1. Chapter 8 Single Sample Tests Part II: Introduction to Hypothesis Testing Renee R. Ha, Ph.D. James C. Ha, Ph.D Integrative Statistics for the Social & Behavioral Sciences

2. Single Sample z-statistic

3. Figure 8.1

4. When do we use the z-test? 1. When the experiment involves a single sample mean and the parameters of the corresponding null hypothesis population are known (μ and σ).

5. When do we use the z-test? 2. When the sampling distribution is normally distributed, which is the case if: a. n ≥ 30 or b. The null hypothesis population of raw scores is known to be normally distributed.

6. Single Sample t test

7. The t critical values are dependent on sample size (n) Now estimating σ from s, and the accuracy of that estimation is dependent on n. Our critical probability values are now going to vary with our sample size, unlike the z distribution in which the probabilities were independent of sample size.

8. Single Sample t test New distribution called the t distribution. It will vary with degrees of freedom (df), which are related to sample size.

9. Single Sample t test Degrees of freedom: The number of scores that are “free to vary” when calculating a statistic. The remaining value or values are then fixed.

10. Single Sample t test Score (X)Sample Mean ( )Deviation 36-3 56 106FIXED VALUE = 4 ∑ Deviations = 0

11. Figure 8.2 Flowchart for choosing the appropriate test

12. Confidence Intervals Confidence interval for the population mean: Range of values with a calculated probability of containing the mean

13. Confidence Intervals Confidence limits for the population mean: The upper and lower values (or boundaries) surrounding the confidence interval.

14. Figure 8.3 Graphic Display of a 95% Confidence Interval

15. Confidence Intervals Confidence limits for the population mean: The upper and lower values (or boundaries) surrounding the confidence interval.

16. Effect Sizes and Power Effect size is a standardized measure of the difference between two (or more) group means; it is the difference in means divided by the shared standard deviation of two or more groups.

17. Effect Sizes and Power For a population with a known standard deviation (σ), you can use Cohen’s d to calculate the effect size. Then you can plug your effect size into a software package to calculate power.