Probability & x-value to the Left: A simple life-hack to calculate a probability to the left if you know the x-value, the population average ( ), and the population standard deviation ( ) is to use Excel. Excel Formula: Find Probability to the Left x = 350, = 500, = 209.76 P(x 350) 36 =NORM.DIST(x, , ,TRUE) =NORM.DIST(350,500,209.76,TRUE) P(x 350) = 0.2373 or 23.73% Create in Excel: Find Probability to the Left x-value (x) Population Average (µ) 350 500 209.76 0.2373 To do the opposite and calculate the x-value to the left if you know the probability (p), the population average ( ), and the population standard deviation ( ) use Excel. Excel Formula: Find x-value to the Left p = 0.20 left, = 500, = 209.76 x=? =NORM.INV(p, , ) =NORM.INV(0.20,500,209.76) x = 323.46 Create in Excel: Find x-value to the Left Probability (p) Population Average (µ) 37 0.2 500 209.76 x= 323.46 Calculate Probability & x-value to the Right: A simple life-hack to calculate probability to the right if you know the x-value, the population average ( ), and the population standard deviation ( ) is to use Excel. When calculating areas to the right, you must do equals to 1 minus the equation. Excel Formula: Find Probability to the Right x = 600, = 500, = 209.76 P(x 600) =1-NORM.DIST(x, , ,TRUE) =1-NORM.DIST(650,500,209.76,TRUE) P(x 600) = 0.8413 or 84.13% Create in Excel: Find Probability to the Right x-value (x) 38 600 Population Average (µ) 500 209.76 0.3168 =1- To do the opposite and calculate the x-vale to the right if you know the probability (p) to the right, the population average ( ), and the population standard deviation ( ) use Excel. Excel Formula: Find x-value to the Right p = 0.20 right (=1-p), = 500, = 209.76 x=? =NORM.INV(1-p, , ) =NORM.INV(1-0.20,500,209.76) x = 323.46 Create in Excel: Find x-value to the Right Probability (p) Population Average (µ) x= 39 0.2 500 209.76 323.46 Calculate Probability between x-values: A simple life-hack to calculate probability between two x-values if you know the x-value1, xvalue2, the population average ( ), and the population standard deviation ( ) is to use Excel. The formula requires that you use the largest xvalue first minus the second x-value. Excel Formula: Find Probability between x-values x1 = 350, x2 = 600, = 500, = 209.76 P(350 x 600) =NORM.DIST(x2, , ,TRUE)NORM.DIST(x1, , ,TRUE) =NORM.DIST(600,500,209.76,TRUE)NORM.DIST(350,500,209.76,TRUE) P(350 x 600) = 0.4460 or 44.60% Create in Excel: Find Probability between x-values x-value1 (x1) x-value2 (x2) 40 350 600 Population Average (µ) 500 209.76 - 0.4460 Probability Formulas: Possible probability outcomes: P(O) =1/n Write probability to the left: P(L) Write probability to the right: P(R) =1-P(L) Excel Formula: Find Probability to the Left -vaule) = Excel Formula: Find x-value to the Left x=? =NORM.INV(x, , ) Excel Formula: Find Probability to the Right P(x 600) = =1-NORM.DIST(x, , ,TRUE) Excel Formula: Find x-value to the Right x=? =NORM.INV(1-p, , ) Excel Formula: Find Probability between xvalues P(350 x 600) = =NORM.DIST(x2, , ,TRUE)NORM.DIST(x1, , ,TRUE) 41 Knowing if something is almost impossible to happen or very likely to happen is good to know. Probability helps us to see when God does the expected or the unexpected. The probability that Sarah would get a baby after passing the normal age of making children helps us to appreciate God in a greater way. The probability of one lost sheep out of one hundred is 1% but God still went after it. Knowing the probability should not prevent us from doing something. It should be used to provide general understanding of the situation. 2.3 Sampling Methods: In most cases, the data collector will be using sample data. There are several sampling methods to collect sample data. Please note that when you are collecting sample data, it should be randomly selected. Stratified sampling is considered one of the best probability methods of collecting data. It identifies all groups in your population and ensures that data is randomly selected from each group. This method is a bit more complicated and time consuming, but it is the best probability sampling method. Here is a good overall view of most of the sampling methods. 42 Non-probability judgment sample: Participants are selected by an expert Non-probability convenience sample: Participants are selected by the easiest way possible Probability simple random sample: Participants are selected randomly from the entire population where every participant has the same opportunity to be selected Probability stratified sample: Participants are randomly selected from each group or section within the entire population Probability systematic sample: Participants are randomly selected based on some type of system or order chosen by the collector (example: Collect data from every third participant) Probability cluster sample: Participants are randomly selected from any group or bunch found within the population 43 Data collection also depends on the type of variable you are using. Here is a quick recap from Chapter 1: Categorical Data: Some type of category or quality (example: Hair color, gender, Numerical Data: Some type of number or quantity. o Discrete: The exact number of something. It is a counted item (example: The number of customers in the donut shop right now). o Continuous: Anything that is measured such as time, voltage, current, height, weight, and the like. It is a number that we round off to make sense of it. Choose the right sampling method if you are the primary source of collecting the data. Remember that you need to collect data randomly. This will get rid of any bias. Aim to collect data from every section of your population randomly. 2.4 Type of Study: There are three types of studies to uncover secrets. A qualitative study looks to understand the how, the what, and/or the why a trend is happening. It primarily uses non-numeric data from an interview. A quantitative study looks to understand numbers to make good decisions. It primarily uses numeric data, but it can also use 44 non-numeric data that is changed (recoded) to numeric data. A Pivot Table is a great tool within Excel to recode data quickly. Lastly, a researcher can use a mixed study which includes both qualitative and quantitative studies to uncover secrets. This book focusses on quantitative studies and research. 2.5 C Collecting Data When collecting data, keep it simple. In some cases, you will just need to collect data internally. In other cases, you will need to collect data externally. Sometimes it requires collecting data both ways, internally and externally. Whichever way you decide remember to keep it as simple as possible. Ask God for direction. Pray about your dilemma Listen and wait for direction 45 Select the source of data: Primary Source Secondary Source Estimate the probability (only if applicable): Subjective Method Classic Method Equal Frequency Method Select sampling/population method (only if applicable): Judgment Convenience Simple Random Stratified Systematic Cluster Select the type of study (only if applicable): Qualitative Study Face-to-Face Interview Telephone Interview Quantitative Study Survey Experiment Mixed Method Study 2.6 Ethical Considerations: 46 There are several ethical considerations to consider when collecting data. Collect data the right way. Always document your sources right away o Write down in-text citation(s) and record all reference(s) o Give credit where credit is due Ensure that you are using randomly selected data and not biased selections Participants should always be treated with respect and dignity o Voluntary participations only o Get approval to collect data always especially if dealing with protected groups such as children, students, o Do not ask leaders to personally get participants o Consider if you want to pay participants and what is an ideal ethical payment o Consider how participants could get the results of the study 47 What are you taking away from collecting data? Dr. Leslie Collecting data is so important. God is the master at collecting data. If God collects data, we should collect data as well. Collecting data is a factual way of learning and knowing what is really happening. Many times, we have a feeling that something is not right. It is exciting to know that we can use a process to see if things are right or wrong. I love that we can look internally and externally for answers. We think that we always must collect information ourselves but that should not always be the case. We can use secondary data that was collected from someone else to make good decisions and recommendations. Angellicia I like knowing the difference between a qualitative and quantitative study. We can use some type of interview to conduct a qualitative study. It uses categorical variables. A survey or experiment can be used to conduct a quantitative study. It uses numbers. No matter which method is used, we should always pay attention to what God has blessed us with. 48 Chapter 2 Practice, Test, and Apply (PTA) Chapter 2 Practice: Calculate the probabilities. Remember to calculate the variable total first. Chapter 2 Quiz: 49 Chapter 2 Apply: Here is the story about The Lost Sheep again. Can you define the dilemma and select how you would collect data? Luke 15:1-7 The Parable of the Lost Sheep 15 Now the tax collectors and sinners were all gathering around to hear Jesus. 