chi square with percentages

I have two sample with a very different size (n=42 and n=282) and I only know the percentages of the dependent variable (with 8 levels).

The difference between the two sample in each level of DV is very large (for example: in the first condition the percentages are 16% and 82% respectively).

I converted the percentages in observed frequencies (for example 16/100*42; 82/100*282; ect.). I performed a chi square 2x8 with spss and the p-value is not significant.
How it is possible that p-value is not significant if the differences between the frequencies of each condition are vary large? This is not the procedure to be followed when you only have the percentages?


Omega Contributor
Your approach seems fine. Can you post your final constructed 2X8 table so we can provide a better response on the rationale?



Omega Contributor
Sorry, I don't open online files :(

What could be happening is that the test is under-powered, given the two distributions are truly different.


Omega Contributor
It would mean the two distributions (proportions for categories) are truly different, but you do not have enough data to make this conclusion. This would be a Type II Error, failing to reject the null hypothesis of no difference in distributions in the sample when the two distributions are truly different in the population.