T Tests Application, unit 8 assignment help

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UNIT 8

  • PRINT
  • T Tests: Application

    INTRODUCTION

    In Unit 8, we will apply our understanding of t tests in an IBM SPSS assignment. As in Unit 6, you will use the Data Analysis and Application (DAA) Template to submit your assignment.TOGGLE DRAWERHIDE FULL INTRODUCTION

    Testing Assumptions: The Shapiro-Wilk Test and the Levene Test

    Recall from Unit 7 that two assumptions of the t test are that:
    1. The outcome variable Y is normally distributed.
    2. The variance of Y scores is approximately equal across groups (homogeneity of variance assumption).

    The Shapiro-Wilk Test

    In addition to a visual inspection of histograms and calculation of skewness and kurtosis values, SPSS provides a formal statistical test of normality referred to as the Shapiro-Wilk test. A perfect normal distribution will have a Shapiro-Wilk value of 1.00. Values less than 1.00 indicate an increasing departure from a perfect normal shape. The null hypothesis of the Shapiro-Wilk test is that the distribution is normal. When the Shapiro-Wilk test indicates a p value less than .05, the normality assumption may be violated, which can be problematic.To obtain the Shapiro-Wilk test in SPSS, follow the step-by-step guide for t tests that is provided in the Unit 8 assignment. SPSS provides the Shapiro-Wilk test output for interpretation. A significant Shapiro-Wilk test ( p < .05) suggests that the distribution is not normal and interpretations may be affected. However, the t test is fairly robust to violations of this assumption when sample sizes are sufficiently large (that is, greater than 100 members).

    The Levene Test

    The homogeneity of variance assumption is tested with the Levene test. The Levene test is automatically generated in SPSS when an independent samples t test is conducted. The null hypothesis for the Levene test is that group variances are equal. A significant Levene test ( p < .05) indicates that the homogeneity of variance assumption is violated. In this case, report the "Equal variances not assumed" row of the t-test output from SPSS. This version of the t test uses a more conservative adjusted degrees of freedom ( df) that compensates for the homogeneity violation. The adjusted df can often result in a decimal number (such as df = 13.4), which is commonly rounded to a whole number in reporting ( df = 13). If the Levene test is not significant (that is, homogeneity is assumed), report the "Equal variances assumed" row of the t-test output from SPSS.

    Proper Reporting of the Independent Samples t Test

    Reporting a t test in proper APA style requires an understanding of several elements, including the statistical notation for an independent samples t test ( t), the degrees of freedom in parentheses, the t value, the probability value, and the effect size. To provide context, provide the means and standard deviations for each group. Warner (2013) also recommends reporting the 95% confidence interval (CI) for the difference in sample means. Consider the following example from Warner (2013, p. 213):
    The mean HRs differed significantly, t(18) = −2.75, p = .013 (two-tailed). Mean HR for the no-caffeine group ( M = 57.8, SD = 7.2) was about 10 bpm lower than mean HR for the caffeine group ( M = 67.9, SD = 9.1). The effect size, as indexed by η 2, was .30; this is a very large effect. The 95% CI for the difference between sample means, M 1M 2, had a lower bound of −17.81 and an upper bound of −2.39.

    t, Degrees of Freedom, and t Value

    The statistical notation for an independent samples t test is t, and following it is the degrees of freedom for this statistical test. The degrees of freedom for t is n1 + n2 − 2, where n1 equals the number of participants in Group 1 and n2 equals the number of participants in Group 2. In the example above, there are 10 people in each group: N = 20 ( n1 = 10; n2 = 10), so the df = 18 ( n1 + n2 − 2). Warner (2013) recommends that the t test should not be conducted with groups of fewer than 10 members. The t value is a ratio of the difference in group means divided by the standard error of the difference in sample means. The t value can be either positive or negative.

