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Lab #7 Preview

Paired Samples t-Test

Purpose

Compare the sample means for two sets of scores obtained from the same individuals, or matched pairs of individuals. Is there a significant difference between the means?

3rd Graders at private school measured twice:

Before 3rd Grade                                       After 3rd Grade

Is there an improvement in IQ scores from before to after 3rd grade as predicted by the school principal?

Measures (DVs):

  • iqbef = IQ before 3rd grade
  • iqaft = IQ after 3rd grade

One-tailed vs. two-tailed test: When there is a prediction about the direction of results, you can use a one-tailed hypothesis test. In SPSS, this involves simply using the One-Sided p value rather than the Two-Sided p value when comparing to your alpha level (.05).

Null Hypothesis: Mean IQ before 3rd grade ≥ Mean IQ after 3rd grade

Alternative Hypothesis: Mean IQ before 3rd < Mean IQ after 3rd grade  (matches prediction)

The paired samples t-test is a test of the null hypothesis. Based on test results, we either:

  1. Reject the null hypothesis (and conclude there is a significant difference), or
  2. Fail to reject the null hypothesis (and conclude the means do not differ in the predicted direction)

APA Style

The APA style write-up for the paired samples t-test follows the same format as for the independent samples t test covered in the previous lab – report the two means, their standard deviations, whether the means differ (and which one is larger/smaller than the other) or do not differ, and the t-statement with the same format of t(df) = xx, p = xx, d = xx.

License

PSYC 200L Intro to Statistics Laboratory 2nd Ed. Copyright © 2025 by Scott Peterson. All Rights Reserved.

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