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A user-friendly SAS program for determining statistical dependence between variables in observational studies
Xiaojie Li
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(socioeconomic status)
Ses(Intelligence)
Intel
association:
significant!
Research finding:
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A regression model for prediction?
dependence of
?Ses on Intel Intel on Ses
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X(Ses)
Y (Intel)
Y = + * X + (model I)
Some social scientists say…
predictor/independent response/dependent
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X (Ses)
Y (Intel)
X = + *Y + (model II)
Others argue…
predictor/independentresponse/dependent
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Statisticians say… (e.g., Hays 1994; Snedecor & Cochran 1989)
Y = + * X + (I)
X = + * Y + (II)arbitrary{
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Which “model” to go?
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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!
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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
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Inequalities: 4 statistics ( variables: X, Y )
• skewness coefficients
γx γy
symmetric or skewed
• higher order corr coefficients
ρ12
ρ21
relatedness of X and Y
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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
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Loose criteria
Model I: γy2 ≤ γx
2 ρ
122 ≤ ρ
212
or
Model II: γy2 ≥ γx
2 ρ
122 ≥ ρ
212
*potential conflict
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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
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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)
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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)
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.infile 'a:\haysVarList.prn' end=final; .infile 'a:\haysData.prn' firstobs=2;.
Input before running
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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
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A few words of …
• help to applied researchers
• statistical dependence
• tomorrow will be better
causality
X
theD-R way
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Acknowledgment
• Associated Students(graduate fellowship program)
• Dr. W. A. Rodriguez (mentor)
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Ses Intel
A regression model for prediction?
dependence of … on …?