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Chapter 12: Q2BSC (page 566)

Two-Way ANOVA If we have a goal of using the data described in Exercise 1 to (1) determine whether age bracket has an effect on pulse rates and (2) to determine whether gender has an effect on pulse rates, should we use one-way analysis of variance for the two individual tests? Why or why not?

Short Answer

Expert verified

No, one-way analysis of variance should not be used to check the effects of gender and age separately.The result will not be the same as obtained after applying a two-way analysis of variance.

Step by step solution

01

Given information

Data are given on the pulse rates of men and women. It is further classified according to three different age groups.

02

One-way and two-way analysis of variance

A one-way ANOVA explains the difference among the three or more groups of single factor in terms of their means.

A two-way analysis of variance is conducted for a set of data that consists of values that differ on two different categories.

It helps assess the difference in the mean values of individual factors; that is, one is the row category, and the other is the column category. This analysis also includes the difference in the mean values due to the combined effect or interaction effect between row and column categories.

03

Difference between the one-way ANOVA and two-way ANOVA

When a two-way analysis of variance is conducted, the interaction effect is also considered.

But, when a one-way analysis of variance is conducted twice, the interaction effect is not considered,so the results are different.

Therefore, a two-way analysis of variance cannot be replaced with a one-way analysis of variance conducted twice.

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