Chapter 8 Single Sample T-Test
Usage: To check for a difference between a sampe mean and a population mean when the population error is unknown.
Requirements: One variable that is interval/ratio and a population mean.
Steps to conducting an single 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 (Cohen’s d)
- Calculate confidence interval (CI).
8.1 Example Setup
8.1.1 Hypotheses
\(\Large H_0: \mu = value\)
\(\Large H_1: \mu \neq value\)
8.1.2 Critical t-Value (CV)
\(\Large df = n - 1\)
\(\Large \alpha = .05\)
\(\Large CV = [check\ table]\)
8.1.3 Calculate t
\(\Large N = number\ of\ scores\)
\(\Large \bar X = \frac{sum}{N}\)
\(\Large \hat s_\bar X = \frac{\hat s}{\sqrt{N}}\)
\(\Large t = \frac{\bar X - \mu}{\hat s_\bar X}\)
8.1.4 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.
8.1.5 Calculate Effect Size
\(\Large d = \frac{\bar X_1 - \bar X_2}{\sqrt{s^2_p}}\)
8.1.6 Calculate Confidence Interval (CI)
\(\Large CI = \bar X_\ \pm\ (t_{critical}* \hat{s}_{\bar X})\)