Analyze two calculations of the t test and when they are reported.
Analyze why there are two different versions (“Equal variances assumed” and “Equal variances not assumed”) of the t test on the SPSS printout and how you decide which one is more appropriate.
Unit 7 -t Tests: Theory and Logic
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. Evaluate research situations using the t test.
2. Identify the assumptions of the independent samples t test.
3. Analyze hypothesis testing for the t test.
4. Understand effect sizes for the t test.
5. Analyze two calculations of the t test and when they are reported.
[u07s1] Unit 7 Study 1- Readings
Use your Warner text, Applied Statistics: From Bivariate Through Multivariate Techniques , to complete the following:
• Read Chapter 5, “Comparing Group Means Using the Independent Samples t Test,” pages 185–218.
This reading addresses the following topics:
◦ Research situations using the independent samples t test.
◦ t-test assumptions.
◦ Factors affecting the size of the t ratio.
◦ Effect sizes.
SOE Learners – Suggested Readings
Stone, E. (2010). t test, independent samples. In N. J. Salkind (Ed.), Encyclopedia of research design (pp. 1552–1556). Thousand Oaks, CA: Sage. doi:10.4135/9781412961288.n475IBM 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.
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Step 2. Generate SPSS output for the Shapiro-Wilk test of normality. (Refer to previous step-by-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…
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· 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.
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· Click the Plots… button.
· In the Explore: Plots dialog box, select the Normality plots with tests option.
· Click Continue and then OK.
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Step 3. Copy the Tests of Normality table and paste it into Section 2 of the DAA Template. Interpret the output.
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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.
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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…
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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.
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· Third, click the Define Groups… button.
· Fourth, in the Define Groups dialog box, assign the corresponding values: Group 1 = 1, Group 2 = 2.
· Fifth, click Continue and then OK.
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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.
image10.pngINTRODUCTION
Units 7 and 8 review the theory, logic, and application of t tests. The t test is a basic inferential statistic often reported in research. You will discover that t tests, as well as analysis of variance (ANOVA) studied in Units 9 and 10, compare group means on some quantitative outcome variable.
Logic of the t Test
Imagine that a researcher compares the mean IQ scores of Class A versus Class B. The mean IQ for Class A is 102 and the mean IQ for Class B is 105. Is there a significant difference in mean IQ between Class A and Class B?
To answer this question, the researcher conducts an independent samples t test. The independent samples t test compares two group means in a between-subjects (between- S) design. In this between- S design, participants in two independent groups are measured only once on some outcome variable.
By contrast, a paired samples t test compares group means in a within-subjects (within- S) design for a single group. Each participant is measured twice on some outcome variable, such as a pretest-posttest design. For example, a researcher could measure self-esteem for a class of students prior to taking a public speaking course (pretest) and then measure self-esteem again after completing the public speaking course (posttest). The paired samples t test determines if there is a significant difference in mean scores from the pretest to the posttest.
Units 7 and 8 focus on the logic and application of the independent samples t test. There are two variables in an independent samples t test: the predictor variable ( X) and the outcome variable ( Y). The predictor variable must be dichotomous, meaning that it can only have two values or groups (for example, male = 1; female = 2). Group membership must be mutually exclusive. In non-experimental designs, group membership is based on some naturally occurring characteristic of a group (such as gender). In experimental designs, participants are randomly assigned to one of two group conditions (for example, treatment group = 1; control group = 2). In contrast to the dichotomous (nominal) predictor variable, the outcome variable must be continuous to calculate a group mean (for example, IQ scores, self-esteem scores).
Assumptions of the t Test
All quantitative statistics, including the independent samples t test, operate under assumptions checked prior to calculating the t test in SPSS. Violations of assumptions can lead to erroneous inferences regarding a null hypothesis. The first assumption is independence of observations. For predictor variable X in an independent samples t test, participants are assigned to one and only one “condition” or “level,” such as a treatment group or control group. This assumption is not statistical in nature; it is controlled by proper research procedures that maintain independence of observations.
