Divergence between JASP and SPSS ouptuts when computing polynomial contrasts for within-sjts designs

mservant

Hi,
I am trying to reproduce David Howell's SPSS analysis of the aiport dataset (attached) in JASP. Dave's analysis is available at https://www.uvm.edu/~dhowell/StatPages/More_Stuff/RepMeasMultComp/RepMeasMultComp.html. When performing the polynomial contrast analysis of the effect of time on stress level (condition near aiport only), SPSS returns F(1, 99) = 1.721 p = .193 for the cubic trend while JASP returns t = 1.261 p = .208:
Obviously the t statistic returned by JASP is not equal to the square root of F returned by SPSS. Could you please clarify why?
Best,
Mat

JohnnyB

Hi Mat,
I just ran the analysis in R to check those results. Here is the code I wrote:

myDat <- read.csv("/home/johnny/Downloads/airport.csv")

# Take subset for "Near" condition
myDat <- subset(myDat, LOCATION == 1)

# Turn data frame into the "long data" format
myDat <- data.frame(y = unname(unlist(myDat[,1:4])), 
                     x = as.factor(rep(1:4, each = 100)), 
                     ID = as.factor(rep(1:100, 4)))

# Set contrast
contrasts(myDat$x) <- contr.poly(4) 

# Run RM ANOVA
myAOV <- aov(y ~ x + Error(ID/x), data=myDat)

# extract relevant contrasts from AOV object
summary(myAOV, split=list(x=list("Linear"=1, "Quad"=2, "Cubic"=3)))
# Returns
#               Df  Sum Sq Mean Sq F value   Pr(>F)    
# x: Cubic    1   14843   14843   1.589    0.208    

So this is the same result as JASP provides.
I did some digging into how these discrepancies arise, and found this post on StackExchange that provides some great insight:
``While the "t-test approach" tests each contrast against its own separate error term, the RM-ANOVA tests each contrast against a pooled error term (hence DF=14), which assumes that the variances of the contrast scores are approximately equal (i.e., sphericity assumption)."
It seems SPSS has the "t-test approach" without the pooled error term, and JASP/aov have the approach with the pooled error term. We have recently implemented the option to switch between pooled/nonpooled error terms for the post-hoc tests, and I do think it's prudent to add the same option to contrasts for those cases where the sphericity assumption has been violated. Thanks for pointing this out to us!
Kind regards,
Johnny