Chapter 9 Independent Samples T-Test
Usage: To check for a difference between two group means.
Requirements: One variable with two levels and a second variable that is interval/ratio.
Steps to conducting an independent samples 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 sample mean, population mean, and 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).
9.1 Example Setup
9.1.1 Hypotheses
\(\Large H_0: \mu_1 - \mu_2 = 0\)
\(\Large H_1: \mu_1 - \mu_2 \neq 0\)
9.1.2 Critical t-Value (CV)
\(\Large df = n - 1\)
\(\Large \alpha = .05\)
\(\Large CV = [check\ table]\)
9.1.3 Calculate t
\(\Large n_{group} = number\ of\ scores\ in\ group\)
\(\Large \bar X_{group} = \frac{sum}{n}\)
\(\Large SS_{group} = \sum X^2_{group} - \frac{(\sum X_{group})^2}{n_{group}}\)
Calculate the previous three for both groups.
\(\Large \hat{s}_{\bar X_1 - \bar X_2} = \sqrt{(\frac{SS_1 + SS_2}{n_1 + n_2 - 2})(\frac{1}{n_1} + \frac{1}{n_2})}\)
\(\Large t = \frac{\bar X_1 - \bar X_2}{\hat{s}_{\bar X_1 - \bar X_2}}\)
9.1.4 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.
9.1.5 Calculate Effect Size
\(\Large \eta^2 = \frac{t^2}{t^2 + df}\)
\(\Large d = \frac{\bar X_1 - \bar X_2}{\sqrt{s^2_p}}\)
9.1.6 Calculate Confidence Interval (CI)
\(\Large CI = (\bar X_1 - \bar X_2)\ \pm\ (t_{critical}* \hat{s}_{\bar X_1 - \bar X_2})\)