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One-Way ANOVA/Two-Way ANOVA

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Hi. This tutorial covers one-way and two-way ANOVA. So let's start just by defining both one-way and two-way ANOVA. But before we do that, let's just quickly talk about ANOVA in general. Remember ANOVA stands for the analysis of variance. It's a type of hypothesis test that tests for equality among multiple population means.

So a one-way ANOVA test is an ANOVA hypothesis test that considers population means based on one characteristic or factor, whereas two-way ANOVA is an ANOVA hypothesis test that consider comparisons between populations based on multiple characteristics. So one-way ANOVA, we're looking at means based on one characteristic. Two-way ANOVA, we're looking at comparing populations based now on multiple characteristics instead of just one.

So we're not going to really go into the calculations too much of one-way and two-way ANOVA. We're just going to look at two different examples and see which is more appropriate-- one-way ANOVA or two-way ANOVA. So example 1, a researcher is interested in the mean weekly wage for different age groups, so age 22 to 24-- to less than 24-- 24 to less than 26, 26 to less than 28, for young professionals at a large company.

Would one-way ANOVA or two-way ANOVA be more appropriate to test the effect of age on mean weekly wage? So are we talking about a two-way ANOVA? Would we use a two-- excuse me-- a one-way ANOVA test or a two-way ANOVA test?

So what I would suggest in this case is to use one-way ANOVA because remember one-way ANOVA considers population means based on one characteristic or one factor. So if we're looking at mean weekly wage, the only thing we're concerned about here is the effect that age has on mean weekly wage so whether or not there's different means among these three age groups. So in this case, we're just going to use one-way ANOVA.

Now let's take a look at example 2. So example 2 now is a researcher is interested in better understanding the effect of both gender and age group on mean weekly wage of young professionals. Now would one-way ANOVA or two-way ANOVA be more appropriate to test the effects of age and gender on mean weekly wage?

So now in this case, we're going to be doing-- we would want to do a two-way ANOVA because remember two-way ANOVA considers comparisons between populations based on multiple characteristics. So now we're comparing different wages based on both age and gender. So we would have our genders being both male and female, and then we would have our different age breakdowns-- 22 to less than 24, 24 to less than 26, 26 to less than 28.

So in that case, we're going to be looking at multiple characteristics affecting our wages here. So this would be-- it would be more appropriate in this case to use two-way ANOVA. So there's just two basic examples on when you would use one-way ANOVA versus two-way ANOVA. So that has been your tutorial on one-way ANOVA and two-way ANOVA. Thanks for watching.