2 But the Pharisees and the teachers of mes 3 4 Then Jesus told them this parable: he leave the ninety-nine in the open country and go after the lost sheep until he finds it? 5 And when he finds it, he joyfully puts it on his shoulders 6 and goes home. Then he calls his friends and neighbors together and says, 7 I tell you that in the same way there will be more rejoicing in heaven over one sinner who repents than over ninety-nine righteous persons who do not need to repent. 50 D Defining the Dilemma Write the dilemma plainly: Within one sentence describe the dilemma! _________________________________________ _________________________________________ Identify the Type of Dilemma (optional): Data Type? Population Sample What type of variable are you dealing with? Categorical Numerical Discrete Continuous Describe all possible outcome: List all your possible outcomes. _________________________________________ C Collecting Data Ask God for direction. Pray about your dilemma Listen and wait for direction Select the source of data: Primary Source Secondary Source Estimate the probability (only if applicable): Subjective Method 51 Classic Method Equal Frequency Method Select sampling/population method (only if applicable): Judgment Convenience Simple Random Stratified Systematic Cluster Select the type of study (only if applicable): Qualitative Study Face-to-Face Interview Telephone Interview Quantitative Study Survey Experiment Mixed Method Study 52 53 Chapter 3 Organizing Data: Does God care about organizing data? Imagine having to live in an environment that is very unorganized . Unorganized environments causes stress, frustration, and chaos. Organizing something is not difficult when we make it a goal. Moses had a similar experience. He led about 1 million Israelites out of captivity in hopes of taking them to the promise land that God had promised them. As they were journeying to the promise land, Moses took on the task of judging the people of Israel as their only judge. During this time, father-in-law came and visited him. He observed what Moses was doing. He knew what Moses was doing would burn him out. He explained to Moses how to delegate this task in an organized way. Can you find the hidden secret of organizing something in the story of Moses? 54 55 God does care about organizing. In the beginning, God created and organized the heavens and the earth. We all were made in the image and likeness advice to Moses made sense. He helped Moses put things in order. When we organize, there will be a weight lifted off our shoulders and we can do more if we organize well. Jethro provided Moses with good advice after explaining what would happen if Moses kept judging the people by himself encouraging Moses to go to God in prayer about his advice. Jethro understood that Moses did not . You should also take the same advice. A simple life-hack when organizing something is to start with prayer. Could you have given Moses the same advice? Yes, Jethro was not saying something that was wise beyond belief. He was simply putting things in order. You can put things in order, but we must never be cleaned unless we set the expectation and hold him accountable for it. God used Jethro to explain the concept to Moses. Who is God using in your life to explain concepts to you? This book will show you general concepts on how to organize data using Microsoft Excel. We will go over categorical data first then numerical data. 56 What did you learn about how God organizes data? Angellicia Everyone knows that God is a God of order. This example shows us how God wants us to think on so many different levels. God wants us to teach and instruct. He wants us to show. All these stages take time to develop. We have to be intentional Dr. Leslie I love the leadership implications that this example shows. Many times, as leaders, we see things and just let it go. We do not take the time to provide advice. Jethro could have easily said that Moses is leading one million persons and he does not care about his advice. We need to understand that our level of influence is impactful, but our approach is everything. Jethro skillfully showed Moses the outcome of what he was doing wrong, right at the beginning, and then he provided him a solution in an organized way, fantastic. 57 3.1 Organizing Categorical Data The first thing that should be done when organizing categorical data is to list everything that is known. List items based on variables and subvariables. If you know the elements, list that as well. Put all the information that you have collected in an organized manner. Let us now organize the categorical variables and sub-variables of Jethro recommendation to Moses. Practice 3.1.1: Open Excel or any other similar tool and create Table. Ensure that you make it look good. Try to mimic or improve upon the example seen in this book. Categorical data can be organized from two main tables, summary table and contingency table. A summary table is a great table to use to represent a variable, sub-variables, and its rankings. Each sub-variable is placed in order of its size to help us 58 understand importance. If there is only one categorical variable along with its sub-variables, then we would use a summary table to organize the data. A contingency table also called a cross-tabulation table, or a pivot table is used to organize two variables and its sub-variables. A good example of a contingency table is organizing two categorical variables such as judgement size and gender. A contingency table allows you to organize, list, and compare those two variables together. It is a great table to understand the data. Here is an overview example of how to organize and tally categorical data. Practice 3.1.2: In Excel, try to create the summary table provided. Then try to create the contingency table provided. 59 Ensure that you make it look good. Try to mimic or improve upon the example seen in this book. 3.2 Organizing Numerical Data Let us continue this process by organizing numerical variables. Suppose sections of persons need a judge to solve their issues daily. The list of persons that need a judge: 124, 135, 117, 121, 124, 137, 126, 146, 158, 130, 132, 113, 112, ,38, 141, 143, 144, 127, 153, 127 Always try to organize numbers from your smallest to your largest number or vice versa. This is called putting numbers in an Ordered Array. It makes sense to the mind when things are organized. Notice that in the summary table previously the data was organized from largest to smallest. In some cases, it may be best to go from the largest number to the smallest number. Organize your data based on what is best. Numerical data can be organized in many ways. The following list are some popular methods: Ordered Array: Organize numbers from smallest to largest values or vice-versa. Frequency Distribution: Count how often (how frequent) numbers appear within a group or class and calculate its percentages. 