Discuss the homogeneity of variance assumption

For this discussion:

• Identify a research question from your professional life or career specialization that can be addressed by an independent samples t test.

• Indicate why a t test would be the appropriate analysis for this research question.

• Describe the variables and their scale of measurement.

• Discuss the expected outcome (for example, “The Group 1 mean score will be significantly greater than the Group 2 mean score because.”)

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.

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 nocaffeine 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% Unit 8 – t Tests: Application

CI for the difference between sample means, M 1 − M 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.