Statistical and methodological considerations for examining program effectiveness

1. Statistical and methodological considerations for examining program effectiveness RP Group Conference Presentation April 1, 2013 Carli Straight, PhD and Giovanni Sosa, PhD Chaffey College

2. Pitfalls of Significance Testing N = 30

3. Pitfalls of Significance Testing Adapted from NSSE (2008)

4. Pitfalls of Significance Testing p < .01 Avg. Grade (GPA Scale) p< .05 p < .01 N = 187 N = 408 N = 200 N = 795

5. Significance Testing: Conclusions • P-values = Sample Size x Effect Size • Greatly influenced by sample size • Do not speak to the magnitude of the difference • Not well understood – even by ‘experts’

6. Practical Significance: Effect Size • Effect Size comes in various forms • Standardized (d, r) • Cohen’s conventions: • d = .20 – small; .50 – moderate; .80 – large • r = .10 – small; .30 – moderate; .50 - large • Discipline specific • Aspirin Example (Rosenthal & Dimateo, 2002)

7. Effect Size Examples N = 30

8. Effect Size Examples Adapted from NSSE (2008)

9. Effect Size Examples d = 1.19 Avg. Grade (GPA Scale) d = .35 d =.86 N = 187 N = 408 N = 200 N = 795

10. Wilson’s Effect Size Calculator http://mason.gmu.edu/~dwilsonb/ma.html

11. Odds Ratios • Reflect a comparison of the relative odds of an occurrence of interest given the exposure to a variable of interest • OR = (A/B)/(C/D) OR = 15.077/2.788 = 5.40

12. Odds Ratios • Interpreting Odds Ratios: • OR = 1.50 – small; 2.50 – moderate; 4.25 – large • OR = 1 => Intervention does not affect odds of outcome • OR > 1 => Intervention associated with higher odds of outcome • OR < 1 => Intervention associated with lower odds of outcome • Converting Odds Ratios to ds and vice versa:

13. Working with Beta Weights Predictors of Course Performance among Fast Track Students Completing both the Pre and Post-Test Self-Efficacy (SE) Measure (N = 623) R2= .22 *p < .05; **p < .01

14. Working with Beta Weights Predictors of Course Performance among Fast Track Students Completing both the Pre and Post-Test Self-Efficacy (SE) Measure (N = 623) R2= .22 *p < .05; **p < .01

15. Basic Steps to Designing a Study that Measures Program Effectiveness Example: How Do Students Perform in Fast-Track Courses? • Select a reference point • Compared to whom/what? • Define what is meant by performance • Course completion rate? • Course success rate? • Retention rate? • Other? • Select appropriate statistical analysis • Conduct analyses and write up results

16. Select Comparable Cohorts Determine what/whom performance outcomes will be measured against • Goal is to select two cohorts that are the same in as many ways as possible, minus participation in the relevant program • Within-Group – observe outcomes of same students in program and out of program (no need for controls) • Between-Group – observe outcomes of different students, some of whom participated in the program and some of whom did not (control for pre-existing group differences)

17. Select Comparable Cohorts • Within group comparisons • Same students, compare performance in Fast-Track and non-Fast-Track courses during same time period • “Do students who earn GORs in both Fast-Track and non-Fast-Track courses perform better, worse, or the same in the two formats?” • Between group comparisons • Different students, one cohort earned a GOR in at least one Fast-Track course and one cohort earned no GORs in a Fast-Track course across the same time period • “Do students who earn GORs in Fast-Track courses perform better, worse, or the same as students who do not earn GORs in Fast-Track courses?” • Select variables to control so that “all else is equal”

18. Within-Group Comparisons • Determine time period of interest • Ensure that there are enough data to make comparisons and that programmatic changes were not implemented during the selected period Chaffey fast-track example: • Fast-track courses were first implemented in spring 2010, but significantly increased starting fall 2011 • To obtain a strong sample size and ensure that some of the kinks were worked out, data were analyzed from fall 2011 and later • Using MIS referential files, select for fall 2011 and spring 2012 terms

19. Within-Group Comparisons • Code your data file so that student behavior in and out of the program can be measured Chaffey fast-track example: • Obtain a list of all fast-track sections from course scheduler or other party on campus • Use obtained list to flag all fast-track sections in MIS file • Search start and end dates and delete short-term sections from file (use xf02 “SESSION-DATE-BEGINNING” and xf03 “SESSION-DATE-ENDING”)

