Unequal Sample Sizes

by Karen Grace-Martin

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My next door neighbor, who is a mycologist (hey, it’s Ithaca–everyone’s a researcher here) asked me a very common statistical question–she was very concerned about her unequal sample sizes.  She was doing a chi-square test and had about 11 observations in one grouping and 18 in the other.

She had already talked with a statistical consultant, who said the unequal samples were not a problem.  But since she still didn’t understand why, she asked me.

As it turns out, I had just finished writing a document called “7 Statistical Issues that Researchers Shouldn’t Worry (So Much) About.”  #4 is unequal sample sizes.

I wrote this because there are a number of issues that are of common concern to researchers but really aren’t a problem in all but the rarest situations.  Yet they eat up a lot of mental energy.

So worry no more–get the report for free at The Analysis Factor, and read all about unequal sample sizes and more.

{ 6 comments… read them below or add one }

Ella

Eating up a lot of mental engergy…Yes, that’s me too!

I understand why unequal sample sizes may not be an issue when working with means, but are large sample size differences ok when conducting a Chi-sq? I have a sample of 35 in one condition and a sample of 150 in another.

Does SPSS factor this into its Chi-sq calculation automatically?
Some advice would be appreciated.

Reply

Karen

Yes and no. The chi-square does take into account the row and column totals, so that essentially it’s testing if the row proportions are the same across columns. That’s where the expected values come in.

And Simpson’s Paradox can become an issue. It basically comes down to whether there are really interactions with a third variable, and if sample sizes differ across that variable.

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Matt

Hi Karen

Could you email me the free report on unequal sample sizes please.

Cheers

Matt

mattalbie@hotmail.com.

Reply

Karen

Hi Matt,

You’ll get it automatically if you sign up for our newsletter mailing list. Just use the form at right.

Karen

Reply

Jerry Suits

What if there is a very big difference in the two sample sizes? Example: 301 in one treatment condition, and 1603 in the other (rows are “Students who PASSED” AND “Students who FAILED”.

Thanks,
Jerry

Reply

Karen

Still not a problem in the one-way model. Power is lower, yes, and you need to pay attention to homogeneity of variance assumptions, but if it’s met, no problem!

Karen

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