    Probability Value

    Appendix B (pp. 1056–1057) of the Warner text provides critical values of t for rejecting the null hypothesis. In the example above, with 18 degrees of freedom and alpha level set to .05 (two-tailed), the table indicates a critical value of ±2.101 to reject the null hypothesis. The obtained t value above is −2.75, which exceeds the critical value required to reject the null hypothesis. SPSS determined the exact p value to be .013. This p value is less than .05, which indicates that the null hypothesis should be rejected for the alternative hypothesis—that is, the two groups are significantly different in mean heart rate.

    Effect Size

    A common index of effect size for the independent samples t test is eta squared (η2). SPSS does not provide this output for the independent samples t test, but it is easily calculated by hand with the following formula: t2 ÷ ( t2 + df). In the example above, the calculation is (−2.75)2 ÷ [(−2.75)2 + 18] = 7.56 ÷ [(7.56 + 18)] = 7.56 ÷ 25.56 = .30. The effect size is interpreted using Table 5.2 in the Warner text (p. 208).

    Confidence Intervals

    Recall that confidence intervals (CIs) were introduced in Unit 2. Standard APA reporting of the independent samples t test should include the 95% confidence interval for the difference in sample means, which is provided in the SPSS output for the t test.The Warner text provides a "Results" example at the end of each chapter for all statistics studied in this course. You are encouraged to review these examples and follow their structure when writing up Section 4, "Interpretation," of the DAA Template.
    Reference
    Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage.

    OBJECTIVES

    To successfully complete this learning unit, you will be expected to:
    1. Interpret SPSS t-test output and draw conclusions.
    2. Articulate a research question, null hypothesis, and alternative hypothesis.
    3. Analyze the application of t tests in your career.
  • LEARNING ACTIVITIESCollapse All|Expand All
  • Toggle Drawer

    [u08s1] Unit 8 Study 1

    Studies

    Readings

    Use your IBM SPSS Statistics Step by Step text to complete the following:
    • Read Chapter 11, "The t Test Procedure." This reading addresses the following topics:
      • Independent samples t test.
      • Paired samples t test.
      • One-sample t test.
      • Significance testing.
      • SPSS commands.
      • Reporting and interpreting SPSS output.

    PSY Learners – Additional Required Readings

    In addition to the other required study activities for this unit, PSY learners are required to read the following:Delphin-Rittmon, M. E., Flanagan, E. H., Bellamy, C. D., Diaz, A., Johnson, K., Molta, V., & . . . Ortiz, J. (2015). Learning from those we serve: Piloting a culture competence intervention co-developed by university faculty and persons in recovery. Psychiatric Rehabilitation Journal. doi:10.1037/prj0000155
  • Toggle Drawer

    [u08a1] Unit 8 Assignment 1

    t Tests

    Resources

    See the Resources area for links to resources that you will use for this assignment:
    • You will complete this assignment using the DAA Template.
    • Read the SPSS Data Analysis Report Guidelines for a more complete understanding of the DAA Template and how to format and organize your assignment.
    • Refer to the IBM SPSS Step-By-Step Guide: t Tests for additional information on using SPSS for this assignment.
    • If necessary, review the Copy/Export Output Instructions to refresh your memory on how to perform these tasks. As with your previous assignments, your submission should be in narrative format with supporting statistical output (table and graphs) integrated into the narrative in the appropriate places (not all at the end of the document).
    You will analyze the following variables in the grades.sav data set:
    • gender
    • gpa

    Step 1: Write Section 1 of the DAA.

    • Provide the context of the grades.sav data set.
    • Include a definition of the specified variables (predictor, outcome) and corresponding scales of measurement.
    • Specify the sample size of the data set.

    Step 2: Write Section 2 of the DAA.

    • Analyze the assumptions of the t test.
    • Paste the SPSS histogram output for gpa and discuss your visual interpretations.
    • Paste SPSS descriptives output showing skewness and kurtosis values for gpa and interpret them.
    • Paste SPSS output for the Shapiro-Wilk test of gpa and interpret it.
    • Report the results of the Levene test and interpret it.
    • Summarize whether or not the assumptions of the t test are met.

