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n | -0.1 | -0.01 | -0.001 | -0.0001 | 0.0001 | 0.001 | 0.01 | 0.1 |
A(n) | 2.8680 | 2.7320 | 2.7196 | 2.7184 | 2.7181 | 2.7169 | 2.7048 | 2.5937 |
From the above values we may conjecture that limn→0– A(n) = 2.718... ; limn→0+ A(n) = 2.718...
Since both one-sided limits seem to coincide, limn→0 A(n) = 2.718...
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Lesson Plan 2
Developing student understanding of fractions such as area, quantity models and length as well as computational procedures ...
Lesson Plan 2
Developing student understanding of fractions such as area, quantity models and length as well as computational procedures that involve the fractions.
GB513 Unit 6: Comprehensive Analysis - Discussion
Unit 6 DiscussionIn the last 5 weeks, you have learned the following analysis methodologies: Descriptive statistics, proba ...
GB513 Unit 6: Comprehensive Analysis - Discussion
Unit 6 DiscussionIn the last 5 weeks, you have learned the following analysis methodologies: Descriptive statistics, probability calculations, normal distribution calculations, hypothesis testing, regression, and forecasting.In this Discussion, you will explore how you can apply these methodologies to current events.Research an article on a current event that centers on a controversial issue where the two sides are claiming opposing views. Then describe how you would analyze the situation to settle the issue if you were involved in this event. For example, if the article was about whether a proposed new law about gun control will reduce deaths, you may describe how you would use hypothesis testing to compare data from states where such laws exist. Or, if the article was about actions to take to reduce gas prices, you could talk about how you would use regression to figure out which factors affected prices at the pump the most.Please note that this Discussion should be limited to how statistical analysis can be applied to current issues. This is not the place to champion a particular position on the issue you are discussing or get into an argument about the various sides of an issue. Remember, you are here to analyze, not proselytize.Please use the template below in your answers, so everyone can easily follow your answers to all the questions (copy and paste to your post).Use this template for your Unit 6 Discussion.Summary of the articleBriefly describe the current event described in the article.Central questionWhat issue or question you will you be focusing on in your analysis? What are the conflicting points of view?There has to be some specific issue in dispute at the center (do tax breaks increase spending, what impacts healthcare costs the most, etc.), and the sides have to be defending a particular position.Do not use examples where the issue is based on opinions or morality. For example, “Should abortion be legal?” is largely a morality question and is not suitable for statistical analysis. Conducting a survey to ask people about their opinions is not the same as analyzing data and making conclusions.MethodologyExplain which methodology you will apply. Provide the relevant details. Where will your data come from? How will the results from this methodology answer the question you described above?For example, if you are going to use forecasting, explain how you will do that and how you will measure your accuracy. How will the forecast settle the issue? If you will do a regression analysis, explain what the dependent and independent variables will be. If you do hypothesis testing, what will the null and alternative hypothesis be?
word Math problems, math homework help
Use the data in the table below to determine how many average candy bars an adult would have to eat to supply the energy n ...
word Math problems, math homework help
Use the data in the table below to determine how many average candy bars an adult would have to eat to supply the energy needed for six hours of running.ItemEnergy (Joules) Energy released by metabolism of 1 average candy bar1×10^6 Energy needed for 1 hour of running (adult)4.3×10^6The adult would have to eataverage candy bars.(Round to the nearest whole number as needed.)
Atlantic International University K12 Student Achievement Article Critique
Assignment #2. Article Critique Assignment. Due by Day 7.
Here are the instructions posted in the Week 7 forum for the A ...
Atlantic International University K12 Student Achievement Article Critique
Assignment #2. Article Critique Assignment. Due by Day 7.
Here are the instructions posted in the Week 7 forum for the Article Critique Assignment:Assignment 2: Article CritiqueThe practice of quantitative research not only involves statistical calculations and formulas but also involves the understanding of statistical techniques related to real-world applications. You might not become a quantitative researcher nor use statistical methods in your profession but as a consumer, citizen, and scholar-practitioner, it will be important for you to become a critical consumer of research, which will empower you to read, interpret, and evaluate the strength of claims made in scholarly material and daily news.For this Assignment, you will critically evaluate a scholarly article related to repeated measures ANOVA.