60 Cumulative Distribution: Add (cumulate) the running count appearing within groups and then calculate each percentage. Practice 3.2: What is the smallest number? ________ What is the biggest number? ________ Place the numbers from the smallest value to the largest value. ____________________ 112, 113, 117, 121, 124, 124, 126, 127, 127, 130, 132, 135, 137, 138, 141, 143, 144, 146, 153, 158 Here is an overview example of how to organize numerical data. The goal is to put things in order. It is not something that will come automatically. You must put in the effort. It must be intentional. 3.3 Excel Organizing Tips: 61 There are many tools such as Excel that can be used to arrange data in an organized way. Here are some basic tips: Ordered Array: The best way to put numbers in an ordered array is to enter your data into columns. Then you can sort from smallest to largest or viceversa. If you have more than one column, select all your data, and select Format as Table. This allows you the opportunity to sort any column. Pivot Tables (PT): Used to create Frequency Distributions, Cumulative Distributions, and/or convert categorical data to numerical data. Here is an example of how to create a Pivot Table (PT): Select all your dataset in Excel Go to Insert Click on Pivot Table (PT) Ensure that all your data is selected in the Select a table or range field Place your PT results either in a New Worksheet or in the Existing Worksheet. It maybe best to place your results in the Existing Worksheet. Then click ok. The PivotTable Fields will appear to the right. Click on and drag the category(ies) into the Rows section Click on and drag the category(ies) into the Column section (if needed) Click on and drag the category(ies) into the Values section o Frequency: Use Count 62 o Frequency Percentage: Use Count and Percent of Parent Row Total o Cumulative Frequency: Use Count o Cumulative Percentage: Use Count and % Group: Right Click on row or column value and select group. o Uncheck Starting at value and set to 0 o Check Ending at value and set to your largest value o Set By to the value you want your grouping to be divided into (example: 10) 3.4 O Organizing Data dentify choice(s) to organize data (if applicable): Pray and ask God for direction Organize Categorical Data Summary Table Contingency Table Organize Numerical Data Ordered Array Pivot Table Frequency Distribution Cumulative Distribution 3.5 Ethical Considerations: 63 There are several ethical considerations to consider when organizing data. Organize data the simplest way possible. Document all steps for organizing data Label all variables and elements correctly Ensure that you are selecting all your applicable data when organizing your data. Any missed data will cause bad results. What is a simple life-hack that you are taking away from organizing data? Angellicia We should put things in order. Do something as simple as putting things from smallest to largest. Do not make it difficult or complicated. You know exactly what you need to do, do it. Dr. Leslie I would recommend a simple life-hack as organizing items in categories such as small, medium, or large. Everyone knows how to put things in order. The hardest part of organizing data is to find the time to do it. When you make the time to organize, it pays you back with joy, peace, and happiness. 64 Chapter 3 Practice, Test, and Apply (PTA) Chapter 3.3 Practice: Open Excel or whatever tool you will use and enter the unsorted satisfaction list of persons that need a judge. Sort your data from smallest to largest. Unsorted Sorted Chapter 3 Quiz: 65 Chapter 3 Apply: Use your sorted data and create a Pivot Table. Instructions can be found in Excel Organizing Tips => Pivot Table. 66 67 Chapter 4 Visualizing Data: How has God visualized His promise? God gathered evidence, during the time of Noah, that man was corrupt and full of violence. Noah, on the other hand, was righteous, blameless among the people, and walked faithfully with God. God decided to destroy mankind and the entire earth, but He decided to save Noah and his family. God destroyed the earth with a flood. Afterwards, He provided Noah and the entire world a sign that we still see today. As we prepare to learn the process of visualizing data, look at the conversation God had with Noah. God made a promise to Noah and us. How has God visualized His promise to us? 68 Genesis 9:12-16 12 the covenant I am making between me and you and every living creature with you, a covenant for all generations to come: 13 I have set my rainbow in the clouds, and it will be the sign of the covenant between me and the earth. 14 Whenever I bring clouds over the earth and the rainbow appears in the clouds, 15 I will remember my covenant between me and you and all living creatures of every kind. Never again will the waters become a flood to destroy all life. 16 Whenever the rainbow appears in the clouds, I will see it and remember the everlasting covenant between God and all living creatures God visualized His promise by providing us His rainbow. He wanted all generations to come to know His promise. Even today when we see a rainbow, we are all in awe. It is an amazing sight. We cannot understand where it starts or where it ends. It is spectacular. We should strive to display data in a spectacular way. 69 What comes to mind when you think about the rainbow? Angellicia The rainbow is a tangible promise. When we visualize things, we put a tangible visual to our data. God put a tangible visual to His promise. Dr. Leslie I love the colors of the rainbow. When God thinks about life, He sees it in terms of colors. I can only imagine what each color actually represent. God has a perfect memory. I think that He put the rainbow for us to see and remember His promise as well. 70 This book will show you general concepts on how to visualize data using Microsoft Excel. Visualizing data is not difficult at all. It is used to display main ideas. 4.1 Bar Chart: A Bar Chart is a good graphical display for visualizing several categories or sub-categorical amounts. The process to create a Bar Chart is simple. Complete Practice 4.1 as an example. Practice 4.1: Open Excel or whichever tool you will use and follow the steps below. Try to mimic or create a better Bar Chart. Select your data (just the numbers) Click on Insert Select Insert Column or Bar Chart Select Clustered Column 71 72 4.2 Pie Chart: A Pie Chart is a good graphical display for visualizing several categories or sub-categorical parts. The process to create a Pie Chart is simple. Complete Practice 4.2 as an example. Practice 4.2: Open Excel or whichever tool you will use and follow the steps below. Try to mimic or create a better Pie Chart. Select your data Click on Insert Select Insert Pie or Doughnut Chart Select Pie 73 74 4.3 Area Chart: An Area Chart is a good graphical display for visualizing and displaying trends within the data. The process to create an Area Chart is simple. Complete Practice 4.3 as an example. Practice 4.3: Open Excel or whichever tool you will use and follow the steps below. Try to mimic or create a better Area Chart. Select the 2 variables (columns) to include labels, sub-categories, and numbers Click on Insert Select Insert Line or Area Chart Select Line o Name the Vertical X-Axis (ex. Satisfaction) o Name the Horizontal Y-Axis (ex. Frequency) 75 76 4.4 Scatter Plot A Scatter Plot is a good graphical display for visualizing and comparing two variables in columns. The process to create a Scatter Plot is simple. Complete Practice 4.4 as an example. Practice 4.4: Open Excel or whichever tool you will use and follow the steps below. Try to mimic or create a better Scatter Plot. Select the 2 variables (columns) to include labels and numbers Click on Insert Select Insert Scatter (X, Y) or Bubble Chart Select Scatter 77 78 4.5 V Visualizing the Dilemma Identify choice(s) to visualize data: Bar Chart Pie Chart Area Chart Scatter Plot 4.6 Ethical Considerations: There are several ethical considerations to consider when visualizing data. Visualize data without presenting so much information that it distracts from the information being displayed. Display all needed data only Do not tweak the data in any way Label all charts, plots, and graphs accordingly Limit visual overload (no pictures or excessive information) Keep your displays simple What are you taking away from visualizing data? Angellicia A visual is a tangible representation of something to remember or be aware of. It is important to add visual reminders of what is happening or could happen. Colors is a good visual way of visualizing data. 79 Dr. Leslie I love the fact that God visualizes things and so should we. We have many tools to visualize data. It is not complicated. We should always do it. Chapter 4 Practice, Test, and Apply (PTA) Chapter 4 Quiz: 80 81 Chapter 5 Analyzing Data: When you think about analyzing data, what do you think about? Dr. Leslie When I think about analyzing data, I think about uncovering secrets. It is not always obvious what is hidden. We must discover what is really hidden and show how we found it. Angellicia When I think about analyzing data, I think about using your noodles, brainstorming, studying, scrutinizing, researching, and doing whatever it takes to understand what is happening. 