dependent t-tests

1. dependentt-tests

2. Factors affecting statistical power in the t-test • Statistical power • ability to identify a statistically significant difference when a difference between means actually exists

3. Decision Table: Correct DECISION R E A L I T Y Truth is everlasting, but our ideas about truth are interchangeable

4. Factors affecting statistical power in the t-test • level • how much risk are YOU willing to take in making a Type I error • Frank & Huck (1986, RQES): Why does everyone use the 0.05 level of significance? Power 0.01 conservative 0.10 liberal

5. Factors affecting statistical power in the t-test • level • df (number of subjects) • affects variability associated with the sample mean & variability within the sample • limited by time & money • GREATER n = GREATER POWER (point of diminishing return)

6. Statistics Humour  One day there was a fire in a wastebasket in the Dean's office and in rushed a physicist, a chemist, and a statistician. The physicist immediately starts to work on how much energy would have to be removed from the fire to stop the combustion. The chemist works on which reagent would have to be added to the fire to prevent oxidation. While they are doing this, the statistician is setting fires to all the other wastebaskets in the office. "What are you doing?" they demanded. "Well to solve the problem, obviously you need a large sample size" the statistician replies.

7. Factors affecting statistical power in the t-test • level • df (number of subjects) • magnitude of the mean difference • how different are the treatments imposed • measurement errors • sampling errors • SIZE OF THE TREATMENT EFFECT

8. Factors affecting statistical power in the t-test • level • df (number of subjects) • magnitude of the mean difference • variability • how specified is your population • control of extraneous variables

9. Estimated Standard Error of the Difference between 2 independent means

10. t-test for independent samples Smaller is better

11. Comparing paired (correlated) measures instead of group (uncorrelated) measures • Match subjects • what factors (variables) might affect time to exhaustion on the exercise bike • daily diet? Fitness level? Genetics? • Height? Weight? Age? • Regular training program?

12. Comparing paired (correlated) measures instead of group (uncorrelated) measures • Match subjects • Repeated measures • measure the SAME subject under both protocols • test & retest • pre & posttest • condition 1 & condition 2

13. Comparing paired (correlated) measures instead of group (uncorrelated) measures • Match subjects • Repeated measures Subject serves as own Control

14. Comparing paired (correlated) measures instead of group (uncorrelated) measures • Match subjects • Repeated measures Subject serves as own Control Intra-subject variability should be LESS than Inter-subject variability

15. Dependent t-test(paired or correlated t-test) • Pairs of scores are matched • same subject in 2 conditions or matched subjects • Question: Does ankle bracing affect load during landing? • IV: brace condition • DV: Vertical GRF

16. Steps to dependent t-test • Set  (0.05) • Set sample size • One randomly selected group • n = 7 • condition 1: Brace • condition 2: No brace • Set Ho (null hypothesis)

17. Ho Null hypothesis Any observed difference between the two conditions will be attributable to random sampling error. HA Alternative hypothesis If Ho is rejected, the difference is not attributable to random sampling error perhaps brace??? Set statistical hypotheses

18. Steps to independent t-test • Set  (0.05) • Set sample size (n = 7) • Set Ho • Test each subject in both conditions with a standardized protocol (drop landings) • Note: condition performance order is randomized across subjects

19. GRF data

20. Steps to dependent t-test • Set  (0.05) • Set sample size (n = 7) • Set Ho • Test each subject in both conditions • Calculate descriptive statistics of each condition • scattergram • mean, SD, n

21. Figure 1. Scattergram of vertical GRF during landing in different brace conditions (N/kg)

22. Descriptive statistics for atble401.sav data

23. Steps to dependent t-test • Set  (0.05) • Set sample size (n = 7) • Set Ho • Test each subject in both conditions • Calculate descriptive statistics of each condition • compare the condition means

24. How to compare the condition means • Even if the two conditions were the same (samples drawn from the same population), would not expect the statistics to be the same • Need a measure of expected variability against which the mean of the difference between paired scores (Xi - Yi) could be compared

25. Paired scores, so the data are somewhat correlated • Calculate the difference between the two conditions for each case (Xi - Yi) • Calculate the Mean Difference • Use the correlation among the pairs of scores to reduce the error term (denominator) used to evaluate the difference between the means

26. t-test for dependent (paired) samples Mdiff t = SEMD

27. GRF data  = -20 Mean Diff = -2.9

28. t-test for dependent (paired) samples Mdiff t = SEMD Standard error of the Mean difference for Paired Scores

29. Estimated Standard Error of the Difference between 2 dependent means ?

30. Estimated Standard Error of the Difference between 2 dependent means If r= 0, this term reduces to the same equation as for independent groups

31. t-test for dependent (paired) samples Mdiff t = SEMD df = ??

32. t-test for dependent (paired) samples Mdiff t = SEMD df = npairs - 1

33. Running the dependent t-test with SPSS • Enter the data as pairs • atble401.sav

34. Reporting paired t-test outcome Table 1. Descriptive statistics of vertical ground reaction force (in N/kg) for the two conditions (n = 7)

35. Reporting t-test outcome * Figure 1. Mean vertical GRF in the two conditions (* p 0.05)

36. Reporting t-test in text Descriptive statistics of the vertical ground reaction force (VGRF) data during landing in the two braced conditions are presented in Table 1 and graphically in Figure 1. A paired t-test indicated that the mean VGRF of 10.9 (SD = 3.5) N/kg in the braced condition was significantly higher ( = 0.05) than the mean VGRF of 8.0 (4.3) N/kg in the unbraced condition (t6 = 3.57, p = 0.012). The mean difference of 2.9 N/kg represents a 36% higher VGRF during the landings with a brace compared to without a brace.

37. What if you set  = 0.01? Descriptive statistics of the vertical ground reaction force (VGRF) data during landing in the two braced conditions are presented in Table 1 and graphically in Figure 1. A paired t-test indicated that the mean VGRF of 10.9 (SD = 3.5) N/kg in the braced condition was ...

38. What if you set  = 0.01? Descriptive statistics of the vertical ground reaction force (VGRF) data during landing in the two braced conditions are presented in Table 1 and graphically in Figure 1. A paired t-test indicated that the mean VGRF of 10.9 (SD = 3.5) N/kg in the braced condition was significantly higher ( = 0.01) than the mean VGRF of 8.0 (4.3) N/kg in the unbraced condition (t6 = 3.57, p = 0.012). The mean difference of 2.9 N/kg represents a 36% higher VGRF during the landings with a brace compared to without a brace. not

39. Statistics Humour A student set forth on a quest To learn which of the world’s beers was best But his wallet was dried out At the first pub he tried out With two samples he flunked the means test Gehlbach, SH (2002) Interpreting the medical literature

40. Mean Difference t = Standard Error Summary: both t-tests are of the form:

41. Mean Difference t = Standard Error To increase statistical power Maximize Minimize

42. Independent no correlation between the two groups Dependent two sets of data (pair of scores) from matched subjects or from the same subject (repeated measures) data are correlated Choosing which t-test to use

43. Time for Lunch