Inferential Statistics

 

An independent-samples t-test was used to test the difference between the mean ratings of the charismatic-teacher-reputation condition and the punitive-teacher-reputation condition. The output from SPSS is shown below.

t-test for Equality of Means
Variances t-value df 2-Tail Sig SE of Diff 95% CI for Diff
Equal
2.45
47
0.018
0.154
(0.068, 0.686)
Unequal
2.45
46.83
0.018
0.154
(0.068, 0.687)

 

 

 

 

SPSS automatically computes the test under the assumption that the variances are equal (row 1) and without making this assumption (row 2). For the present data, the sample variances are nearly identical so the two tests yield the same results. The t test of the difference between means (Charismatic - Punitive) results in a t of 2.45.

Is this value of t is significant at the 0.05 level?
Yes
No
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The lower limit on the difference between the charismatic instructor's and the punitive instuctor's rating based on the 95% confidence interval is

0.018
0.154
0.068
0.686
0.687
Blank


SInce the t test is significant, the data support the conclusion that instructor reputation affects ratings.

An analysis of variance can also be used to test the difference between means. The ANOVA summary table computed using the Analysis Lab is shown below. Note that the square root of the F of 6.02576 equals (within rounding error) the t of 2.45 and that the p value is the same as the p value from the t test.

 

Assumptions
The t test and the analysis of variance both assume:

  1. Each score is sampled independently and randomly. The independence assumption is met. Strictly speaking, the selection of subjects was not completely random. However, the assignment of subjects to conditions was random, and this is the critical consideration in studies such as this one.
  2. The scores are normally distributed within each of the two populations. This assumption appears to be violated to a moderate degree because the descriptive statistics reveal that the distributions are positively skewed. The data analysis lab's procedure for assessing the consequences of this violation shows that the violation is of no practical importance in this case.
  3. The variance in each of the populations is equal. There is no evidence that this assumption is violated.