The second assumption is that outcome variable Y is continuous and normally distributed. This assumption is checked by a visual inspection of the Y histogram and calculation of skewness and kurtosis values. A researcher may also conduct a Shapiro-Wilk test in SPSS to check whether a distribution is significantly different from normal. The null hypothesis of the Shapiro-Wilk test is that the distribution is normal. If the Shapiro-Wilk test is significant, then the normality assumption is violated. In other words, a researcher wants the Shapiro-Wilk test to not be significant at p < .05.
Unit 7 -t Tests: Theory and Logic
The third assumption is referred to as the homogeneity of variance assumption. Ideally, the amount of variance in Y scores is approximately equal for Group 1 and Group 2. This assumption is checked in SPSS with the Levene test. The null hypothesis of the Levene test is that group variances are equal. If the Levene test is significant, then the homogeneity assumption is violated. In other words, a researcher wants the Levene test to not be significant at p < .05. SPSS output for the t test provides two versions of the t test: “Equal variances assumed” and “Equal variances not assumed.” The statistics you present depend on the outcome of the Levene test. If the Levene test is not significant, researchers report the “Equal variances assumed” version of the t test. If the Levene test is significant, researchers report the more conservative “Equal variances not assumed” calculation of the t test.
Hypothesis Testing for a t Test
The null hypothesis for a t test predicts no significant difference in population means, or H0: µ1 = µ2. A
directional alternative hypothesis for a t test is that the population means differ in a specific direction, such as H1: µ1 > µ2 or H1: µ1 < µ2. A non-directional alternative hypothesis simply predicts that the population means
differ, but it does not stipulate which population mean is significantly greater ( H1: µ1 ≠ µ2). For t tests, the
standard alpha level for rejecting the null hypothesis is set to .05. SPSS output for a t test showing a p value of less than .05 indicates that the null hypothesis should be rejected; there is a significant difference in population means. A p value greater than .05 indicates that the null hypothesis should not be rejected; there is not a significant difference in population means.
Effect Size for a t Test
There are two commonly reported estimates of effect size for the independent samples t test, eta squared
(η2) and Cohen’s d. Eta squared is analogous to r2 studied in Units 5 and 6. It estimates the amount of variance in Y that is attributable to group differences in X. Eta squared ranges from 0 to 1.00, and it is
interpreted similarly to r2 in terms of small (.02), medium (.13), and large (.26) effect sizes. Eta squared is calculated as a function of an obtained t value and the study degrees of freedom.
Cohen’s d is an alternate effect size representing the difference between the means of the two groups divided by the standard deviation of the variable of interest for both groups combined (pooled standard deviation). A small Cohen’s d indicates a high degree of overlap in population means (see Figure 3.4 on p. 106 of the Warner text). A large Cohen’s d indicates a low degree of overlap in population means (see Figure 3.5 on p. 106 of the Warner text). A Cohen’s d of .20 is considered a small effect, .50 is a medium effect, and .80 is a large effect. Larger effect sizes indicate findings of greater practical or clinical significance.
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. Evaluate research situations using the t test.
2. Identify the assumptions of the independent samples t test.
3. Analyze hypothesis testing for the t test.
4. Understand effect sizes for the t test.
5. Analyze two calculations of the t test and when they are reported.
[u07s1] Unit 7 Study 1 – Readings Use your Warner text, Applied Statistics: From Bivariate Through Multivariate Techniques , to complete the following:
• Read Chapter 5, “Comparing Group Means Using the Independent Samples t Test,” pages 185–218. This reading addresses the following topics:
◦ Research situations using the independent samples t test. ◦ t-test assumptions. ◦ Factors affecting the size of the t ratio. ◦ Effect sizes.
SOE Learners – Suggested Readings Stone, E. (2010). t test, independent samples. In N. J. Salkind (Ed.), Encyclopedia of research design (pp.
1552–1556). Thousand Oaks, CA: Sage. doi:10.4135/9781412961288.n475
[u07d2] Unit 7 Discussion 2 – Two Versions of Independent Samples t Test Analyze why there are two different versions (“Equal variances assumed” and “Equal variances not assumed”) of the t test on the SPSS printout and how you decide which one is more appropriate.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 first-person 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.
SPSS Data Analysis Report Guidelines
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.