To prepare*Review the Article Critique Assignment Guide in the Walden Library, listed in the Week 2 Learning Resources.*Search the Walden Library for a quantitative article that applies repeated measures ANOVA.Write a 2- to 3-page critique of the research you found in the Walden Library that includes responses to the following prompts:
*Why did the authors select repeated measures ANOVA in the research?*Do you think this test was the most appropriate choice? Why or why not?*Did the authors display the results in a figure or table?*Does the results table stand alone? In other words, are you able to interpret the study from it? Why or why not?Please post question on any element or concept regarding Repeated Measures ANOVA in this forum.
SNHU Housing Price Prediction Model for DM Pan National Real Estate Company Paper
Competencies
In this project, you will demonstrate your mastery of the following competencies:
Apply statistical techni ...
SNHU Housing Price Prediction Model for DM Pan National Real Estate Company Paper
Competencies
In this project, you will demonstrate your mastery of the following competencies:
Apply statistical techniques to address research problems
Perform regression analysis to address an authentic problem
Overview
The purpose of this project is to have you complete all of the steps of a real-world linear regression research project starting with developing a research question, then completing a comprehensive statistical analysis, and ending with summarizing your research conclusions.
Scenario
You have been hired by the D. M. Pan National Real Estate Company to develop a model to predict housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the housing prices based square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.
Directions
Using the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator for what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate Data spreadsheet (both found in the Supporting Materials section) for your statistical analysis.
Note: Present your data in a clearly labeled table and using clearly labeled graphs.
Specifically, include the following in your report:
Introduction
Describe the report: Give a brief description of the purpose of your report.
Define the question your report is trying to answer.
Explain when using linear regression is most appropriate.
When using linear regression, what would you expect the scatterplot to look like?
Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.
Data Collection
Sampling the data: Select a random sample of 50 houses.
Identify your response and predictor variables.
Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.
Data Analysis
Histogram: For your two variables, create histograms.
Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
Interpret the graphs and statistics:
Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
Compare and contrast the shape, center, spread, and any unusual characteristic for your sample of house sales with the national population. Is your sample representative of national housing market sales?
Develop Your Regression Model
Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.
Explain if a regression model is appropriate to develop based on your scatterplot.
Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
Identify any possible outliers or influential points and discuss their effect on the correlation.
Discuss keeping or removing outlier data points and what impact your decision would have on your model.
Find r: Find the correlation coefficient (r).
Explain how the r value you calculated supports what you noticed in your scatterplot.
Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.
Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
Interpret regression equation: Interpret the slope and intercept in context.
Strength of the equation: Provide and interpret R-squared.
Determine the strength of the linear regression equation you developed.
Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the square footage of your home.
Conclusions
Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
Did you see the results you expected, or was anything different from your expectations or experiences?
What changes could support different results, or help to solve a different problem?
Provide at least one question that would be interesting for follow-up research.
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relations ...
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relationship exists between an intervention and an outcome, there is a difference between groups, or there is a correlation between two constructs, it does not always provide a default measure for its importance. Although relationships are significant, they can be very minute relationships, very small differences, or very weak correlations. In the end, we need to ask whether the relationships or differences observed are large enough that we should make some practical change in policy or practice.For this Discussion, you will explore statistical significance and meaningfulness.To prepare for this Discussion:Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance.Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of statistical power and significance testing.Review the American Statistical Association’s press release and consider the misconceptions and misuse of p-values.Consider the scenario:A research paper claims a meaningful contribution to the literature based on finding statistically significant relationships between predictor and response variables. In the footnotes, you see the following statement, “given this research was exploratory in nature, traditional levels of significance to reject the null hypotheses were relaxed to the .10 level.”By Day 3Post your response to the scenario in which you critically evaluate this footnote. As a reader/reviewer, what response would you provide to the authors about this footnote?Scenarios are listed as follows:
1. The p-value was slightly above conventional threshold, but was described as
“rapidly approaching significance” (i.e., p =.06).
