# Equality of three (selective)

1. Jan 27, 2010

### dumbest

first of all , hello everyone

you can see who i am depending on my nickname ,

but

i have one question :

" Three factory creates the same item ,

from the first factory is selected 250 item and 10 of them is defective
from the second factory 200 and 9 of them is defective
from the third 150 and 11 of them is defective

a=0.1 ( Alpha = 0.1 )

question is : test hypothesis about equality of these "selections" ( i don`t know how to say exactly ) "

should i test the first two of them using " Two-proportion z-test " and then test one of them and third using again " Two-proportion z-test " .......... ?

anyone ?

Last edited: Jan 27, 2010
2. Jan 27, 2010

### EnumaElish

You can test them in pairs, with the caveat that pairwise tests are not transitive: if x = y and y = z are both statistically significant, it does not follow that x = z is also stat. significant. In your case, they may turn out to be consistent; I haven't tried.

The alternative is to use ANOVA for three Binomial distributions. You can estimate within-group (sample) variances using the binomial variance formula njpj(1-pj) for the j'th group, then set it equal to the sample variance, sn2 (substitute nj for n) then solve for the sum of squared deviations from the mean for the j'th sample (j = 1, 2, 3).

3. Jan 27, 2010

### dumbest

i think they must be consistent ,

because the alternative way ( anova ... ) will take more time and that way is not defined by teacher yet ...

students do not know what is Anova ...