2-way ANOVA

[zstatman]

I am running the ANOVA with binary IVs (1 = Yes, 2 = No) and a scale DV
below


UNIANOVA PSSoverall BY destype jastype
  /METHOD=SSTYPE(3)
  /INTERCEPT=INCLUDE
  /PLOT=PROFILE(destype*jastype)
  /EMMEANS=TABLES(OVERALL)
  /EMMEANS=TABLES(destype) COMPARE ADJ(BONFERRONI)
  /EMMEANS=TABLES(jastype) COMPARE ADJ(BONFERRONI)
  /EMMEANS=TABLES(destype*jastype)
  /PRINT=ETASQ HOMOGENEITY DESCRIPTIVE OPOWER
  /PLOT=SPREADLEVEL
  /CRITERIA=ALPHA(.05)
  /DESIGN=destype jastype destype*jastype.

The questionable part is that I get a negative Adjusted R-square. Comments
appreciated

Will

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[Alex Reutter]

Adjusted R-square = R^2 - (1-R^2)p/(C-p*)

where p=#predictors, C=sum of case weights, p*=#coefficients in the model.  Adjusted R-square can easily be negative if destype and jastype have a lot of categories relative to the number of cases.

Alex

From:	Statmanz <[hidden email]>
To:	[hidden email]
Date:	11/20/2009 08:52 AM
Subject:	2-way ANOVA
Sent by:	"SPSSX(r) Discussion" <[hidden email]>

---

I am running the ANOVA with binary IVs (1 = Yes, 2 = No) and a scale DV
below


UNIANOVA PSSoverall BY destype jastype
 /METHOD=SSTYPE(3)
 /INTERCEPT=INCLUDE
 /PLOT=PROFILE(destype*jastype)
 /EMMEANS=TABLES(OVERALL)
 /EMMEANS=TABLES(destype) COMPARE ADJ(BONFERRONI)
 /EMMEANS=TABLES(jastype) COMPARE ADJ(BONFERRONI)
 /EMMEANS=TABLES(destype*jastype)
 /PRINT=ETASQ HOMOGENEITY DESCRIPTIVE OPOWER
 /PLOT=SPREADLEVEL
 /CRITERIA=ALPHA(.05)
 /DESIGN=destype jastype destype*jastype.

The questionable part is that I get a negative Adjusted R-square. Comments
appreciated

Will

[Granaas, Michael]

"The questionable part is that I get a negative Adjusted R-square. Comments
appreciated"

Off the top of my head you have little/no effect and a smallish sample size.

We adjust r-square by inflating the error (1-R^2) and then subracting from 1.

With a a sample size of N=40 the inflation factor will be (N - 1)/(N-k-1) = 39/36 = 1.0833333

If R^2 = .05 then the inflated error is 1.083333(1 -.05) = 1.029ish

The inflated error, subtracted from 1, gives and adj-R^2 of -.029ish.

Michael
****************************************************
Michael Granaas             [hidden email]
Assoc. Prof.                Phone: [phone]
Dept. of Psychology         FAX:  [phone]
University of South Dakota
414 E. Clark St.
Vermillion, SD 57069
*****************************************************
________________________________________
From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Statmanz [[hidden email]]
Sent: Friday, November 20, 2009 8:49 AM
To: [hidden email]
Subject: 2-way ANOVA

I am running the ANOVA with binary IVs (1 = Yes, 2 = No) and a scale DV
below


UNIANOVA PSSoverall BY destype jastype
  /METHOD=SSTYPE(3)
  /INTERCEPT=INCLUDE
  /PLOT=PROFILE(destype*jastype)
  /EMMEANS=TABLES(OVERALL)
  /EMMEANS=TABLES(destype) COMPARE ADJ(BONFERRONI)
  /EMMEANS=TABLES(jastype) COMPARE ADJ(BONFERRONI)
  /EMMEANS=TABLES(destype*jastype)
  /PRINT=ETASQ HOMOGENEITY DESCRIPTIVE OPOWER
  /PLOT=SPREADLEVEL
  /CRITERIA=ALPHA(.05)
  /DESIGN=destype jastype destype*jastype.

The questionable part is that I get a negative Adjusted R-square. Comments
appreciated

Will

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
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[Bruce Weaver]

Alex Reutter wrote

Adjusted R-square = R^2 - (1-R^2)p/(C-p*)

where p=#predictors, C=sum of case weights, p*=#coefficients in the model.
 Adjusted R-square can easily be negative if destype and jastype have a
lot of categories relative to the number of cases.

Alex

But DESTYPE and JASTYPE are both dichotomous.  So wouldn't the sample size have to be EXTREMELY small for there to be a lot of categories relative to the number of cases?  What is the sample size--you never said in your original message.  And what is the value of the unadjusted R-square?  I suspect it is very close to 0.

By the way, the formula I'm familiar with (from Dave Howell's book) is:

   adj. R-square = 1 - [ (1-R^2)(N-1) / (N-p-1) ]

where N = number of cases, and p = the number of predictor variables in the model.

On another matter, why are you using COMPARE  ADJ(BONFERRONI) for the main effects?  There are only two levels, so if the F-test for the main effect is significant, the two levels differ significantly.  You don't need any further contrasts, and I expect the contrasts obtained via COMPARE will be equivalent to the F-tests on the main effects.  

For the interaction, on the other hand, you might want to do this to get the simple main effects:

  /EMMEANS=TABLES(destype*jastype) COMPARE(destype) ADJ(BONFERRONI)

OR...

  /EMMEANS=TABLES(destype*jastype) COMPARE(jastype) ADJ(BONFERRONI)

HTH.