Planned Contrast: Execution (Conceptual)

1. Must predict pattern of interaction before gathering data. Predict that Democratic women will be most opposed to gun instruction in school, compared to Democratic men, Republican men, and Republican women.

0

1

2

3

4

5

Republican Democrat

Rat

ing Male

Female

Post Hoc Tests

Do female democrats differ from other groups?

1 = Male/Republican 5.002 = Male/Democrat 4.503 = Female/Republican 4.754 = Female/Democrat 2.75

Conduct six t tests? NO. Why not? Will capitalizes on chance.

Solution: Post hoc tests of multiple comparisons. 

Post hoc tests consider the inflated likelihood of Type I error

Kent's favorite—Tukey test of multiple comparisons, which is the most generous.

NOTE: Post hoc tests can be done on any multiple set of means, not only on planned contrasts.

Conducting Post Hoc Tests

1. Recode data from multiple factors into single factor, as per planned contrast. 2. Run oneway ANOVA statistic 3. Select "posthoc tests" option.

ONEWAY gunctrl BY genparty /CONTRAST= -1 -1 -1 3 /STATISTICS DESCRIPTIVES /MISSING ANALYSIS /POSTHOC = TUKEY ALPHA(.05).

Selected post-hoc test

Note: Not necessary to conduct planned contrast to conduct post-hoc test

Descriptives

gunctrl

4 5.0000 .81650 .40825 3.7008 6.2992 4.00 6.004 4.5000 1.29099 .64550 2.4457 6.5543 3.00 6.004 4.7500 .95743 .47871 3.2265 6.2735 4.00 6.004 2.7500 .95743 .47871 1.2265 4.2735 2.00 4.00

16 4.2500 1.29099 .32275 3.5621 4.9379 2.00 6.00

male republicanmale democratfemale republicanfemale democratTotal

N Mean Std. Deviation Std. Error Lower Bound Upper Bound

95% Confidence Interval forMean

Minimum Maximum

ANOVA

gunctrl

12.500 3 4.167 4.000 .03512.500 12 1.04225.000 15

Between GroupsWithin GroupsTotal

Sum ofSquares df Mean Square F Sig.

Post hoc Tests, Page 1

Multiple Comparisons

Dependent Variable: gunctrlTukey HSD

.50000 .72169 .898 -1.6426 2.6426

.25000 .72169 .985 -1.8926 2.39262.25000* .72169 .039 .1074 4.3926-.50000 .72169 .898 -2.6426 1.6426-.25000 .72169 .985 -2.3926 1.89261.75000 .72169 .125 -.3926 3.8926-.25000 .72169 .985 -2.3926 1.8926.25000 .72169 .985 -1.8926 2.3926

2.00000 .72169 .070 -.1426 4.1426-2.25000* .72169 .039 -4.3926 -.1074-1.75000 .72169 .125 -3.8926 .3926-2.00000 .72169 .070 -4.1426 .1426

(J) genpartymale democratfemale republicanfemale democratmale republicanfemale republicanfemale democratmale republicanmale democratfemale democratmale republicanmale democratfemale republican

(I) genpartymale republican

male democrat

female republican

female democrat

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound95% Confidence Interval

The mean difference is significant at the .05 level.*.

Post Hoc Tests, Page 2

Data Management Issues

Setting up data file

Checking accuracy of data

Disposition of data Why obsess on these details?  Murphy's Law

If something can go wrong, it will go wrong, and at the worst possible time.

Errars Happin!

Creating a Coding Master

1. Get survey copy 2. Assign variable names 3. Assign variable values 4. Assign missing values 5. Proof master for accuracy 6. Make spare copy, keep in file drawer

Coding Master

variable names

variable values

Note: Var. values not needed for scales

Cleaning Data Set

1. Exercise in delay of gratification 2. Purpose: Reduce random error 3. Improve power of inferential stats.

Complete Data Set

Note: Are any cases missing data?

Are any “Minimums” too low? Are any “Maximums” too high?

Do Ns indicate missing data?

Do SDs indicate extreme outliers?

Checking Descriptives

Do variables correlate in the expected manner?

Checking Correlations Between Variables

Using Cross Tabs to Check for Missing or Erroneous Data Entry

Case A: Expect equal cell sizesGender 

Oldest Youngest Only Child

Males 10 10 20

Females 5 15 20

TOTAL 15 25 40

Case B: Impossible outcomeNumber of Siblings 

Oldest Youngest Only Child

None 4 3 6

One 3 4 0

More than one 3 4 2

TOTAL 10 10 8

Storing Data

Raw Data

1. Hold raw data in secure place

2. File raw data by ID #

3. Hold raw date for at least 5 years post publication, per APA Automated Data

1. One pristine source, one working file, one syntax file

2. Back up, Back up, Back up

` 3. Use external hard drive as back-up for PC

File Raw Data Records By ID Number

01-20 21-40 41-60 61-80 81-100 101-120

COMMENT SYNTAX FILE GUN CONTROL STUDY SPRING 2007

COMMENT DATA MANAGEMENT

IF (gender = 1 & party = 1) genparty = 1 .EXECUTE .IF (gender = 1 & party = 2) genparty = 2 .EXECUTE .IF (gender = 2 & party = 1) genparty = 3 .EXECUTE .IF (gender = 2 & party = 2) genparty = 4 .EXECUTE .

COMMENT ANALYSES

UNIANOVA gunctrl BY gender party /METHOD = SSTYPE(3) /INTERCEPT = INCLUDE /PRINT = DESCRIPTIVE /CRITERIA = ALPHA(.05) /DESIGN = gender party gender*party .