    Step 3: Write Section 3 of the DAA.

    • Specify a research question related to gender and gpa.
    • Articulate the null hypothesis and alternative hypothesis.
    • Specify the alpha level.

    Step 4: Write Section 4 of the DAA.

    • Paste the SPSS output of the t test.
    • Report the results of the SPSS output using proper APA guidelines (refer to the Unit 8 Introduction and the "Results" example from the Warner text in Chapter 5). Include the following:
      • t.
      • Degrees of freedom.
      • p value.
      • Effect size.
      • Interpretation of effect size.
      • Means and standard deviations for each group.
      • Mean difference.
      • 95% confidence interval of the difference of sample means.
    • Interpret the results against the null hypothesis.

    Step 5: Write Section 5 of the DAA.

    • Discuss the implications of this t test as it relates to the research question.
    • Conclude with an analysis of the strengths and limitations of the t test.
    Submit your DAA Template as an attached Word document in the assignment area.

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PICKERING HEIDI 1 DEVERS GAIL 1 PARK SANDRA 1 LANGFORD BLAIR 2 STEPHEN LIZA 1 HUANG JOE 2 ethnicity 2 4 4 3 2 4 2 5 4 3 1 4 4 4 4 5 2 4 4 4 2 2 5 4 3 3 1 2 1 4 2 4 2 2 4 4 2 2 5 4 3 3 3 3 5 5 year 2 3 4 2 4 3 3 2 3 3 4 3 3 1 3 3 4 3 3 4 2 3 3 3 4 2 3 2 2 3 3 3 3 3 3 3 3 3 4 3 3 3 4 3 3 3 lowup 1 2 2 1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 section 2 2 2 2 1 3 3 1 1 2 2 3 1 2 3 3 2 1 2 1 2 2 3 1 3 2 2 1 2 2 2 3 1 2 2 3 2 1 3 1 3 1 2 1 2 3 gpa 1.18 2.19 2.46 3.98 1.84 3.9 2.84 3.57 3.95 3.49 2.32 2.35 2.45 2.9 2.33 2.54 1.66 2.74 2.51 2.54 3.7 3.9 2.21 2.46 1.14 2.09 2.34 2.03 2.8 2.25 2.28 3.02 2.38 1.91 3.53 2.61 2.8 2.66 2.77 3.84 2.38 2.34 3.17 3.42 2.72 2.47 506467 SCARBROUGH CYNTHE 515586 FIALLOS LAUREL 519444 RATHBUN DAWNE 546022 HAMIDI KIMBERLY 553919 KWON SHELLY 554809 JONES LISA 574170 HURRIA WAYNE 576008 BULMERKA HUSIBA 576141 MISHALANY LUCY 594463 CRUZADO MARITESS 595177 WILLIAMS OLIMPIA 615115 VASENIUS RUSS 616095 SPRINGER 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1.33 3.9 3.9 2.96 3.9 3.35 3.84 3.45 3.57 3.05 1.24 1.77 3.64 2.56 1.24 1.5 3.9 3.58 1.61 1.77 2.57 2.96 3.13 3.9 2.27 2.43 2.88 2.4 3.01 3.9 4 2.22 2.56 1.95 3.9 3.54 3.66 2.56 2.92 3.9 2.31 extcr 1 2 2 1 1 1 2 1 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 1 1 2 1 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 review 2 1 2 1 1 2 1 2 2 1 1 2 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 1 2 1 1 2 2 2 1 quiz1 6 10 10 7 7 10 10 10 10 10 7 8 8 3 5 5 5 8 5 10 3 10 9 6 2 6 10 10 4 10 6 10 8 9 6 10 7 8 6 10 4 7 8 10 8 0 quiz2 5 10 7 8 8 10 9 9 10 10 8 10 8 8 5 8 7 9 9 9 6 8 10 9 5 5 8 10 6 9 7 10 9 8 7 10 6 6 8 10 7 6 8 10 9 5 quiz3 7 7 8 7 10 10 10 10 10 9 6 10 10 4 7 6 4 10 5 10 2 10 9 10 4 4 10 10 5 10 9 10 10 10 7 10 9 7 9 10 6 8 8 10 9 0 quiz4 6 6 9 7 8 9 10 10 10 10 7 10 10 6 6 4 7 7 6 10 6 10 9 9 5 7 10 10 4 10 6 9 10 10 9 10 8 8 5 9 4 7 10 9 8 2 quiz5 3 9 7 6 10 9 10 10 9 10 10 9 6 8 4 10 6 10 10 7 6 8 9 9 6 6 7 9 5 8 8 9 9 6 9 10 8 7 8 10 7 9 9 10 10 5 final 53 54 57 68 66 74 63 71 74 75 59 71 69 55 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Template Use this file for all assignments that require the DAA Template. Although the statistical tests will change from week to week, the basic organization and structure of the DAA remains the same. Update the title of the template. Remove this text and provide a brief introduction. Section 1: Data File Description 1. Describe the context of the data set. You may cite your previous description if the same data set is used from a previous assignment. 2. Specify the variables used in this DAA and the scale of measurement of each variable. 