On-line resources

1. On-line resources • http://wise.cgu.edu/powermod/index.asp • http://wise.cgu.edu/regression_applet.asp • http://wise.cgu.edu/hypomod/appinstruct.asp • http://psych.hanover.edu/JavaTest/NeuroAnim/stats/StatDec.html • http://psych.hanover.edu/JavaTest/NeuroAnim/stats/t.html • http://psych.hanover.edu/JavaTest/NeuroAnim/stats/CLT.html • Note demo page

2. Statistical power is how “sensitive” a study is detecting various associations (magnification metaphor) If you think that the effect is small (.01), medium, (.06) or large (.15), and you want to find a statistically significant difference defined as p<.05, this table shows you how many participants you need for different levels of “sensitivity” or power.

3. If you think that the effect is small (.01), medium, (.06) or large (.15), and you want to find a statistically significant difference defined as p<.01, this table shows you how many participants you need for different levels of “sensitivity” or power.

4. What determines power? • Number of subjects • Effect size • Alpha level Power = probability that your experiment will reveal whether your research hypothesis is true Power = 1 - type 2 error Power = 1 - beta

5. How increase power? • Increase region of rejection to p<.10 • Increase sample size • Increase treatment effects • Decrease within group variability

7. What is adequate power? .50 (most current research) .80 (recommended) How do you know how much power you have? Guess work Two ways to use power: 1. Post hoc to establish what you could find 2. Determine how many participants need

9. 5 steps to hypothesis testing • Restate the research question as an alternative hypothesis and a null hypothesis about the populations. • Determine the characteristics of the comparison distribution. • Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. • Determine your sample’s score on the comparison distribution. • Decide whether to reject the null hypothesis.

10. Comparison table

11. Terms to know • Random selection • Convenience or haphazard selection • Random assignment • http://onlinestatbook.com/stat_sim/sampling_dist/index.html

12. Example 1 A doctor gives a patient a new type of anti-depressant. Is there any improvement compared to a larger population of depressed population? Assume that depression scores follow a "normal curve" (Population) M = 69.5 SD = 14.1 X = 41

13. 5 steps 1. Convert research questions to statistical hypotheses.   Null Hypothesis: Alternative Hypothesis  2. What are the characteristics of our comparison distribution? Why can we use the normal curve? Not all distributions are normal.  3. Determine "cut-off" scores.   Conventional level of statistical significance One tailed vs. two tailed  4. Determine your observation or sample score. Convert observation to Z score.  5. Accept or reject the NULL hypothesis. How would we write it down?

14. Z score distribution http://davidmlane.com/hyperstat/z_table.html

15. Example 2 Is memory affected by stress? Ask 25 people to give a talk and then remember a set of photographs. Mean recall = 48, SD=7, General population mean=53 Shift to a sample of observations from a single observation. 3 key characteristics of a distribution of means. • Mean of distribution of means is the same as the original population of individual scores. • Spread of distribution is narrower than spread of individual scores (so we need to correct for that!) • The shape is normal (but requires a sample size of 30 and normal distribution of scores for the sample to make this assumption)

16. Distribution of means graphs

17. How do we correct the problem? Formula

18. Comparison of three types of distributions

19. What if don’t know population? • Move to t-tests