82 Does God analyze data? Have you ever considered how God analyzes people? What does He really look at? Does He look at our smile, head size, or swag. There was a king of Israel called Saul and he was anointed by God to be king, the first king of Israel. Over time, Saul stopped trusting in God. God told the prophet Samuel to go to the house of Jesse and anoint one of his sons to be king. As you read and listen to the following story, ask, and answer the question, what is God looking at (analyzing) when searching for a king? 83 1 Samuel 16:6-12 Samuel Anoints David 6 When they arrived, Samuel saw Eliab LORD anointed stands here before the LORD 7 But the LORD consider his appearance or his height, for I have rejected him. The LORD does not look at the things people look at. People look at the outward appearance, but the LORD 8 Then Jesse called Abinadab and had him pass in front of Samuel. But Samuel LORD has not chosen this one 9 Jesse then had Shammah pass LORD 10 Jesse had seven of his sons pass before Samuel, but Samuel LORD has not chosen 11 12 So he sent for him and had him brought in. He was glowing with health and had a fine appearance and handsome features. Then the LORD 84 God is not concerned about our appearance. God is concerned about our heart. He wants to know where our heart is. The heart of the matter is the life, consistency, or key tendency of the matter. When we analyze data, we want to look at the data in terms of its key tendencies, the heart. This book will look at analyzing data in three ways, descriptive statistics, hypothesis testing, and regression analysis. 5.1 Descriptive Statistics: There are many key tendencies that can be analyzed when describing data. It describes and summarizes collected information. The formulas have been substantially validated and verified over time. This book will not spend time explaining the formulas. Instead, it will focus on finding results in the quickest way possible. Here are the formulas. Definitions: The three main descriptive statistics definitions that are important are: 85 Average: It is also called the mean, Mu (µ), or x-bar ( ). It looks at all your data and provides a normal or typical or common point of all the data. The average is used the most in statistics. Standard Deviation: It provides a good understanding of how far away values are from the average. The variance and the standard deviation are saying the same thing. The standard deviation is a measurement that is easier for the human brain to comprehend. Coefficient of Variation: It compares 2 or more variations together. (Example: Comparing the heart or variation of Abinadab compared to David) Here are important symbols to be reminded of: Manually calculating data will be time consuming and not practical for huge amounts of data. We want to provide you with the quickest way possible to do descriptive statistics. Using Excel, Google Sheets, or the like, it can take 15 seconds or less 86 when using an Excel Add-ins called, Data Analysis ToolPak. Stop and check your Excel, Google sheet, or the like to see if you have the Data Analysis ToolPak included. Appendix B shows how to install a Data Analysis ToolPak for Mac, Windows, Google Sheets/Excel Online users. The manual time-consuming process within Excel to calculate descriptive statistics is as followed: What if we were to say that there is a quick and simple way to make all those calculations within 15 seconds or less? Would you be interested in learning how to do it? Let us show you how to do 87 it. The steps to quickly calculate all descriptive statistics in 15 seconds or less are as followed: 1. Click Data 2. Click Data Analysis 3. Select Descriptive Statistics 4. Enter the Input Range (select the label and all values) 5. Select the Output option called Output Range (select an empty cell where the results should appear) 6. Check both the checkboxes called, Summary Statistics & Confidence Level for Mean 7. Click OK 88 Google Sheets/Excel Online Add-on follows a similar pattern. 1. Click Add-ons 2. Click XLMiner Analysis ToolPak and select Start 3. Select Descriptive Statistics 4. Enter the Input Range (select the label and all values) 5. Enter the Output Range value (enter the cell where the results will appear) 6. Check both the checkboxes called, Summary Statistics & Confidence Level for Mean 7. Click OK 89 The output results are as followed: Practice 5.1 Try to create a descriptive statistic using the Satisfaction values seen here. Your goal is to perform a descriptive statistic within 15 seconds or less. If you can do it, great job! If you cannot do it in 15 seconds or less, practice until you do. 90 5.2 Hypothesis Testing: Hypothesis testing is another way to uncover the secrets of the data. Hypothesis testing allows us to test against an assumption, a status quo, or something that is known to be true. It tells us if the sample data is considered true or false based on the population . Leaders put things to the test. Let us take the story of Job in the bible as an example. In the book of Job, Satan went into the presence of God and God asked him if he had considered Job as a righteous and an upright man. In the presence of God, Satan said, yes, Job only serves You because You have Your edge of protection around him. If You take your edge of protection from him, he will curse You to Your face. If I was God, I might have wiped Satan out of existence right there and then. How could Satan, in the presence of God, challenge God? The level of disrespect is alarming. How did God react to Satan? God told Satan to go and test your claim. A good leader will test even if there is overwhelming past evidence. That is what hypothesis testing does. Satan should have known that whatever God says is 100% true. As a leader, be gracious. If God was gracious and kind to 91 Satan, should you not be gracious and kind to the devils you may lead? Satan went after Job with everything that he had. Job lost children, wealth, friendships, and even his health. Job went from a respected person to a scorned person. Job had no idea that his ruin was based on a conversation that happened in heaven. It was easy for Job to give up and stop trusting in God, but he kept believing in God. Suddenly, the testing period was over. Job got back double for his trouble. He got back all that he lost and more. God was right. Satan provided an alternative that was wrong. Whatever God says is 100% true. As a leader, you can test ideas by using hypothesis testing. Do not be a leader that is not willing to see if things have changed. God has given us all the ability to analyze data by testing it. The assumption, status quo, and/or something that is known to be true is called the NULL hypothesis (H0). It is the area that you are confident about and where most of the data falls. The NULL (H0) will always have an equals-to sign H0 is where most of your data falls. Mu zero (µ0) is equal to the population average. It is also called the Hypothesized value. The NULL hypothesis is written as such: H0: µ = µ0 92 H0 µ0 The two lines that separate the area of confidence (H0) is called, critical values. Critical values are the boundaries that show the beginning and ending point of the area that is known to be true, status quo, or historical data (H0). The left critical value is called the Lower Limit. The right critical value is called the Upper Limit. Example (H0) Claim: The average plain donuts sold in a day is 300. The NULL hypothesis is written as such. H0: µ = 300 The opposite of the NULL hypothesis assumption is called the alternative hypothesis (Ha). This is what the researcher wants to test or prove. The alternative will never include the equals to sign or µ0), then it is a right tailed test or upper tailed test Note: The sign in the alternative hypothesis reveals the tail that is being rejected. 