An independent samples t test was used to determine whether student satisfaction
levels in a quantitative reasoning course differed between the traditional classroom
and on-line environments. The samples consisted of students in four face-to-face
classes at a traditional state university (n = 65) and four online classes offered at
the same university (n = 69). Students reported their level of satisfaction on a fivepoint
scale, with higher values indicating higher levels of satisfaction. Since the
study was exploratory in nature, levels of significance were relaxed to the .10 level.
The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face
class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the
online sections (M = 3.89, SD = 1.4). We therefore conclude that on average,
students in online quantitative reasoning classes have higher levels of satisfaction.
The results of this study are significant because they provide educators with
evidence of what medium works better in producing quantitatively knowledgeable
practitioners.
2. A results report that does not find any effect and also has small sample size
(possibly no effect detected due to lack of power).
A one-way analysis of variance was used to test whether a relationship exists
between educational attainment and race. The dependent variable of education
was measured as number of years of education completed. The race factor had
three attributes of European American (n = 36), African American (n = 23) and
Hispanic (n = 18). Descriptive statistics indicate that on average, European
Americans have higher levels of education (M = 16.4, SD = 4.6), with African
Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average
lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not
significant F (2,74) = 1.789, p = .175, indicating there are no differences in
educational attainment across these three races in the population. The results of
this study are significant because they shed light on the current social conversation
about inequality.
3. Statistical significance is found in a study, but the effect in reality is very small (i.e.,
there was a very minor difference in attitude between men and women). Were the
results meaningful?
An independent samples t test was conducted to determine whether differences
exist between men and women on cultural competency scores. The samples
consisted of 663 women and 650 men taken from a convenience sample of public,
private, and non-profit organizations. Each participant was administered an
instrument that measured his or her current levels of cultural competency. The
© 2016 Laureate Education, Inc. Page 2 of 2
cultural competency score ranges from 0 to 10, with higher scores indicating higher
levels of cultural competency. The descriptive statistics indicate women have
higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD =
2.1). The results were significant t (1311) = 2.0, p <.05, indicating that women are
more culturally competent than are men. These results tell us that gender-specific
interventions targeted toward men may assist in bolstering cultural competency.
4. A study has results that seem fine, but there is no clear association to social
change. What is missing?
A correlation test was conducted to determine whether a relationship exists
between level of income and job satisfaction. The sample consisted of 432
employees equally represented across public, private, and non-profit sectors. The
results of the test demonstrate a strong positive correlation between the two
variables, r =.87, p < .01, showing that as level of income increases, job
satisfaction increases as well. Press release as follows:AMERICAN STATISTICAL ASSOCIATION RELEASES STATEMENT ON
STATISTICAL SIGNIFICANCE AND P-VALUES
Provides Principles to Improve the Conduct and Interpretation of Quantitative
Science
March 7, 2016
The American Statistical Association (ASA) has released a “Statement on Statistical Significance
and P-Values” with six principles underlying the proper use and interpretation of the p-value
[http://amstat.tandfonline.com/doi/abs/10.1080/00031305.2016.1154108#.Vt2XIOaE2MN]. The ASA
releases this guidance on p-values to improve the conduct and interpretation of quantitative
science and inform the growing emphasis on reproducibility of science research. The statement
also notes that the increased quantification of scientific research and a proliferation of large,
complex data sets has expanded the scope for statistics and the importance of appropriately
chosen techniques, properly conducted analyses, and correct interpretation.
Good statistical practice is an essential component of good scientific practice, the statement
observes, and such practice “emphasizes principles of good study design and conduct, a variety
of numerical and graphical summaries of data, understanding of the phenomenon under study,
interpretation of results in context, complete reporting and proper logical and quantitative
understanding of what data summaries mean.”
“The p-value was never intended to be a substitute for scientific reasoning,” said Ron
Wasserstein, the ASA’s executive director. “Well-reasoned statistical arguments contain much
more than the value of a single number and whether that number exceeds an arbitrary
threshold. The ASA statement is intended to steer research into a ‘post p<0.05 era.’”
