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The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.
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Two-Sample Hypothesis Test for Proportions Segmented By Dimensions - Conflicting Results
I decided to turn my comment into an answer.
What you are experiencing is an example of Simpson's Paradox, where a marginal result can be in the opposite direction of a conditional result. In this ca …