Chapter 10 Repeated Measures T-Test
Usage: To check for a difference between means from the same group.
Requirements: Two variables that are interval/ratio.
Steps to conducting an repeated measures t-test:
- Write out null and alternative hypotheses
- Determine critical t-value for rejection of null hypothesis
A. Use degrees of freedom (df) and alpha level
- Calculate t-value for your data
A. You must first find the mean difference and the estimated standard error.
- Compare your calculated t-value to the critical t-value
A. If your calculated value is greater than the critical value, you reject the null hypothesis
B. If your calculated value is less than the critical value, you fail to reject the null hypothesis
- Calculate effect size (eta squared \(\eta^2\) or Cohen’s d)
- Calculate confidence interval (CI).
10.1 Example Setup
10.1.1 Hypotheses
\(\Large H_0: \mu_a = \mu_b\)
\(\Large H_1: \mu_a \neq \mu_b\)
10.1.2 Critical t-Value (CV)
\(\Large df = n - 1\)
\(\Large \alpha = .05\)
\(\Large CV = [check\ table]\)
10.1.3 Calculate t
\(\Large N = number\ of\ participants\)
\(\Large \bar D = \bar X_a - \bar X_b\)
\(\Large SS_{D} = \sum D^2 - \frac{(\sum D)^2}{N}\)
\(\Large \hat{s}_D^2 = \frac{SS_D}{N - 1}\)
\(\Large \hat{s}_D = \sqrt{\hat{s}_D^2}\)
\(\Large \hat{s}_{\bar D} = \frac{\hat{s}_D}{\sqrt{N}}\)
\(\Large t = \frac{\bar D}{\hat{s}_{\bar D}}\)
10.1.4 Compare Observed t to CV
If t is greater than the CV, reject the null hypothesis.
If t is less than the CV, fail to reject the null hypothesis.
10.1.5 Calculate Effect Size
\(\Large \eta^2 = \frac{t^2}{t^2 + df}\)
\(\Large d = \frac{\bar X_1 - \bar X_2}{\sqrt{s^2_p}}\)
10.1.6 Calculate Confidence Interval (CI)
\(\Large CI = (\bar D)\ \pm\ (t_{critical}* \hat{s}_{\bar D})\)