94 Claim 1: If the claim is that the average plain donuts sold in a day is less than 300, then write the alternative first understanding that H0 is listed first and has an opposite sign including the equal sign. Ha: µ < 300 Ha H0 300 Claim 2: If the claim is that the average plain donuts sold in a day is greater than 300, then write the alternative first understanding that H0 is listed first and has an opposite sign including the equal sign. Ha: µ > 300 Ha H0 300 95 Claim 3: If the claim is that the average plain donuts sold in a day is not 300, then write the alternative first understanding that H0 is listed first and has an opposite sign including the equal sign. H0: µ = 300 Ha: µ In most cases, statisticians use a standard true zone, historical zone, or probability confidence level also called the NULL hypothesis (H0) of 95%. Since probability is between 0 and 1, the probability is written for 95% as 0.95. The Z values (lower limit and upper limit boundaries) at the probability 0.95 is -1.96 and/or +1.96. The outer tail . Reject or Do Not Reject the NULL (H0): We can now test to see if we need to accept H0 or reject H0. This is done by calculating the test statistics to determine if the test statistic appear in the H0 confidence zone or if it appears in the Ha zone. If the test statistic (yellow dot) appears in the H0 confidence zone (unshaded area), we 96 say that we do not reject the NULL hypothesis. There is insufficient evidence that the sample average is different from the population average. If the test statistic (yellow dot) appears in the Ha zone, we say that we reject the NULL hypothesis. There is sufficient evidence that the sample average is different from the population average. The whole point of hypothesis testing is to calculate and know when to reject or accept the NULL hypothesis (H0). 97 Note: The Z-stat score and the p-value score provides the same results. You can use either the Z-stat score or the p-value score to determine if to reject or accept the NULL hypothesis. They both provide the same answer. Here is the rule for the pvalue: If the p-value is , then reject H0 Practice 5.2: Reject or Do Not Reject H0 Based on the bell-shaped curve and the test statistic (yellow dot), determine if we should Reject or Do Not Reject H0. Practice 5.2.1: Reject H0 Do Not Reject H0 Practice 5.2.2: 98 Reject H0 Do Not Reject H0 Practice 5.2.3: Reject H0 Do Not Reject H0 We will teach you the art of setting up a template to automatically calculate these results. We recommend that you setup a template in three color-coded ways: Gray: Setup cells where you enter all the known values 99 Blue: Setup cells where you have formulas and automatic calculations being done Green: Setup cells where you can automatically calculate the test statistics and determine if to accept or reject the NULL hypothesis (H0) There are three main templates used in this book to calculate the test statistic: Known Population Standard Deviation Template Known Sample Standard Deviation Template Known Population Proportion Template This book will simplify each specific calculation by providing templates to calculate the test statistic. The test statistic is used to determine if to accept or reject the NULL hypothesis (H0). A simple life-hack is to use templates and understand what the template is doing. Each template should be selected based on information known about your data. In most cases, you will conduct a hypothesis test for a Known Sample Standard Deviation. 100 If , use this template to find the test statistic and determine if to accept or reject H0. If the test statistic falls in the red area, then reject the NULL hypothesis. There is sufficient (overwhelming) evidence that the sample data is not like the population data. Note: In most cases you will not know the Population Standard Deviation. Sample Size (n) =count(values) Sample Average (mean) =average(values) Population Standard Deviation (StdevP or ) =STDEV.P(values) =SQRT(Variance) 101 Select the H0 and Ha Two Tail H0: µ = µo Ha: µ < µo Ha: µ > µo Hypothesized (Hypo) =µ0 Confidence Coefficient (Coe) Level of Significance (alpha) =1-Coe 0.95 0.05 Standard Error (StdError) =StdevP/SQRT(n) Test Statistic (Z-stat) =(mean-Hypo)/StdError Left Tail Critical Value (LTcrit) =NORM.S.INV(alpha) Right Tail Critical Value (RTcrit) =NORM.S.INV(1-alpha) Two Tailed: Left Tail Critical Value (2LTcrit) =NORM.S.INV(alpha/2) Two Tailed: Right Tail Critical Value (2RTcrit) =NORM.S.INV(1-alpha/2) Accept or Reject Zstat: Left Tail =IF(Zstat>LT,"Do not reject","Reject") Accept or Reject Zstat: Right Tail =IF(Zstat2LT,Zstat=alpha,"Do not reject","Reject") Accept or Reject p-value: Right Tail =IF(pvalueRT>=alpha,"Do not reject","Reject") Accept or Reject p-value: Two Tail =IF(2Tpvalue>=alpha,"Do not reject","Reject") X-Lower Limit =mean-CONFIDENCE.NORM(alpha,std,n) X-Upper Limit =mean+CONFIDENCE.NORM(alpha,std,n) 103 Known Sample Standard Deviation (s) If you know the sample standard deviation (s), use this template to find the test statistic and determine if to accept or reject H0. If the test statistic falls in the red area, then reject the NULL hypothesis. There is sufficient (overwhelming) evidence that the sample data is not like the population data. Note: In most cases you will know the Sample Standard Deviation. We will focus most of our attention on this template to determine if to accept or reject the NULL hypothesis (H0). Known Sample Standard Deviation (s) Sample Size (n) =count(values) Sample Average (mean) =average(values) Sample Standard Deviation (s) =STDEV.S(values) =SQRT(Variance) Select the H0 and Ha Two Tail H0: µ = µo Ha: µ < µo 104 Right Tail Ha: µ > µo Hypothesized (Hypo) =µ0 Confidence Coefficient (Coe) Level of Significance (alpha) =1-Coe Standard Error (StdError) =s/SQRT(n) Test Statistic (t-stat) =(Mean-Hypo)/StdError Degrees of Freedom (df) =n-1 Left Tail Critical Value (LT) =T.INV(alpha,df) Right Tail Critical Value (RT) =T.INV(1-alpha,df) Two Tailed: Left Tail (2LT) =T.INV(alpha/2,df) Two Tailed: Right Tail (2RT) =T.INV(1-alpha/2,df) Accept or Reject tstat: Left Tail =IF(t-stat>LT,"Do not reject","Reject") Accept or Reject tstat: Right Tail =IF(t-stat2LT,t-stat=alpha,"Do not reject","Reject") 105 0.95 0.05 Accept or Reject p-value: Right Tail =IF(pvalueRT>=alpha,"Do not reject","Reject") Accept or Reject p-value: Two Tail =IF(2Tpvalue>=alpha,"Do not reject","Reject") X-Lower Limit =mean-CONFIDENCE.T(alpha,s,n) X-Upper Limit =mean+CONFIDENCE.T(alpha,s,n) 106 Known Population Proportion (p) If you know the population proportion (p), use this template to find the test statistic and determine if to accept or reject H0. If the test statistic falls in the red area, then reject the NULL hypothesis. There is sufficient (overwhelming) evidence that the sample data is not like the population data. Known Population Proportion (p) Sample Size (n) =count(values) Sample Proportion Value (SP) Sample Proportion (pbar) =SP/n Select the H0 and Ha Two Tail H0: µ = µo Ha: µ < µo Ha: µ > µo Hypothesized (Hypo) =p0 Confidence Coefficient (Coe) 107 0.95 Level of Significance (alpha) =1-Coe Standard Error (StdError) =SQRT(Hypo*(1-Hypo)/n) Test Statistic (Z-stat) =(pbar-Hypo)/StdError Left Tail Critical Value (LT) =NORM.S.INV(alpha) Right Tail Critical Value (RT) =NORM.S.INV(1-alpha) Two Tailed: Left Tail Critical Value (2LT) =NORM.S.INV(alpha/2) Two Tailed: Right Tail Critical Value (2RT) =NORM.S.INV(1-alpha/2) Accept or Reject Zstat: Left Tail =IF(Zstat>LT,"Do not reject","Reject") Accept or Reject Zstat: Right Tail =IF(Zstat2LT,Zstat=alpha,"Do not reject","Reject") Accept or Reject p-value: Right Tail =IF(pvalueRT>=alpha,"Do not reject","Reject") Accept or Reject p-value: Two Tail =IF(2Tpvalue>=alpha,"Do not reject","Reject") p-Lower Limit =pbar-CONFIDENCE.NORM(alpha,StdError,n) 108 0.05 -1.64 1.64 -1.96 1.96 p-Upper Limit =pbar+CONFIDENCE.NORM(alpha,StdError,n) Hypothesis testing is a great tool to use. A simple life-hack in using hypothesis testing would be to setup a template that can be used in any situation. If you take the time to ensure that the template is setup correctly, it will pay dividends in the future. You will be able to conduct hypothesis testing to see if a claim is true or false. Let us practice using hypothesis testing for a known sample deviation. Let us use the satisfaction output result to conduct a hypothesis test. Suppose that the claim is that the average population average (mean) is not a score of 130. Use the Known Sample Standard Deviation (s) template to determine if to reject or do not reject the NULL Hypothesis. 