“Over time it appears the p-value has become a gatekeeper for whether work is publishable, at
least in some fields,” said Jessica Utts, ASA president. “This apparent editorial bias leads to the
‘file-drawer effect,’ in which research with statistically significant outcomes are much more
likely to get published, while other work that might well be just as important scientifically is
never seen in print. It also leads to practices called by such names as ‘p-hacking’ and ‘data
dredging’ that emphasize the search for small p-values over other statistical and scientific
reasoning.”
The statement’s six principles, many of which address misconceptions and misuse of the pvalue,
are the following:
1. P-values can indicate how incompatible the data are with a specified statistical model.
2. P-values do not measure the probability that the studied hypothesis is true, or the
probability that the data were produced by random chance alone.
3. Scientific conclusions and business or policy decisions should not be based only on
whether a p-value passes a specific threshold.
4. Proper inference requires full reporting and transparency.
5. A p-value, or statistical significance, does not measure the size of an effect or the
importance of a result.
6. By itself, a p-value does not provide a good measure of evidence regarding a model or
hypothesis.
The statement has short paragraphs elaborating on each principle.
In light of misuses of and misconceptions concerning p-values, the statement notes that
statisticians often supplement or even replace p-values with other approaches. These include
methods “that emphasize estimation over testing such as confidence, credibility, or prediction
intervals; Bayesian methods; alternative measures of evidence such as likelihood ratios or
Bayes factors; and other approaches such as decision-theoretic modeling and false discovery
rates.”
“The contents of the ASA statement and the reasoning behind it are not new—statisticians and
other scientists have been writing on the topic for decades,” Utts said. “But this is the first time
that the community of statisticians, as represented by the ASA Board of Directors, has issued a
statement to address these issues.”
“The issues involved in statistical inference are difficult because inference itself is challenging,”
Wasserstein said. He noted that more than a dozen discussion papers are being published in
the ASA journal The American Statistician with the statement to provide more perspective on
this broad and complex topic. “What we hope will follow is a broad discussion across the
scientific community that leads to a more nuanced approach to interpreting, communicating,
and using the results of statistical methods in research.”
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Lesson Plan 2
Developing student understanding of fractions such as area, quantity models and length as well as computational procedures ...
Lesson Plan 2
Developing student understanding of fractions such as area, quantity models and length as well as computational procedures that involve the fractions.
GB513 Unit 6: Comprehensive Analysis - Discussion
Unit 6 DiscussionIn the last 5 weeks, you have learned the following analysis methodologies: Descriptive statistics, proba ...
GB513 Unit 6: Comprehensive Analysis - Discussion
Unit 6 DiscussionIn the last 5 weeks, you have learned the following analysis methodologies: Descriptive statistics, probability calculations, normal distribution calculations, hypothesis testing, regression, and forecasting.In this Discussion, you will explore how you can apply these methodologies to current events.Research an article on a current event that centers on a controversial issue where the two sides are claiming opposing views. Then describe how you would analyze the situation to settle the issue if you were involved in this event. For example, if the article was about whether a proposed new law about gun control will reduce deaths, you may describe how you would use hypothesis testing to compare data from states where such laws exist. Or, if the article was about actions to take to reduce gas prices, you could talk about how you would use regression to figure out which factors affected prices at the pump the most.Please note that this Discussion should be limited to how statistical analysis can be applied to current issues. This is not the place to champion a particular position on the issue you are discussing or get into an argument about the various sides of an issue. Remember, you are here to analyze, not proselytize.Please use the template below in your answers, so everyone can easily follow your answers to all the questions (copy and paste to your post).Use this template for your Unit 6 Discussion.Summary of the articleBriefly describe the current event described in the article.Central questionWhat issue or question you will you be focusing on in your analysis? What are the conflicting points of view?There has to be some specific issue in dispute at the center (do tax breaks increase spending, what impacts healthcare costs the most, etc.), and the sides have to be defending a particular position.Do not use examples where the issue is based on opinions or morality. For example, “Should abortion be legal?” is largely a morality question and is not suitable for statistical analysis. Conducting a survey to ask people about their opinions is not the same as analyzing data and making conclusions.MethodologyExplain which methodology you will apply. Provide the relevant details. Where will your data come from? How will the results from this methodology answer the question you described above?For example, if you are going to use forecasting, explain how you will do that and how you will measure your accuracy. How will the forecast settle the issue? If you will do a regression analysis, explain what the dependent and independent variables will be. If you do hypothesis testing, what will the null and alternative hypothesis be?
