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I have a dataset of 400k rows, but even then, about 10% of my expected values are less than 1. Does this make the results of my chi squared independence test completely worthless? And if so, are there any alternatives that would fit my specific situation?

Am I allowed to just multiply the dataset by some number to make all expected values greater than 1?

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    $\begingroup$ Fixed title. I have a few different table types, some are 5x3, others are 2x10, etc. $\endgroup$ – tonychen Jul 17 '17 at 13:05
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Difficult to say without you presenting to us some of your tables!

Am I allowed to just multiply the dataset by some number to make all expected values greater than 1?

Definitely not. The effect of that would just be to multiply the Chisquared statistic with the same number, and it would not solve any problems. What you could do is to try simulations, like the option simulate.p.value in the R function chisq.test. But show us some of your tables ...

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Chi square test is not advised when sample sizes are low, specially with cells having expected counts <1. The way to proceed in your case is a bit controversial: some sources recommend using chi square with continuity correction (although most recent sources advise against this), while other sources encourage the usage of Fisher's exact test in this situation (although it can be overly conservative sometimes).

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