ASA Connect

Hi,

I am a beginner at using the two way ANOVA test and have a question.
Most of the information I have read and videos I have watched always have the groups with equal sample size.
Lets say 20 Girls and 20 Boys vs some other factors (age or test scores). What if the data is broken down as lets say 35 Boys and 5 Girls, would the two way ANOVA be the
appropriate test to conduct? If not could you recommend a different test.

Thank you for your time.
Kelly Fitzpatrick

If we assume the variability of each group is the same, having equal numbers in each group is best. That's why the want you to make groups equal sized. If one group has a much larger variability than the other, then giving more samples to the group with the larger variability is appropriate. (For future reference)

For your sizes, I'd think there is an issue because you have so few samples in one group. Suppose you have Test Score =f (gender, test type). With your data, you might only have 2 girls with test A and 3 girls with test B. If the girls really are indicative of the larger groups, then your ANOVA is fine. If you had say, 400 boys and 100 girls, I wouldn't have an issue. But just five seems a bit too low for me. 

Perhaps a 1way ANOVA with 3 groups, boys test A, boys test B, Girls, will work. 

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Andrew Ekstrom

Original Message:
Sent: 02-19-2016 21:45
From: Kelly Fitzpatrick
Subject: Two Way ANOVA

Hi,

I am a beginner at using the two way ANOVA test and have a question.
Most of the information I have read and videos I have watched always have the groups with equal sample size.
Lets say 20 Girls and 20 Boys vs some other factors (age or test scores). What if the data is broken down as lets say 35 Boys and 5 Girls, would the two way ANOVA be the
appropriate test to conduct? If not could you recommend a different test.

Thank you for your time.
Kelly Fitzpatrick

The main effects for a fixed effect unbalanced two-way analysis of variance/covariance F-statistics are still exact.  Your problem may arise in the interaction F-statistic.  This is particularly true under heteroscedasticity (unequal variances).  Programs such as BMDP, SAS, SYSStat, SPSS, and even Minitab would provide solutions for such cases using Greenhouse-Geiser, Hyuenfeldt, Satterthwaite and similar estimates which are still fairly close to being exact.  Make sure about the degrees of freedom estimates for those cases.  There maybe other solutions under GLM.  The requirement for balanced design (such as  yours) are in old software and books.  We have come a long way from that!

Ajit K. Thakur, Ph.D.

Retired Statistician

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Ajit Thakur
Associate Director

Original Message:
Sent: 02-19-2016 21:45
From: Kelly Fitzpatrick
Subject: Two Way ANOVA

Hi,

I am a beginner at using the two way ANOVA test and have a question.
Most of the information I have read and videos I have watched always have the groups with equal sample size.
Lets say 20 Girls and 20 Boys vs some other factors (age or test scores). What if the data is broken down as lets say 35 Boys and 5 Girls, would the two way ANOVA be the
appropriate test to conduct? If not could you recommend a different test.

Thank you for your time.
Kelly Fitzpatrick