Consider a scenario where a two-way contingency table is analyzed by a chi-squared test of independence and a significant result is found. Now, it turns out that this table is an aggregation of data from two subgroups which are heterogenous and one much bigger than the other. When analysed at the sub-group level, both groups give a non-significant result. How is this best explained ?
Edit: I managed to find the paper where I read about this. They explain it as Simpson's Paradox. http://www.amstat.org/publications/jse/secure/v7n3/datasets.morrell.cfm