3. Specify sample size (N). Section 2: Testing Assumptions 1. Articulate the assumptions of the statistical test. 2. Paste SPSS output that tests those assumptions and interpret them. Properly integrate SPSS output where appropriate. Do not string all output together at the beginning of the section. 3. Summarize whether or not the assumptions are met. If assumptions are not met, discuss how to ameliorate violations of the assumptions. Section 3: Research Question, Hypotheses, and Alpha Level 1. Articulate a research question relevant to the statistical test. 2. Articulate the null hypothesis and alternative hypothesis. 3. Specify the alpha level. Section 4: Interpretation 1. Paste SPSS output for an inferential statistic. Properly integrate SPSS output where appropriate. Do not string all output together at the beginning of the section. 2. Report the test statistics. 2 DATA ANALYSIS AND APPLICATION TEMPLATE 3. Interpret statistical results against the null hypothesis. Section 5: Conclusion 1. State your conclusions. 2. Analyze strengths and limitations of the statistical test. 3 DATA ANALYSIS AND APPLICATION TEMPLATE References Provide references if necessary. 4 IBM SPSS Step-by-Step Guide: t Tests Note: This guide is an example of creating t test output in SPSS with the grades.sav file. The variables shown in this guide do not correspond with the actual variables assigned in Unit 8 Assignment 1. Carefully follow the Unit 8 Assignment 1 instructions for a list of assigned variables. Screen shots were created with SPSS 21.0. Assumptions of t Tests To complete Section 2 of the DAA for Unit 8 Assignment 1, you will generate SPSS output for a histogram, descriptive statistics, and the Shapiro-Wilk test. (Levene test output will appear in Section 4 of the DAA). Refer to the Unit 8 assignment instructions for a list of assigned variables. The example variables lowup and final are shown below. Step 1. Open grades.sav in SPSS. 1 Step 2. Generate SPSS output for the Shapiro-Wilk test of normality. (Refer to previous stepby-step guides for generating histogram output and descriptives output for the Unit 8 assignment variables.) • On the Analyze menu, point to Descriptive Statistics and click Explore… • In the Explore dialog box, move the assigned Unit 8 variables into the Dependent List box. The final variable is used as an example below. • Click the Plots… button. 2 • In the Explore: Plots dialog box, select the Normality plots with tests option. • Click Continue and then OK. Step 3. Copy the Tests of Normality table and paste it into Section 2 of the DAA Template. Interpret the output. Note: The Levene test is also generated as part of the SPSS t-test output for Section 4 (discussed next). You do not have to provide the Levene test output twice. You can report and interpret it in Section 2 and then provide the actual output in Section 4. 3 Reporting of t Tests DAA Section 4 involves generating the t-test output and interpreting it. The example variables of lowup (lower division = 1; upper division = 2) and final are shown below. Step 1. Generate SPSS output for the t test. • On the Analyze menu, point to Compare Means and click Independent-Samples T Test… Step 2. In the Independent-Samples T Test dialog box: • First, move the Unit 8 Assignment 1 dependent variable into the Test Variable(s) box. • Second, move the Unit 8 assignment variable into the Grouping Variable box. Notice the (? ?) after the variable. The values of the independent variable are assigned in the next step. • Third, click the Define Groups… button. 4 • Fourth, in the Define Groups dialog box, assign the corresponding values: Group 1 = 1, Group 2 = 2. • Fifth, click Continue and then OK. Step 3. Copy the output for the independent samples test and paste it into Section 4 of the DAA Template. Then interpret it as described in the Unit 8 assignment instructions. 