word Math problems, math homework help
Use the data in the table below to determine how many average candy bars an adult would have to eat to supply the energy n ...
word Math problems, math homework help
Use the data in the table below to determine how many average candy bars an adult would have to eat to supply the energy needed for six hours of running.ItemEnergy (Joules) Energy released by metabolism of 1 average candy bar1×10^6 Energy needed for 1 hour of running (adult)4.3×10^6The adult would have to eataverage candy bars.(Round to the nearest whole number as needed.)
Atlantic International University K12 Student Achievement Article Critique
Assignment #2. Article Critique Assignment. Due by Day 7.
Here are the instructions posted in the Week 7 forum for the A ...
Atlantic International University K12 Student Achievement Article Critique
Assignment #2. Article Critique Assignment. Due by Day 7.
Here are the instructions posted in the Week 7 forum for the Article Critique Assignment:Assignment 2: Article CritiqueThe practice of quantitative research not only involves statistical calculations and formulas but also involves the understanding of statistical techniques related to real-world applications. You might not become a quantitative researcher nor use statistical methods in your profession but as a consumer, citizen, and scholar-practitioner, it will be important for you to become a critical consumer of research, which will empower you to read, interpret, and evaluate the strength of claims made in scholarly material and daily news.For this Assignment, you will critically evaluate a scholarly article related to repeated measures ANOVA.
To prepare*Review the Article Critique Assignment Guide in the Walden Library, listed in the Week 2 Learning Resources.*Search the Walden Library for a quantitative article that applies repeated measures ANOVA.Write a 2- to 3-page critique of the research you found in the Walden Library that includes responses to the following prompts:
*Why did the authors select repeated measures ANOVA in the research?*Do you think this test was the most appropriate choice? Why or why not?*Did the authors display the results in a figure or table?*Does the results table stand alone? In other words, are you able to interpret the study from it? Why or why not?Please post question on any element or concept regarding Repeated Measures ANOVA in this forum.
SNHU Housing Price Prediction Model for DM Pan National Real Estate Company Paper
Competencies
In this project, you will demonstrate your mastery of the following competencies:
Apply statistical techni ...
SNHU Housing Price Prediction Model for DM Pan National Real Estate Company Paper
Competencies
In this project, you will demonstrate your mastery of the following competencies:
Apply statistical techniques to address research problems
Perform regression analysis to address an authentic problem
Overview
The purpose of this project is to have you complete all of the steps of a real-world linear regression research project starting with developing a research question, then completing a comprehensive statistical analysis, and ending with summarizing your research conclusions.
Scenario
You have been hired by the D. M. Pan National Real Estate Company to develop a model to predict housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the housing prices based square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.
Directions
Using the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator for what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate Data spreadsheet (both found in the Supporting Materials section) for your statistical analysis.
Note: Present your data in a clearly labeled table and using clearly labeled graphs.
Specifically, include the following in your report:
Introduction
Describe the report: Give a brief description of the purpose of your report.
Define the question your report is trying to answer.
Explain when using linear regression is most appropriate.
When using linear regression, what would you expect the scatterplot to look like?
Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.
Data Collection
Sampling the data: Select a random sample of 50 houses.
Identify your response and predictor variables.
Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.
Data Analysis
Histogram: For your two variables, create histograms.
Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
Interpret the graphs and statistics:
Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
Compare and contrast the shape, center, spread, and any unusual characteristic for your sample of house sales with the national population. Is your sample representative of national housing market sales?
Develop Your Regression Model
Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.