109 Is there sufficient evidence to prove that the sample mean (132.4) is different from the population mean (130)? H0: µ = 130 Enter data into the Known Sample Standard Deviation Excel Template: Known Sample Standard Deviation (s) Sample Size (n) =count(values) Sample Average (mean) =average(values) Sample Standard Deviation (s) =STDEV.S(values) =SQRT(Variance) 20 132.4 12.67 Select the H0 and Ha Two Tail H0: µ = µo Two Tail H0: µ = µo Ha: µ < µo Ha: µ > µo 110 Hypothesized (Hypo) =µ0 130 What is the result? Either the results to accept or reject z-stat and pvalue can be used. Accept or Reject tstat: Two Tail =IF(AND(t-stat>2LT,tstat=alpha,"Do not reject","Reject") Do not reject What is the Conclusion? There is insufficient evidence to prove that the sample mean (132.4) is different from the population mean (130). Note: If the results had said, Reject, then the conclusion would have said, there is sufficient evidence to prove that the sample mean (x) is different from the population mean (x). 5.3 Regression Analysis: Regression analysis is one of the best analysis tools used to determine the strength of a relationship, make predictions, and make forecast. It looks at a dependent (reliant on) variable and compares it with one or more independent (nonreliant) variable(s). A simple line formula helps us understand the strength, make a prediction, and make forecast. 111 In our story where Samuel had to choose a king, the dependent variable and independent variables would be as followed. Each categorical variable must be converted into numbers to understand the relationship. Dependent Variable: Choosing a king Independent Variables o Appearance o Heart Regression analysis allows us to see the correlation (strength) between two variables. Correlation measures the linear relationship between two variables. Positive relationships go up. Negative 112 relationships go down. No relationship neither goes up or down. Regression: Determines the impact from the independent variable(s) on the dependent variable using the displayed line formula. The best way to present Regression Analysis is to use DCOVAS: Defining Data: o Comparison: Relate Variables o Independent Variable(s){x}: 1 or more o Dependent Variable{y}: 1 o Question: Determine the predictive power of one or more independent variable on a dependent variable o H0: There is no significant prediction of _____ (dependent variable) by _____ (independent variable 1), and/or _____ (independent variable 2), and/or _____ 113 o Ha: There is a significant prediction of _____ (dependent variable) by _____ (independent variable 1), and/or _____ (independent variable 2), and/or _____ Collecting Data: Use survey data or secondary data Organizing Data: Format Data into Tables Visualizing Data: Use a scatter Plot Analyzing Data: Use a statistical tool (Excel, SPSS) & document your results o Excel: Data Analysis Regression o No, there is no significant prediction of _____ (dependent variable) by _____ (independent variable 1), and/or _____ (independent variable 2), and/or _____ If Fstat is < Fcrit value, then do not reject the null hypothesis or If your one-tail p-value is greater than your level of significance, then do not reject the null hypothesis (ex. p-value = 0.06 > level of significance = 0.05 Do Not Reject H0) o Yes, there is a significant prediction of _____ (dependent variable) by _____ (independent variable 1), and/or _____ (independent variable 2), and/or _____ If Fstat is > Fcrit, then reject the null hypothesis or 114 If your one-tail p-value is less than your level of significance (example: alpha = 0.05), then reject the null hypothesis (ex. pvalue = 0.04 < alpha = 0.05 then Reject H0) We can use the Data Analysis tool to calculate regression analysis. Suppose that we were to survey David and his brothers and asked them two questions about their appearance and their heart with God. From a scale of 1 to 10, how would you rate your appearance? How often do you talk with God daily? Take that number and multiply it by 52 weeks. Here are their imaginary results: Here are the steps to perform regression analysis within Excel. 1. Click Data 2. Click Data Analysis 3. Select Regression and click OK 115 4. Enter dependent (y) and independent variables (x) 5. Check Labels if selected and Confidence Level 95% 6. Click OK The Output Results: 116 Understanding the results: Adjusted R Square: It tells us how well the variables relate to each other. The closer the number is to 1 the better the relationship. In our example, the Adjusted R Square value was 0.79 or 79%. This would show a good relationship between variables. Note: Some Adjusted R Square values might be low naturally. You have to know what you are testing and what is its average Adjusted R Square value. F: Also called the F-stat value. It is the overall test statistic value. It tells if the variables are independent or dependent on each other. Typically, a large F-stat value(over 7) shows that the variables are dependent of each other. In our example, the F-stat value was 14.11. Typically, this means that the variables are dependent on each other. Note: F-stat values are right-tailed test. To calculate the critical value use an Excel formula. If F-stat is greater that F-crit, then the variables are dependent on each other. 117 =F.INV.RT(probability, deg_freedom1, deg_freedom2) =F.INV.RT(0.05,2,5) = 5.79 Significance F: Also called the overall p-value (probability value). If the overall p-value is very low and less than the alpha value, then the variables are dependent on each other. Remember that both the p-value and the test statistic (F-stat) must produce the same identical results. In our example, the Significance F value was 0.009 which is less than 0.05 alpha value. Intercept Coefficient (b0): This is the y-intercept value. If all the points of the data were plotted on a scatter plot and a trendline was drawn in the middle of all the dots, where the line hits the y-axis would be considered the y-intercept. In our example, b0 is 60.19. 118 Appearance Coefficient (b1): This is the slope of the first independent variable. It tells the story of how many x-values will produce a y-value as it relates to the trendline. In our example, b1 is -3.36. The negative value represents a downward trend. Heart Coefficient: (b2): This is the slope of the second independent variable. It tells the story of how many x-values will produce a y-value as it relates to the trendline. In our example, b2 is 0.06. The positive value represents an upward trend. 119 P-value: The p-value is different from the Significance F value. This p-value explains which independent variable effects the dependent variable the most. Remember, if the p-value is less than the alpha value, then the variables are dependent on each other. In our example we have two p-values: Appearance P-value = 0.33. This value is greater than 0.05 alpha value. Therefore, appearance is independent of selecting a king. Heart P-value = 0.003. This value is less than 0.05 alpha value. Therefore, the heart is dependent on selecting a king. Making Predictions & Forecasting: The line formula allows us to make predictions and forecast. We can only make predictions and forecast within the data values being compared on a scatter plot. Predictions outside those values will not be supported by your data. Look at the prediction zone for selecting a king based on the heart. 120 We can select different x-values and make predictions. For example, we can predict the y-axis number if we know the x-axis values and b-values. First, let us create an Excel template for predictions. Cre...
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CLC - Titanic Survival: Exploratory Data Analysis

