# Unequal Sample Sizes

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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.

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{ 12 comments… read them below or add one }

G K Deshmukh

How to deal with the problems of unequal subgroup size of a categorical moderator? eg Male = 120, Female =64

Quinn

I’ve done a Pretest-Posttest and I have an unequal number of participants. One group has 23 and the other group have 25. Yes. The difference is quite small. I am using a 1-tailed ttest. Should I use ANOVA?

Mia

I ran binary logistic regression and had 2 groups: 80 female, 20 male. Will this be a problem? Thank you!

Karen Grace-Martin

Hi Mia,

I can’t tell. Is that the predictor or response variable? Seems like a strange response variable.

Ails

I have unequal samples of approximately 90 participants in 1 group and 120 in the second group. I was planning to carry out multiple regression analyses and wondering if the unequal groups might be a problem?

Karen Grace-Martin

There is no real problem. If you look at the marginal means, there may be differences depending on which software you use.

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.

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.

Matt

Hi Karen

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

Cheers

Matt

Karen

Hi Matt,

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

Karen

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