Explain if a regression model is appropriate to develop based on your scatterplot.
Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
Identify any possible outliers or influential points and discuss their effect on the correlation.
Discuss keeping or removing outlier data points and what impact your decision would have on your model.
Find r: Find the correlation coefficient (r).
Explain how the r value you calculated supports what you noticed in your scatterplot.
Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.
Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
Interpret regression equation: Interpret the slope and intercept in context.
Strength of the equation: Provide and interpret R-squared.
Determine the strength of the linear regression equation you developed.
Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the square footage of your home.
Conclusions
Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
Did you see the results you expected, or was anything different from your expectations or experiences?
What changes could support different results, or help to solve a different problem?
Provide at least one question that would be interesting for follow-up research.
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relations ...
Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance
As a scholar-practitioner, it is important for you to understand that just because a hypothesis test indicates a relationship exists between an intervention and an outcome, there is a difference between groups, or there is a correlation between two constructs, it does not always provide a default measure for its importance. Although relationships are significant, they can be very minute relationships, very small differences, or very weak correlations. In the end, we need to ask whether the relationships or differences observed are large enough that we should make some practical change in policy or practice.For this Discussion, you will explore statistical significance and meaningfulness.To prepare for this Discussion:Review the Learning Resources related to hypothesis testing, meaningfulness, and statistical significance.Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of statistical power and significance testing.Review the American Statistical Association’s press release and consider the misconceptions and misuse of p-values.Consider the scenario:A research paper claims a meaningful contribution to the literature based on finding statistically significant relationships between predictor and response variables. In the footnotes, you see the following statement, “given this research was exploratory in nature, traditional levels of significance to reject the null hypotheses were relaxed to the .10 level.”By Day 3Post your response to the scenario in which you critically evaluate this footnote. As a reader/reviewer, what response would you provide to the authors about this footnote?Scenarios are listed as follows:
1. The p-value was slightly above conventional threshold, but was described as
“rapidly approaching significance” (i.e., p =.06).
An independent samples t test was used to determine whether student satisfaction
levels in a quantitative reasoning course differed between the traditional classroom
and on-line environments. The samples consisted of students in four face-to-face
classes at a traditional state university (n = 65) and four online classes offered at
the same university (n = 69). Students reported their level of satisfaction on a fivepoint
scale, with higher values indicating higher levels of satisfaction. Since the
study was exploratory in nature, levels of significance were relaxed to the .10 level.
The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face
class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the
online sections (M = 3.89, SD = 1.4). We therefore conclude that on average,
students in online quantitative reasoning classes have higher levels of satisfaction.
The results of this study are significant because they provide educators with
evidence of what medium works better in producing quantitatively knowledgeable
practitioners.
2. A results report that does not find any effect and also has small sample size
(possibly no effect detected due to lack of power).
A one-way analysis of variance was used to test whether a relationship exists
between educational attainment and race. The dependent variable of education
was measured as number of years of education completed. The race factor had
three attributes of European American (n = 36), African American (n = 23) and
Hispanic (n = 18). Descriptive statistics indicate that on average, European
Americans have higher levels of education (M = 16.4, SD = 4.6), with African
Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average
lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not
significant F (2,74) = 1.789, p = .175, indicating there are no differences in
educational attainment across these three races in the population. The results of
this study are significant because they shed light on the current social conversation
about inequality.
3. Statistical significance is found in a study, but the effect in reality is very small (i.e.,
there was a very minor difference in attitude between men and women). Were the
results meaningful?
An independent samples t test was conducted to determine whether differences
exist between men and women on cultural competency scores. The samples
consisted of 663 women and 650 men taken from a convenience sample of public,
private, and non-profit organizations. Each participant was administered an
instrument that measured his or her current levels of cultural competency. The
© 2016 Laureate Education, Inc. Page 2 of 2
cultural competency score ranges from 0 to 10, with higher scores indicating higher
levels of cultural competency. The descriptive statistics indicate women have
higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD =
2.1). The results were significant t (1311) = 2.0, p <.05, indicating that women are
more culturally competent than are men. These results tell us that gender-specific
interventions targeted toward men may assist in bolstering cultural competency.