Overview
The sinking of the Titanic is one of the most infamous shipwrecks in history.

While there was some element of luck involved in surviving, it seems some groups of people were more likely to su

You will use the DCOVAS framework. Reference Reading: The Statistician In You: Simple Everyday Life-Hacks (TSIY)
• Define the problem
• Collect data from the appropriate source(s)
• Organize data using tables
• Visualize data using a chart or graph
• Analyze data using a tool and/or calculation(s)
• Solution: Provide a conclusion and solution

Data Set

Tasks (All students must complete this section individually)

3.

Visualize: Create a bar chart of the pivot table (refer to Chapter 4 in TSIY).

6.

Solution: Create and submit one PowerPoint and the combined Excel file.

Putting It All Together:

1.
2.
3.
4.

Create a roles and responsibility slide.
Introduction Slide (Define): Define the problem
Collect Slide: Describe the process to collect your group's data with emphasis on randomization.
Organize and Visualize Slides: Include your pivot tables and bar charts.

7.

References: Cite two or more sources.

Deliverables
As a group, one person needs to submit:



One group PowerPoint presentation (8-12 slides) include all the components listed in the "Tasks" section.

Instructions for Pivot Table:

Instructions for Descriptive Statistics: Click on Insert => Data Analysis => Descriptive Statistics

CLC - Titanic Survival: Exploratory Data Analysis

Overview

The sinking of the Titanic is one of the most infamous shipwrecks in history.
On April 15, 1912, during her maiden voyage, the widely considered “unsinkable” RMS Titanic sank after colliding
with an iceberg. Unfortunately, there weren’t enough lifeboats for everyone onboard, resulting in the death of
While there was some element of luck involved in surviving, it seems some groups of people were more likely to survive than
In this Collaborative Learning Community (CLC) assignment, you will work as a group and explore the Titanic
passenger sample dataset to answer the questions: what sorts of people were more likely to survive using
You will use the DCOVAS framework. Reference Reading: The Statistician In You: Simple Everyday Life-Hacks (TSIY).
• Define the problem
• Collect data from the appropriate source(s)
• Organize data using tables
• Visualize data using a chart or graph
• Analyze data using a tool and/or calculation(s)
• Solution: Provide a conclusion and solution

Variable
Survived
Pclass
Gender
Age
Fare
Variable
pclass

Variable Definition
Definition
Key
Survival
0 = No, 1 = Yes
Ticket class
1 = 1st, 2 = 2nd, 3 = 3rd
Sex
male, female
Age in years
Passenger fare
Variable Notes
Notes
A proxy for socio-economic status (SES)

Data Set
The "CLC - Titanic Survival: Exploratory Data Analysis" Excel spreadsheet contains data for 700 of the real Titanic
passengers. Each row represents one person. The columns describe different attributes about the passengers
including whether they survived (Survived), their social-economic status (Pclass), their gender (Gender), their age
(Age), and the fare they paid (Fare).