20. Within-Group Comparisons • Delete all cases in which a student did not earn a GOR in fall 2011 or spring 2012 • Create coding system for fast-track and full-term sections (e.g., compute two new variables, fast-track = 1 if section is fast-track and full-term = 1 if section is full-term) • Aggregate number of fast-track sections and number of full-term sections by student id and term (this will give you two new variables in your dataset that reflect a count of GORs each student earned in fast-track and full-term courses for each semester)

21. Within-Group Comparisons • Select for students whose behavior reflects program participation and program non-participation across the selected time period Chaffey fast-track example: • Select cases in which the sum of fast-track GORs >= 1 and the sum of full-term GORs >= 1 (i.e., student has taken at least one fast-track and one full-term course) • Save selected cases to a new file

22. Within-Group Comparisons • Compare performance outcomes of same students in program and out of program Success Rate N = 4,153 All College Same students

23. Between-Group Comparisons • Determine time period of interest • Ensure that there are enough data to make comparisons and that programmatic changes were not implemented during the selected period Chaffey fast-track example: • Fast-track courses were first implemented in spring 2010, but significantly increased starting fall 2011 • To obtain a strong sample size and ensure that some of the kinks were worked out, data were analyzed from fall 2011 and later • Using MIS referential files, select for fall 2011 and spring 2012 terms

24. Between-Group Comparisons • Code data file so that two distinct cohorts, one of which participated in the program and one of which did not participate in the program, are identified Chaffey fast-track example: • Obtain a list of all fast-track sections from course scheduler or other party on campus • Use obtained list to flag all fast-track sections in MIS file • Aggregate number of fast-track sections by student id and term (this will give you a new variable in your dataset that reflects a count of GORs each student earned in fast-track courses for each semester)

25. Between-Group Comparisons • Remove all records in which a GOR was not assigned • Create cohort variable with two mutually exclusive groups • Cohort 1 consists of anyone who earned a GOR in a fast-track course during the specified term (i.e., fast-track variable >= 1) • Cohort 2 consists of anyone who earned a GOR in a course or courses other than fast-track during the specified term (i.e., fast-track variable = 0)

26. Between-Group Comparisons • Compare cohort groups on a variety of pre-existing variables to measure differences outside of program participation (these will guide you in setting up controls for the next step) Chaffey fast-track example: • Gender, Ethnicity, Age, DPS Status, Enrollment Status, Academically Disadvantaged Status, First Generation Status, Term Units Attempted, Term Units Earned, Cumulative Units Attempted, Cumulative Units Earned, Cumulative GPA, Self-Efficacy, Assessment Scores

27. Example of Categorical Variable Comparisons

28. Example of Continuous Variable Comparisons *Fast-Track Students n = 2,689, Non-Fast-Track Students n = 16,643 ** Fast-Track Students n = 1,565, Non-Fast-Track Students n = 9,408

29. Between-Group Comparisons • Note where non-programmatic differences exist between cohort 1 and cohort 2, if observed Chaffey fast-track example: • Selecting for differences of d = .25 or higher, fast-track and non-fast-track students were different in three areas: first-generation college status, term units attempted, and term units earned

30. Between-Group Comparisons • Conduct analyses to compare cohort 1 and cohort 2 performance outcomes, controlling for observed pre-existing differences between groups Chaffey fast-track example: • Calculate a partial correlation to measure the relationship between cohort group and course success, while “controlling” for the effects of first generation status and units attempted (not units completed because it is too highly correlated with units attempted)

31. Between-Group Comparisons Correlates of Course Success among Students Earning a GOR in Fall 2011 (N = 19,431) *p < .01

32. Cohort Comparison Conclusions • Students who earned at least one GOR each in fast-track and full-term courses in fall 2011 demonstrated statistically significantly higher course success rates in fast-track courses than in full-term courses. These findings, however, were not determined to be practically significant because of the large sample sizes and small effect size values. • Students who earned at least one GOR in a fast-track course in fall 2011 demonstrated course success rates that were not statistically significantly or practically different from course success rates of students who did not earn any GORs in fast-track courses in fall 2011.