4. A study has results that seem fine, but there is no clear association to social
change. What is missing?
A correlation test was conducted to determine whether a relationship exists
between level of income and job satisfaction. The sample consisted of 432
employees equally represented across public, private, and non-profit sectors. The
results of the test demonstrate a strong positive correlation between the two
variables, r =.87, p < .01, showing that as level of income increases, job
satisfaction increases as well. Press release as follows:AMERICAN STATISTICAL ASSOCIATION RELEASES STATEMENT ON
STATISTICAL SIGNIFICANCE AND P-VALUES
Provides Principles to Improve the Conduct and Interpretation of Quantitative
Science
March 7, 2016
The American Statistical Association (ASA) has released a “Statement on Statistical Significance
and P-Values” with six principles underlying the proper use and interpretation of the p-value
[http://amstat.tandfonline.com/doi/abs/10.1080/00031305.2016.1154108#.Vt2XIOaE2MN]. The ASA
releases this guidance on p-values to improve the conduct and interpretation of quantitative
science and inform the growing emphasis on reproducibility of science research. The statement
also notes that the increased quantification of scientific research and a proliferation of large,
complex data sets has expanded the scope for statistics and the importance of appropriately
chosen techniques, properly conducted analyses, and correct interpretation.
Good statistical practice is an essential component of good scientific practice, the statement
observes, and such practice “emphasizes principles of good study design and conduct, a variety
of numerical and graphical summaries of data, understanding of the phenomenon under study,
interpretation of results in context, complete reporting and proper logical and quantitative
understanding of what data summaries mean.”
“The p-value was never intended to be a substitute for scientific reasoning,” said Ron
Wasserstein, the ASA’s executive director. “Well-reasoned statistical arguments contain much
more than the value of a single number and whether that number exceeds an arbitrary
threshold. The ASA statement is intended to steer research into a ‘post p<0.05 era.’”
“Over time it appears the p-value has become a gatekeeper for whether work is publishable, at
least in some fields,” said Jessica Utts, ASA president. “This apparent editorial bias leads to the
‘file-drawer effect,’ in which research with statistically significant outcomes are much more
likely to get published, while other work that might well be just as important scientifically is
never seen in print. It also leads to practices called by such names as ‘p-hacking’ and ‘data
dredging’ that emphasize the search for small p-values over other statistical and scientific
reasoning.”
The statement’s six principles, many of which address misconceptions and misuse of the pvalue,
are the following:
1. P-values can indicate how incompatible the data are with a specified statistical model.
2. P-values do not measure the probability that the studied hypothesis is true, or the
probability that the data were produced by random chance alone.
3. Scientific conclusions and business or policy decisions should not be based only on
whether a p-value passes a specific threshold.
4. Proper inference requires full reporting and transparency.
5. A p-value, or statistical significance, does not measure the size of an effect or the
importance of a result.
6. By itself, a p-value does not provide a good measure of evidence regarding a model or
hypothesis.
The statement has short paragraphs elaborating on each principle.
In light of misuses of and misconceptions concerning p-values, the statement notes that
statisticians often supplement or even replace p-values with other approaches. These include
methods “that emphasize estimation over testing such as confidence, credibility, or prediction
intervals; Bayesian methods; alternative measures of evidence such as likelihood ratios or
Bayes factors; and other approaches such as decision-theoretic modeling and false discovery
rates.”
“The contents of the ASA statement and the reasoning behind it are not new—statisticians and
other scientists have been writing on the topic for decades,” Utts said. “But this is the first time
that the community of statisticians, as represented by the ASA Board of Directors, has issued a
statement to address these issues.”
“The issues involved in statistical inference are difficult because inference itself is challenging,”
Wasserstein said. He noted that more than a dozen discussion papers are being published in
the ASA journal The American Statistician with the statement to provide more perspective on
this broad and complex topic. “What we hope will follow is a broad discussion across the
scientific community that leads to a more nuanced approach to interpreting, communicating,
and using the results of statistical methods in research.”
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