Linear models are amazingly robust to distributional assumptions, so long as the sample size is relatively large, and you aren't near the points where the distributional assumption breaks down. For instance, try the code below. Even when the total sample size is ten per group, GLM does a pretty good job of giving a p-value close to that for the chi squared type stats. Only the exact test for small proportions is grossly different in p value, and under these conditions, I wouldn't trust chi squared either.
If it came down to detecting small changes, or the proportions were near 0 or 1, then the distributional assumptions make a difference in the final conclusion, and more powerful and appropriate methods need to be applied. And personally, I hate making an assumption I know is wrong. But the Central Limit Theorem, Law of Large Numbers and Tchebychev's theorem all seem to protect the unwary.
Code for comparing:
data one;
input grp response weight1 weight2 weight3 weight4;
cards;
1 0 40 4 4 1
1 1 60 96 6 9
2 0 60 8 6 2
2 1 40 92 4 8
;
proc freq data=one;
table grp*response/all exact;
weight weight1;
run;
proc freq data=one;
table grp*response/all exact;
weight weight2;
run;
proc freq data=one;
table grp*response/all exact;
weight weight3;
run;
proc freq data=one;
table grp*response/all exact;
weight weight4;
run;
proc glm data=one;
class grp;
model response=grp;
freq weight1;
run;
proc glm data=one;
class grp;
model response=grp;
freq weight2;
run;
proc glm data=one;
class grp;
model response=grp;
freq weight3;
run;
proc glm data=one;
class grp;
model response=grp;
freq weight4;
run;
quit;
Good luck.
Steve Denham
