STATISTICAL AND METHODOLOGICAL CONSIDERATIONS FOR EXAMINING PROGRAM EFFECTIVENESSCarli Straight, PhD and Giovanni Sosa, PhDChaffey College

RP Group Conference PresentationApril 1, 2013

Pitfalls of Significance Testing

Assessment Item

Number CorrectPretest

Number CorrectPosttest

Statistically Significant?

Item 1 19 24 NoItem 2 12 16 NoItem 3 26 30 NoItem 4 7 10 NoItem 5 13 21 NoItem 6 5 13 NoItem 7 10 15 NoItem 8 6 16 NoItem 9 3 15 NoAvg. Correct 5.00 7.50 No

N = 30

Pitfalls of Significance Testing

NSSEBenchmark

Sample UniversityN > 1000

Comparison Group

N > 10,000Statistically Significant?

Level of Academic Challenge 65.8 55.6 Yes

Active and Collaborative Learning

57.7 50.1 Yes

Student-Faculty Interaction 42.8 41.2 Yes

Enriching Educational Experiences

44.0 39.8 Yes

Supportive Campus Environment

62.7 56.9 YesAdapted from NSSE (2008)

Pitfalls of Significance Testing

Low SE Medium SE High SE0.00

1.00

2.00

3.00

4.00

2.29

3.153.47

N = 187 N = 408 N = 200

N = 795

Avg

. Gra

de (G

PA S

cale

)

p < .01

p < .05

p < .01

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’

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)

pooled

CT

sXXd

211

21

22

12

nn

nsnss ctpooled

Effect Size Examples

Assessment Item

Number CorrectPretest

Number CorrectPosttest

Statistically

Significant?

Effect Size (d)

Item 1 19 24 No .37Item 2 12 16 No .27Item 3 26 30 No .75Item 4 7 10 No .22Item 5 13 21 No .55Item 6 5 13 No .60Item 7 10 15 No .34Item 8 6 16 No .71Item 9 3 15 No .93Avg. Correct 5.00 7.50 No .61N = 30

Effect Size Examples

NSSEBenchmark

Sample UniversityN > 1000

Comparison Group

N > 10,000

Statistically

Significant?

Effect Size (d)

Level of Academic Challenge 65.8 55.6 Yes .72

Active and Collaborative Learning

57.7 50.1 Yes .44

Student-Faculty Interaction 42.8 41.2 Yes .08

Enriching Educational Experiences

44.0 39.8 Yes .23

Supportive Campus Environment 62.7 56.9 Yes .30Adapted from NSSE (2008)

Effect Size Examples

Low SE Medium SE High SE0.00

1.00

2.00

3.00

4.00

2.29

3.153.47

N = 187 N = 408 N = 200

N = 795

Avg

. Gra

de (G

PA S

cale

)

d =.86

d = .35

d = 1.19

Wilson’s Effect Size Calculator

http://mason.gmu.edu/~dwilsonb/ma.html

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)

Successful

Not Successf

ulTotal

Medium SE

392 26 418

Low SE 145 52 197OR = 15.077/2.788 = 5.40

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: 81.1ln ORd )*81.1( deOR

Working with Beta Weights

Predictor B (SE) BetaSelf-Efficacy (Post)** .09 (.01) .42Age Range** .13 (.03) .18Af. American vs. Others* -.31 (.15) -.08

Hispanic vs. Others -.14 (.09) -.07First-Gen Status .06 (.08) .03Asian vs. Others .10 (.16) .03Gender -.01 (.08) -.002

Work Hours <.01 (<.01) .005

R2= .22 *p < .05; **p < .01

Predictors of Course Performance among Fast Track Students Completing both the Pre and Post-Test Self-Efficacy (SE) Measure (N = 623)

Working with Beta Weights

Predictor B (SE) Beta Zero-Order r

Semi-Partial r

Effect Size |d|

Self-Efficacy (Post)** .09 (.01) .42 .42 .41 .90

Age Range** .13 (.03) .18 .19 .18 .36Af. American vs. Others* -.31 (.15) -.08 -.05 -.07 .14

Hispanic vs. Others -.14 (.09) -.07 -.12 -.05 .10

First-Gen Status .06 (.08) .03 .05 .03 .05Asian vs. Others .10 (.16) .03 .07 .02 .04Gender -.01 (.08) -.002 -.11 -.002 .004

Work Hours <.01 (<.01) .005 .05 .005 .01

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

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

Select Comparable CohortsDetermine 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)

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”

Within-Group Comparisons1) 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

Within-Group Comparisons2) 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”)

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)

Within-Group Comparisons3) 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

Within-Group Comparisons4) Compare performance outcomes of same

students in program and out of program

Fast-Track GORs

Full-Term GORs

All Fall 2011 GORs

65.0%

70.0%

75.0%

80.0%77.4%

70.0%71.3%d = .17

d = .03

d = .14

N = 55,368

N = 4,546N =

4,153Same students All College

Succ

ess

Rate

Between-Group Comparisons

1) 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

Between-Group Comparisons2) 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)

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)

Between-Group Comparisons3) 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

Example of Categorical Variable Comparisons

Background Characteristics

Fast-Track Students

Non-Fast-Track Students

|d|

n % n %

Gender Female 1,402 51.9 9,560 57.1 .10 Male 1,174 43.5 6,575 39.3 .09 Unknown 123 4.6 597 3.6 .05 First Generation Yes 596 26.3 4,007 28.1 .27 No 1,669 73.7 10,264 71.9

Example of Continuous Variable Comparisons

Academic Characteristics

Fast-Track Students (n =

2,699)

Non-Fast-Track Students (n =

16,732)

|d|

M SD M SD

Term Units Att

10.08 4.61 8.50 4.33 .36

Term Units Earn

7.21 4.89 5.79 4.59 .31

Cum Units Att

31.41 26.91 31.80 27.98 .01

Cum Units Earn

28.26 24.95 28.77 26.69 .02

Cum GPA* 2.57 1.04 2.42 1.12 .14Self-Efficacy**

5.98 .83 5.93 .84 .06

*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

Between-Group Comparisons4) 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

Between-Group Comparisons5) 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)

Between-Group Comparisons

Zero-Order r Partial r Effect

Size |d|Cohort Group .01 .00 .02Term Units Attempted* .06 .00 .12First-Generation Status* -.03 -.03 .06*p < .01

Correlates of Course Success among Students Earning a GOR in Fall 2011 (N = 19,431)

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.