A user-friendly SAS program for determining statistical dependence between variables in observational studies

Xiaojie Li

(socioeconomic status)

Ses(Intelligence)

Intel

association:

significant!

Research finding:

A regression model for prediction?

dependence of

?Ses on Intel Intel on Ses

X(Ses)

Y (Intel)

Y = + * X + (model I)

Some social scientists say…

predictor/independent response/dependent

X (Ses)

Y (Intel)

X = + *Y + (model II)

Others argue…

predictor/independentresponse/dependent

Statisticians say… (e.g., Hays 1994; Snedecor & Cochran 1989)

Y = + * X + (I)

X = + * Y + (II)arbitrary{

Which “model” to go?

D-R solution Dodge & Rousson. 2001. Am. Stat. 55:51–54.

• model-specific inequalities

• check what’s observed

• model can be determined

What great help to researchers!

My research objective

• the D-R method 1) requires complex computations;

2) not available in stat packages

• goal: to implement in SAS

easy for researchers to apply D-R

Inequalities: 4 statistics ( variables: X, Y )

• skewness coefficients

γx γy

symmetric or skewed

• higher order corr coefficients

ρ12

ρ21

relatedness of X and Y

Strict criteria

• Model I (Y dependent on X):

γy2 ≤ ρ

122 ≤ ρ

212 ≤ γx

2

• Model II (X dependent on Y):

γy2 ≥ ρ

122 ≥ ρ

212 ≥ γx

2

Loose criteria

Model I: γy2 ≤ γx

2 ρ

122 ≤ ρ

212

or

Model II: γy2 ≥ γx

2 ρ

122 ≥ ρ

212

*potential conflict

Implementing in SAS

• 6-page long & macro-based

• 2 data files:1) list of variables 2) actual data

• specify path in SAS• run and output:

suggested modelcriteria usedassumptions checked

A demonstration Hays (1994) Statistics 5th ed.

• origins of gender stereotyping in young girls

• 4 variables: sports interest scores

(MomInt, DadInt, GirlInt)PE teacher evaluation on girl’s

athleticism(PeEval)

GirlInt

DadInt

MomInt

PeEval

GirlInt DadInt MomInt PeEval 24 23 25 8 30 32 30 13 25 25 25 15 . . . .

haysVarList.prn

haysData.prn

2 data files (in Excel)

.infile 'a:\haysVarList.prn' end=final; .infile 'a:\haysData.prn' firstobs=2;.

Input before running

Determining statistical dependence between two variables (Via Dodge and Rousson's loose criteria) Note:"-" indicates conflict using the two loose criteria

Obs pair dependent independent

1 GirlInt vs. DadInt DadInt GirlInt 2 GirlInt vs. PeEval PeEval GirlInt

3 GirlInt vs. MomInt - - 4 DadInt vs. MomInt - -

5 DadInt vs. PeEval - - 6 MomInt vs. PeEval - -

Output from SAS

A few words of …

• help to applied researchers

• statistical dependence

• tomorrow will be better

causality

X

theD-R way

Acknowledgment

• Associated Students(graduate fellowship program)

• Dr. W. A. Rodriguez (mentor)

Ses Intel

A regression model for prediction?

dependence of … on …?