5 SPSS DATA ANALYSIS REPORT GUIDELINES For the SPSS data analysis report assignments in Units 6, 8, and 10, you will use the Data Analysis and Application (DAA) Template with the five sections described below. As shown in the IBM SPSS step-by-step guides, label all tables and graphs in a manner consistent with Capella's APA Style and Format guidelines. Citations, if needed, should be included in the text and references included in a reference section at the end of the report. The organization of the report should include the following five sections: Section 1: Data File Description (One Paragraph) 1. Describe the context of the data set. Cite a previous description if the same data set is used from a previous assignment. To increase the formal tone of the DAA, avoid firstperson perspective "I." For example, do not write, "I ran a scatter plot shown in Figure 1." Instead, write, "Figure 1 shows. . . ." 2. Specify the variables used in this DAA and the scale of measurement of each variable. 3. Specify sample size (N). Section 2: Testing Assumptions (Multiple Paragraphs) 1. Articulate the assumptions of the statistical test. 2. Paste SPSS output that tests those assumptions and interpret them. Properly embed SPSS output where appropriate. Do not string all output together at the beginning of the section. In other words, interpretations of figures and tables should be near (that is, immediately above or below) where the output appears. Format figures and tables per APA formatting. Refer to the examples in the IBM SPSS step-by-step guides. 3. Summarize whether or not the assumptions are met. If assumptions are not met, discuss how to ameliorate violations of the assumptions. Section 3: Research Question, Hypotheses, and Alpha Level (One Paragraph) 1. Articulate a research question relevant to the statistical test. 2. Articulate the null hypothesis and alternative hypothesis for the research question. 3. Specify the alpha level (.05 unless otherwise specified). Section 4: Interpretation (Multiple Paragraphs) 1. Paste SPSS output for an inferential statistic and report it. Properly embed SPSS output where appropriate. Do not string all output together at the beginning of the section. In other words, interpretations of figures and tables should be near (that is, immediately above or below) where the output appears. Format figures and tables per APA formatting. 2. Report the test statistics. For guidance, refer to the "Results" examples at the end of the appropriate chapter of your Warner text. 3. Interpret statistical results against the null hypothesis. Section 5: Conclusion (Two Paragraphs) 1. Provide a brief summary (one paragraph) of the DAA conclusions. 2. Analyze strengths and limitations of the statistical test.
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Running head: DATA ANALYSIS AND APPLICATION TEMPLATE

Data Analysis and Application (DAA) Template
Learner Name
Capella University

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DATA ANALYSIS AND APPLICATION TEMPLATE

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Data Analysis and Application (DAA) Template
The data being considered in this case aims at providing a better understanding of some
factors that influence student performance levels. It focuses on some quizzes, which have been
done as well as considering the GPA of each student. Therefore, it is vital to employ statistical
analysis to have a better understanding of these factors.
Section 1: Data File Description
The analysis aims and establishing any significant relationship that exists between two
unrelated groups within the data set. Therefore, the best statistical tool that is important in
this case is independent sample t-test. The variables that are considered in this case are
the GPA and gender. GPA is measured on a ratio ...


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