Tasks (All students must complete this section individually)
1. Collect: On the "DefineCollectRawData" tab, sort the "recordShuffler" column from smallest to largest
(descending). Copy the first randomized 150 rows of raw data (only Column C to G). Do not include the labels.
2. Organize: Paste the first randomized 150 records to the "OrganizeVisualizeDataset" tab. Create a pivot table
3. Visualize: Create a bar chart of the pivot table (refer to Chapter 4 in TSIY).
4. Analyze: Create a descriptive statistic of the "Fare" column. What is the average and standard deviation for
the survivors? Compare your results with a Titanic research fact (refer to Chapter 4.1 in TSIY).
5. Paste the data from each CLC member into the "SummaryResults" tab and perform descriptive statistics on
this new increased sample size. Then, complete the table. Note: Compare individual group member results to
6. Solution: Create and submit one PowerPoint and the combined Excel file.

Putting It All Together:

As a group, prepare and submit ONE group PowerPoint presentation (8-12 slides) based upon the combined
group analysis, calculations, and conclusions data set. The presentation should include speaker notes and
address the following:
1. Create a roles and responsibility slide.
2. Introduction Slide (Define): Define the problem
3. Collect Slide: Describe the process to collect your group's data with emphasis on randomization.
4. Organize and Visualize Slides: Include your pivot tables and bar charts.
5. Analyze Slides: Compare your group's averages and standard deviations. Explain the differences in a
6. Conclusion: Compare and contrast your group's results and validate it with Titanic research fact(s). The
rainbow is a sign (solution) that the earth will never completely flood again. What is your group’s
7. References: Cite two or more sources.

Deliverables
As a group, one person needs to submit:
• The Excel worksheet containing each individual group members calculations as well as the combined data
and completed summary table from the "SummaryResults" tab. Each student’s Excel file with all the tables,
• One group PowerPoint presentation (8-12 slides) include all the components listed in the "Tasks" section.
Instructions for Pivot Table:

Instructions for Descriptive Statistics: Click on Insert => Data Analysis => Descriptive Statistics

re likely to survive than others.

PassengerId
127
93
174
380
570
663
288
614
585
540
443
313
34
453
375
224
632
543
181
269
627
392
268
141
285
491
366
588
377
61
602
565
230
250
528
496
421
417
45
97
98
466
422
700
198
78

Name
Survived
Corn, Mr. Harry
0
Baxter, Mr. Quigg Edmond
0
Bazzani, Miss. Albina
1
Rouse, Mr. Richard Henry
0
Hodges, Mr. Henry Price
0
Mudd, Mr. Thomas Charles
0
Adahl, Mr. Mauritz Nils Martin
0
Emanuel, Miss. Virginia Ethel
1
McNamee, Mr. Neal
0
Fischer, Mr. Eberhard Thelander
0
Davies, Mr. Alfred J
0
Johansson, Mr. Erik
0
Laroche, Miss. Simonne Marie Anne Andree 1
Silvey, Mrs. William Baird (Alice Munger)
1
Renouf, Mr. Peter Henry
0
de Pelsmaeker, Mr. Alfons
0
Ponesell, Mr. Martin
0
Karun, Miss. Manca
1
Mellors, Mr. William John
1
Navratil, Master. Edmond Roger
1
Otter, Mr. Richard
0
Allison, Mrs. Hudson J C (Bessie Waldo Daniels)0
Blackwell, Mr. Stephen Weart
0
Klasen, Mr. Klas Albin
0
del Carlo, Mr. Sebastiano
0
Longley, Miss. Gretchen Fiske
1
Gee, Mr. Arthur H
0
Abbott, Mr. Rossmore Edward
0
Karlsson, Mr. Nils August
0
Waelens, Mr. Achille
0
Nirva, Mr. Iisakki Antino Aijo
0
Troutt, Miss. Edwina Celia "Winnie"
1
Connolly, Miss. Kate
1
Moraweck, Dr. Ernest
0
Edvardsson, Mr. Gustaf Hjalmar
0
Skoog, Miss. Mabel
0
Butt, Major. Archibald Willingham
0
Quick, Miss. Phyllis May
1
Goodwin, Master. William Frederick
0
Webber, Miss. Susan
1
White, Mr. Percival Wayland
0
Chapman, Mr. John Henry
0
LeRoy, Miss. Bertha
1
Sutehall, Mr. Henry Jr
0
Hamalainen, Mrs. William (Anna)
1
Petranec, Miss. Matilda
0

Pclass
3
1
1
3
2
2
3
3
3
3
3
3
2
1
2
3
2
3
2
2
2
1
1
3
2
1
1
3
3
3
3
2
3
2
3
3
1
2
3
2
1
2
1
3
2
3

Gender
male
male
female
male
male
male
male
female
male
male
male
male
female
female
male
male
male
female
male
male
male
female
male
male
male
female
male
male
male
male
male
female
female
male
male
female
male
female
male
female
male
male
female
male
female
female

Age

Fare
30
8.05
24 247.5208
32 76.2917
50
8.05
50
13
16
10.5
30
7.25
5
12.475
24
16.1
18
7.7958
24
24.15
22
7.7958
3 41.5792
39
55.9
34
21
16
9.5
34
13
4 13.4167
19
10.5
2
26
39
13
25
151.55
45
35.5
18
7.8542
29 27.7208
21 77.9583
47
38.5
16
20.25
22
7.5208
22
9
41
7.125
27
10.5
22
7.75
54
14
18
7.775
9
27.9
45
26.55
2
26
11
46.9
32
13
54 77.2875
37
26
30 106.425
25
7.05
24
14.5
28
7.8958

140
75
478
558
550
690
131
447
395
566
128
194
472
651
435
201
178
360
316
80
541
653
586
572
62
83
555
52
158
501
642
444
697
291
290
241
125
336
54
190
634
26
77
352
355
308
72

Smith, Mr. James Clinch
0
Greenfield, Mr. William Bertram
1
Brocklebank, Mr. William Alfred
0
Cleaver, Miss. Alice
1
Astor, Mrs. John Jacob (Madeleine Talmadge Force)
...


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