ONEWAY gunctrl BY genparty /CONTRAST= -1 -1 -1 3 /STATISTICS DESCRIPTIVES /MISSING ANALYSIS /POSTHOC = TUKEY ALPHA(.05).

Save Syntax File!!!

Research Project NotebookPurpose: All-in-one handy summary of research project

Content:   1. Administrative (timeline, list of staff, etc.)2. Overview of Research3. Experiment Materials

* Surveys* Consents, debriefings* Manipulations* Procedures summary/instructions

4. IRB materials* Application* Approval

5. Data* Coding forms* Syntax file* Primary outcomes

Correlation

Class 20

Today's Class Covers

What and why of measures of association

Covariation

Pearson's r correlation coefficient

Partial Correlation

Comparing two correlations

Non-Parametric correlations

Do Variables Relate to One Another?

Is teacher pay related to performance?

Is exercise related to illness?

Is CO2 related to global warming?

Is platoon cohesion related to PTSD?

Is TV viewing related to shoe size?

Positive

Negative

Positive

Negative

Zero

Exercise and Illness

1. How many times a week do you exercise? _____

2. How many days have you missed school this term due to illness? _____

3. How many hours of sleep do you get each night? ____

Interpreting Correlations

[C]    Sleep Hours

[A] Exercise

[B] Illness

A --> B Exercise reduces illness

B --> A Illness reduces exercise

C --> (A & B) Third variable (sleep) affects exercise and illness simultaneously

Exercise and Illness Data (fabricated)

subject exerise.days sleep.hours sick.days1 5 7 0

2 3 6 2

3 4 8 1

4 6 7 1

5 2 6 3

6 4 7 1

7 1 5 7

8 7 6 3

9 4 7 3

10 3 6 3

11 5 7 2

12 2 6 4

13 3 5 2

14 3 6 4

Description of Data

Scatterplot: Exercise and Days Sick

Regression Line

Co-variation8

7

6

5

4

3

2

1

01 2 3 4 5 6 7 8 9 10 11 12 13 14

exercise dayssick days

Subject Number

# Da

ys

Covariation Formula

cov (x,y) =Σ (Xi – X) (Yi – Y)

N – 1

cov(exercise, sickness) =(-3.32) + (0.40) + (-0.46) …+ (-1.02)

14-1

= -23/13 = -1.77

Problem with Covariation

"To all health and exercise researchers: Please send us your exercise and health covariations."

Team 1: exercise = days per week exercise, covariation = -1.77

Team 2: exercise = hours per week exercise, covariation = -34.00

What if we all we have are the covariations?

How do we compare them?

How would we know, in this case, whether Team 1 showed a larger, smaller, or equal covariation than did Team 2?

Pearson Correlation Coefficient

r = covxy

sxsy

r = Σ (Xi – X) (Yi – Y)

(N – 1)

sxsy

Pearson r (“rho”): -1.00 to + 1.00

=

Using R2 to Interpret Correlation

R2 = r2 = amount of variance shared between correlated variables.

Correl: exercise.hours, sick.days = .613

R2 = .6132 = .376

“About 38% of variability in sick days is explained by variability in exercise hours.”

Variation in Sick Days Explained by Exercise Hours

 Exercise hours = .376%

0 2.5 7

Number of Sick Days Last Term

R2 = .6132 = .376

Partial Correlation

Issue: How much does Variable 1 explain Variable 2, AFTER accounting for the influence of Variable 3?

Sickness and Exercise Study: How much does exercise explain days sick, AFTER accounting for the influence of nightly hours of sleep?

Partial Correlation answers this question.

Partial Correlations in SPSS

PARTIAL CORR /VARIABLES= sleep.hours sick.days by exercise.days /SIGNIFICANCE=TWOTAIL /MISSING=LISTWISE.

PARTIAL CORR /VARIABLES= sleep.hours exercise.days by sick.days /SIGNIFICANCE=TWOTAIL /MISSING=LISTWISE.

Non-Parametric CorrelationsAssumptions of Correlations

1. Normally distributed data

2. Homogeneity of variance

3. Interval data (at least)

What if Assumptions Not Met?

Spearman's rho: Data are ordinal.

Kendall's tau: Data are ordinal, but small sample, and many scores have the same ranking

Parametric CorrelationsAssumptions of Correlations

1. Normally distributed data

2. Homogeneity of variance

3. Interval data (at least)

Var. A Var. B

Watch TV

1 hr 2 hr 3 hr 4 hr 5 hr

Eat Fast Food

1 day 2 day 3 day 4 day 5 day

Non-Parametric Correlations

Var. A Var. B

Watch TV

Never Daily Weekly Monthly Yearly

Eat Fast Food

Never Daily Weekends Holidays Leap Years

What if Assumptions Not Met?

Spearman's rho: Data are ordinal.

Kendall's tau: Data are ordinal, but small sample, and many scores have the same ranking.

Comparing Correlations

Issue: How do we know if one correlation is different from another?

Example:  Is the nightly-sleep / sick days correl. different from the TV hours /sick days correl?

Difference Between Correlations

Link to calculator for two ind. samples correlationshttp://faculty.vassar.edu/lowry/rdiff.html

Diff. Between 2 Independent correlations

Diff. Between 2 dependent = correlations

tdifference = (rxy - rzy) √(n-3) (1 + rxz)

2 (1-r2xy -r2

xz - r2zy + 2rxyrxzrzy)

z = zr1 - zr2

1

n1 - 3+

1

n2 - 3

Note: Assumes independent samples

Partial Correlation

Sick DaysExercise DaysSleep Hours

var. explained = .376

var. explained = .27 var. explained by exercise alone (.04)

var. explained by sleep alone (.04)

var. explained by exercise + sleep (.21)