Question

Trouble with arcsine transform and z-test:
My data look like this:
Group A:
Samples: 8
Proportion: 0.625
Group B:
Samples: 7
Proportion: 0.857

I carried out an arcsine transform (transformed value = arcsine(sqrt(x)) in radians) and ran a Z-test to see if these proportions were significantly different. I ran the Z-test on the transformed data and came back with p<0.01, but running it with untransformed data got me p>0.15. Did I do something wrong? Does it matter if arcsine is evaluated in terms of radians or degrees?
Any help is welcome. Thanks.

Answer 1

I should add, the data are presence/absence (like approval ratings in politics).
They look like:
Group A: 0 0 0 1 1 1 1 1
Group B: 0 1 1 1 1 1 1 1

Answer 2

Okay, good. The first thing is that the data must be from 1 to -1, so I was going to ask you about your data.

And yes, arcsin must be in radians.

Answer 3

^*In this case, the arcsin used in the transform must be found in radians.

Answer 4

And also, didn't you say Groub B had n=7?

Answer 5

ah yes.
*group B: 0 1 1 1 1 1 1

Answer 6

Hmmmm, take a look at this by the way; it may help: http://rfd.uoregon.edu/files/rfd/StatisticalResources/arcsin.txt

Answer 7

"arcsine is not good for small sample sizes (n)" Should I just drop the use of the arcsine transform and go with the basic proportions?

Answer 8

Sure. Do you have the choice to use a logistic regression, though? Personally, that's what I would use.

Answer 9

Yes, this is open-ended data analysis for a class project.

Answer 10

I'll look into that. Thanks. (I may be back tomorrow)

Answer 11

No problem! Good luck!