Both count the the frequencies of the combinations of these categories. There are a number of different chi-square tests, but the two that can seem concerning in this context are the Chi-Square Test of Independence and The Chi-Square Test of Homogeneity. (This article is about ANOVA (and t-tests), but I’ve updated to include Chi-Square tests after getting a lot of questions). So you may get a big mean difference between the marital statuses, but it’s really being driven by age. The effect of marital status cannot be distinguished from the effect of age. In other words, the two factors are not independent of each other. So unequal sample sizes.Īnd say the younger group has a much larger percentage of singles than the older group. Let’s say there are twice as many young people as old. Let’s unpack this.įor example, in a two-way ANOVA, let’s say that your two independent variables ( factors) are Age (young vs. Real issues with unequal sample sizes do occur in factorial ANOVA in one situation: when the sample sizes are confounded in the two (or more) factors. It generally involves one or more interaction terms. Problems in Factorial ANOVAįactorial ANOVA includes all those ANOVA models with more than one crossed factor. Unbalanced t-tests have the same practical issues with unequal samples, but it doesn’t otherwise affect the validity or bias in the test. And the between-groups F statistic will be the square of the t statistic you got in your t-test. In fact, if you run your t-test as an ANOVA, you’ll get the same p-value. Independent samples t-tests are essentially a simplificiation of a one-way ANOVA for only two groups. Yes, this all holds true for independent samples t-tests The extra 270 didn’t help the power of this particular test. It’s just that you could have stopped with 30 controls. So if you have 30 individuals with Treatment A and 40 individuals with Treatment B and 300 controls, that’s fine. It just means the power you have is based on the smaller sample. That doesn’t bias your test or give you incorrect results. It’s very common to just happen to get a larger sample of one group compared to the others. If your grouping is a natural one, you’re not making decisions based on a total number of individuals. So if you have a specific number of individuals to randomly assign to groups, you’ll have the most power if you assign them equally. Power is based on the smallest sample size, so while it doesn’t hurt power to have more observations in the larger group, it doesn’t help either. The statistical power of a hypothesis test that compares groups is highest when groups have equal sample sizes. The only problem is if you have unequal variances and unequal sample sizes. If you have unequal variances and equal sample sizes, no problem. So if you have equal variances in your groups and unequal sample sizes, no problem. According to Keppel (1993), there is no good rule of thumb for how unequal the sample sizes need to be for heterogeneity of variance to be a problem. But that’s not true when the sample sizes are very different. The main practical issue in one-way ANOVA is that unequal sample sizes affect the robustness of the equal variance assumption.ĪNOVA is considered robust to moderate departures from this assumption. Assumption Robustness with Unequal Samples Two Practical Issues for Unequal Sample Sizes in One-Way ANOVA 1. They don’t invalidate an analysis, but it’s important to be aware of them as you’re interpreting your output. That’s not a big deal if you’re aware of it.īut there are a few real issues with unequal sample sizes in ANOVA. Instead of the grand mean, you need to use a weighted mean. Nice properties in ANOVA such as the Grand Mean being the intercept in an effect-coded regression model don’t hold when data are unbalanced. Sums of squares require a different formula* if sample sizes are unequal, but statistical software will automatically use the right formula. Because she was making you calculate everything by hand. In your statistics class, your professor made a big deal about unequal sample sizes in one-way Analysis of Variance (ANOVA) for two reasons.ġ.
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