How Statistics Can Empower Your Research? Part II

1. How Statistics Can Empower Your Research? Part II Xiayu (Stacy) Huang Bioinformatics Shared Resource Sanford | Burnham Medical Research Institute

2. Outline • Summary of Previous Talk • Descriptive & inferential statistics • Student’s T test, one-way ANOVA • More common statistical tests and applications • Repeated measures one-way ANOVA • Two-way ANOVA • Power analysis • Common data transformation methods

3. Summary of previous talk • Descriptive statistics • Measure of central tendency, dispersion, etc. • Inferential statistics • Hypothesis, errors, p-value, power • Three statistical tests and their applications • Two sample unpaired test, paired t test and one way ANOVA Power point presentation at http://bsrweb.burnham.org

4. one-way anova example • Goal:studying the effect of mice genotypes on their learning skills on rotarod. • Dependent variable: number of seconds staying on a rotarod

5. Decision tree

6. Decision tree----one-way anova

7. Assumption check in graphpad prism

8. Data analysis in graphpad prism Variance check

9. Repeated measures one-way anova • Compares the means of 3 or more groups • Repeated measurements on the same group of subjects • Assumptions: • Sampling should be independent and randomized. • Equal sample size per group preferred. • Sphericity or homogeneity of covariance • Data is normally distributed.

10. Application of repeated measures one-way anova in biology Days

11. Repeated measures one-way anova example • Goal:studying the effect of practice on maze learning for rats. • independent variable : days • dependent variable: number of errors made each day Rat_1 Rat_2 Rat_3

12. Decision tree----one-way repeated anova

13. table format in graphpad prism– repeated measures one-way anova

14. Data format and choosing analysis methods

15. Data analysis in graphpad prism

16. Analysis result

17. One-way repeated anova compared with regular one-way anova

18. Two-way anova • One dependent variable and two independent variables or factors • Assumptions • samples are normally or approximately normally distributed • The samples from each treatment group must be independent • The variances of the populations must be equal • equal sample size per treatment group preferred • Treatment group • all possible combinations of the two factors

19. Two-way anova • Main effect • Effect of individual factor • Interaction effect • Effect of one factor on the other • Hypotheses • The population means of the first factor A are equal • The population means of the second factor B are equal • There is no interaction between the two factors • Test • F test: mean square for each main effect and the interaction effect divided by the within variance

20. Main effects • Asprin • Ibuprophen • Asprin • Ibuprophen B--Treatment A--Time Pain score B A 1st hr 2nd hr 1st hr 2nd hr II. Main effect of treatment only I. No main effects for both time and treatment • Asprin • Ibuprophen • Asprin • Ibuprophen 1st hr 2nd hr 1st hr 2nd hr III. Main effect of time only IV. Main effects of time and treatment

21. Main effect and interaction effect • Asprin • Ibuprophen • Asprin • Ibuprophen Pain score 1st hr 1st hr 2nd hr 2nd hr V. Interaction effect only VI. Main effect of time only and interaction effect • Asprin • Ibuprophen • Asprin • Ibuprophen 1st hr 2nd hr 1st hr 2nd hr VII. Main effect of treatment only and interaction effect VIII. Main effects of time and treatment, and interaction effect

22. Two-way anova experimental design I. Balanced design with equal replication (Best) II. Proportional design replication (Acceptable) III. One replication only (Not recommended) IV. Disproportional design (Bad)

23. Application of two-way anova in biology 0 mM 50 mM 75 mM Microarray: Time-dose relationship

24. Two-way anova with replication example Study the effect of gender and anti-cancer drugs on tumor growth

25. Decision tree– factorial anova

26. table format in prism—two-way anova

27. Data format and choosing analysis methods

28. Choosing model

29. Analysis result

30. Two-way repeated measures anova example Goal: Investigating gender and caffeine consumption on the effect of memory Independent variables: gender and caffeine consumptions Dependent variable: memory score

31. Decision tree----two-way repeated anova

32. Table format– two-way repeated measures anova

33. Data format and analysis methods

34. Choosing model

35. Analysis result Matching not effective???

36. Reconsidering regular two-way anova

37. Outline • Summary of Previous Talk • Descriptive & inferential statistics • Student’s T test, one-way ANOVA • More common Statistical tests and Applications • Repeated-measures one-way ANOVA • Two-way ANOVA • Power analysis • Common data transformation methods

38. Power analysis • Power depends on: • Sample size ( ) • Standard deviation ( or ) • Minimal detectable difference ( ) • False positive rate ( ) • Power analysis includes: • Sample size required • Effect size or Minimal detectable difference • Power of the test effect size

39. Power analysis software/packages • G*Power (free!!!) • Optimal design (free!!!) • SPSS sample power • PASS • SAS proc power, Stata sampsi, etc • Mplus for more advanced/complicated analysis • Many free on-line programs • http://www.stat.uiowa.edu/~rlenth/Power/

40. Two independent sample power analysis--input and output parameters in G*Power • Sample size required • Input parameters • Effect size ( ) • False positive rate ( ) • Minimum Power ( ) • Ratio of two sample sizes • Output parameters • Noncentrality parameter ( ) • Critical t • Degree of freedom • Sample size for each group • Total sample size • Actual power

41. Two independent samples power analysis--input and output parameters in G*Power • Effect size • Input parameters • False positive rate • Minimum power • Sample size for each group • Output parameters • Noncentrality parameter • Critical t • Degree of freedom • Effect size • Minimal detectable difference

42. Compute sample size– two independent samples

43. Determining effect size– two independent samples

44. Analysis results– two independent samples

45. Compute effect size– two independent samples

46. X-y plot for a range of values

47. Factor affecting power—two independent samples • Power increases as total sample size increases • Power increases as effect size increases • Power increases as significance level increases

48. One-way anova power analysis--input and output parameters in G*Power • Sample size required • Input parameters • Effect size ( ) • False positive rate ( ) • Minimum Power ( ) • Number of groups • Output parameters • Noncentrality parameter ( ) • Critical F • Degree of freedom • Total sample size • Actual power

49. One-way anova sample power analysis--input and output parameters in G*Power • Effect size • Input parameters • False positive rate • Minimum power • Total sample size • Number of groups • Output parameters • Noncentrality parameter • Critical F • Numerator and denominator degree of freedom • Effect size • Minimal detectable difference

50. Compute sample size-- one-way anova