Recognizing a balanced design in two-way ANOVA hypothesis testing

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to recognize a balanced design in two-way ANOVA hypothesis testing.  Here's our problem statement: Researchers randomly select and weigh men and women.  Their weights are entered in the table below so that each cell includes five weights.  Is the result a balanced design?  Why or why not?

Solution

Well, here we have our samples here in the table.  And we notice we have the same number of samples for each of the cells in the table.  This is what it means when it's talking about balanced design.  So here we've got five samples, and here we've got five samples.  You don't have any more samples for any combination of row factor or column factor than you do for any other.  And that's what it means by balanced design.  So we see we have five samples for each of the cells in our table.  So that means that we do have a balanced design.  Excellent!

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