Identifying Types of Correlation Questions

For each of the following: 1) identify the type of model or model comparison that would be used to test each

2) tell the significance test that would be used

3) depict the RH: using the proper notation

Easy Stuff -- one research hypothesis per statement arranged in groups (simple, control, multiple)

Simple

Undergraduate grade point average (ugpa) is a better correlated with graduate school grades (grad) for male than for female graduate students.

Comparing a correlation across populations. Fisher’s Z-test RH: rugpa,grad male > rugpa,grad female

Undergraduate grade point average (ugpa) is correlated with graduate school grades (grad).

Simple correlation RH: rugpa,grad > 0

Undergraduate grade point average (ugpa) is a better correlated with graduate school grades (grad) than is the quantitative GRE (greq).

Comparing correlated correlations Steiger’s Z RH: rugpa,grad > rgreq, grad

Control

Undergrad grade point average (ugpa) is correlated with graduate school grades (grad), even after controlling both for IQ (iq).

Partial RH: rugpa,grad.iq

Undergraduate grade point average (ugpa) is correlated with graduate school grades (grad), even after controlling undergraduate grade point average for the difficulty of the college that was attended (dif) and the age of the student (age).

Multiple Semi-partial RH: rgrad(ugpa.dif,age)

Undergraduate grade point average (ugpa) is correlated with graduate school grades (grad), even after controlling both for IQ (iq) and parents education (pe).

Multiple Partial RH: rgrad,ugpa.iq,pe

Undergraduate grade point average (ugpa) is correlated with graduate school grades (grad), even after controlling undergraduate grade point average for the difficulty of the college that was attended (dif).

Semi-partial RH: rgrad(ugpa.dif)

Multiple

A combination of undergraduate grades (ugpa) and a rating derived from the letters (let) of recommendation (using a 5-point scale) will work better for predicting graduate school grades than will using the three GRE scores (greq, grev, grea).

Non-tested MR models Steiger’s Z RH: R²grad.ugpa,let > R²grad.greq,grev,grea

A combination of undergraduate grades (ugpa) and a rating derived from the letters (let) of recommendation (using a 5-point scale) will predict graduate school grades better for males than for females.

Comparing MR across groups Fisher’s Z & Steiger’s Z RH: R²grad.ugpa,letmale > R²grad.ugpa,letfemale

A combination of undergraduate grades (ugpa) and a rating derived from the letters (let) of recommendation (using a 5-point scale) will successfully predict graduate school grades.

Multiple regression RH: R²grad.ugpa,let > 0

Using all three GRE scores (greq, grev, grea) will better predict graduate school grades (grad) than will using just the verbal and quantitative scores.

Nested MR ModelsR²Δ F-test R²grad.greq,grev,grea > R²grad.grev,greq

A combination of undergraduate grades (ugpa) and a rating derived from the letters (let) of recommendation (using a 5-point scale) will predict graduate school grades better than it will predict number of publications (pub).

Comparing MR across criterion variables Steiger’s Z RH: R²grad.ugpa,let > R²pub.ugpa,let
More Interesting -- "Pluck the corelational questions from the less-than-coherent ramblings of the researcher".

Hint #1: Go slowly and be very complete -- sometimes a brief comment requires multiple analyses!!

Hint#2: Whenever you have to choose between partial and semi-partial types of correlations (sometimes the researcher won't specify which they are considering) carefully consider whether or not it "makes sense" to control both or only one of the main variables for the control variable(s)

The study is about correlates of social skills among adolescents (11-16 yrs).

I expect that age is not as well correlated with social skills as is IQ,

rskills,age < rskills,IQ Steiger’s Z

but that both are poorly correlated with social skills compared to the number of siblings an adolescent has.

rskills,age < rskills,nsibsrskills,IQ < rskills,nsibs Steiger’s Z

Then again, all these correlations are probably higher for females than for males

rskills,age & rskills,nsibs & rskills,IQ Females > rskills,age & rskills,nsibs & rskills,IQ Males 3 Fisher’s Z

and the same is true for the multiple regression model (predicting social skills from IQ and number of siblings).

R²skills.IQ,nsibs Females > R²skills.IQ,nsibs Males Fisher’s Z for R² Steiger’s Z for structure

Even when you control for age, there is a substantial correlation between number of siblings and social skills,

rskills,nsibs.age > 0

but this correlation goes away when you also control for parents' social skills,

rskills,nsibs.age,pss = 0

which is better correlated with social skills than any of the other variables.

rskills,pssrskills,age & rskills,nsibs & rskills,IQSteiger’s Z

In fact, I'll bet that parents' social skills is better correlated with adolescent's social skills than all the rest of the variable combined.

r²skills,pss > R²skills.age,nsibs,IQSteiger’s Z

But, remember that we expect that age and IQ will do as well as if you also include the number of siblings.

R²skills.age,IQ > R²skills.age,nsibs.IQR²Δ F-test

Oh yeah, back to the earlier thought, if you only control for age there still a correlation between number of siblings and social skills,

rskills,nsibs.age > 0

but when you split the sample into males and females, this really only happens for males.

rskills,nsibs.age > 0 males rskills,nsibs.age = 0 females

The good news is that all of these relationship ships should hold up whether we use the "Marks" or the "Schubert & Grinsby" social skills indices.

Would have to compare each correlation or model including skills using the two criteria