1. Winslow Homer: “On The Stile” 1878

2. INFERENTIAL PROBLEM SOLVING Hypothesis Testing and t-tests Chapter 6:133-149

3. QUESTION: Suppose you have a REALLY GOOD QUESTION...

4. And you want a “scientific” answer… Let’s say you would like to know if gender influences height (Are men taller than women?)... What steps might you take to solve this problem?

5. Step 1: State your Hypothesis: Turn your question (Are men taller than women?) Into A Null Hypothesis: Null “guess” (Men are no taller than women)

6. STEP 2: Get representative samples:

7. Next Steps: 1. Measure the heights of a group of men and a group of women… 2. Calculate the means of each group 3. Compare the means of the two groups… 4. VOILA! Make your conclusion! But what if the women were basketball players, and the men were gymnasts?

8. Horrors! Horrors! You publish a conclusion that is false! Avoiding this tragic situation: 1. Avoid “TYPE I Errors: You conclude MEN ARE taller, when in fact they are not 2. Avoid “TYPE II Errors: You conclude MEN ARE NOT taller, when in fact they are 1. Reducing the Risk: Sampling 2. Accepting some Risk: p = Probability

9. A Word About Sampling… Researchers want to know the characteristics of a large group or “Population” (i.e. all women vs all men). IMPOSSIBLE!! However a representative “sample” can be selected Results are then inferred to also apply to the population. Samples are randomly selected Must be large enough to detect differences and minimize the impact of “outliers”

10. How Big of a Sample? Depends: Type of Question (experimental, descriptive, correlational, survey…) Degree of Accuracy required Normal variability observed In General: For “quasi-experimental” (like this) you need about 30

11. PED 471: Height Histogram Spring 2001

12. One More Time: Compare Mean Heights and Standard Deviations: Does the male group overlap The female group? If so, how much?

13. What are the Statistics Used? We can compare means of two groups: Groups can be “Independent” (Cross-sectional – men vs women) Or “Dependent” (Longitudinal: Pre-Post)

14. The Paired t-test: Analyzes whether or not the difference in means between the two groups are in fact Statistically Significant Evaluates the “overlap” of the variability of each mean Determines the PROBABILITY that by rejecting the Null Hypothesis, you would be WRONG Written as p <.05

15. One Last Detail: TAILS: TAILS: The ends of the normal distribution: One-tailed t-Test: One-tailed t-Test: Men will be taller (the tall end of the normal distribution) Two-tailed t-Test: Two-tailed t-Test: Men will be different (could be taller or could be shorter…either end of the distribution)

16. Finally: Using the t-Test, determine the probability (p) of making a false conclusion: P<0.05 means that there is less than a 5% chance that the measured difference is not a true representation of the populations (TYPE I Error)

17. Let’s try it Let’s try it... Use your height and shoe size database 1. State the Null Hypothesis about heights and shoe sizes between genders 2. Determine the samples (dependent or independent-paired) 3. Determine the acceptable probablility of making a Type I Error (p <.05) 4. Determine whether your hypothesis is one or two tailed…

18. And Run It! Analyze the Means of the Men’s and Women’s heights and shoe sizes with the TTEST in EXCEL

19. \\Nss- data\vol1\teachers\BaEngeb1\my _docs\PED471\ht.ss.data.xls

20. SUMMARY: State the Null Hypothesis: A “neutral” guess about the expected group differences Select Representative Sample from which we will infer a conclusion about the Population Determine the acceptable probability of making a Type I Error in your conclusion

21. Summary Continued Summary Continued: When your question involves comparing two means, determine: Independent Groups OR Dependent (pre-post test) Groups Determine the hypothetical “Tails” (1 or 2) Use the t-Test to calculate Statistical Significance: The acceptable probability of making a Type I Error in your conclusion is less than P < 0.05 (Less than 5%)

22. Hoop Shoot Lab: We will do an experiment to help us answer this question: Does 5 minutes warm-up improve free throw accuracy? Write your null hypothesis, samples, probability of Type I Error, and number of tails Design an experiment using this class as your “sample”…