Can chi-square test be performed on data that does not have normal or gaussian distribution?
One of the chi-square tests I am performing results in percentage points less than the 12.59 (α=0.05, v=6) using cross-tabulation. Therefore, I cannot reject the null hypothesis.
Is there a test that I can perform to confirm the alternative hypothesis?
Added clarification 30nov2011:
I will attempt to clarify some of the issues raised in these comments. Please be gentle on me as I am not trained in statistics. In fact, thanks to the unimaginative curriculum and teaching, I abhorred statistics taught in engineering school. Just trying to help my wife with a project.
So, we are trying to establish a weak (if at all) relationship/dependence between 2 different attributes of a dataset. To accomplish this, we have generated a cross-tabulation.
One of the attributes matches perfectly with a lognormal distribution (acc. to Minitab) as the data points and the lines are almost coincident. We have used the k-means clustering algorithm to group the lognormal attribute into 3 broad categories (large, medium and small).
Next, we are trying to perform a chi-square test on the cross-tabulation. df = 6. But, not having sufficient insight into this, I am not sure what the result of 6.8 percentage points supposed to mean for the null hypothesis. Per our understanding, the null hypothesis is "two attributes are not related".
I am wondering what the next step should be. Further progress hinges upon confirming or denying the existence of a relationship. (Note, we do not have to determine the relationship. However, I wouldn't mind getting some insight into the relationship in this process.)