10.7
Two-Way ANOVA
A two-way ANOVA compares three or more sample means categorized by two factors.
Consider comparing the height of males and females from three age groups. Age is the row factor, and gender is the column factor.
State the null hypothesis that age and gender show no interaction effect on the mean height.
The interaction effect is visualized as two line segments formed by connecting the mean values of each factor.
The line segments of age and gender are roughly parallel, showing that the mean height of males and females is not affected by age and gender simultaneously.
Calculating the F statistic and P-value confirms no interaction effect, showing that age or gender independently affects mean height. We fail to reject the null hypothesis.
Next, check if age or gender affects mean height.
Separately state the null hypothesis, and compute the F statistic and P-values for age and gender.
Since age doesn't substantially affect mean height, we fail to reject the null hypothesis.
Whereas gender substantially affects the mean height. So, the null hypothesis is rejected.
The two-way ANOVA is an extension of the one-way ANOVA. It is a statistical test performed on three or more samples categorized by two factors - a row factor and a column factor. Ronald Fischer mentioned it in 1925 in his book 'Statistical Methods for Researchers.'
The two-way ANOVA analysis initially begins by stating the null hypothesis that there is an interaction effect between the two factors of a dataset. This effect can be visualized using line segments formed by joining the means for each factor. If the line segments are not parallel, an interaction between the two factors exists. In other words, the two factors simultaneously affect the values in a given dataset. If the two lines are parallel, then no interaction effect is observed. Calculating the F statistic for interaction effect can confirm this graphical representation. If the calculated P-value of the F statistic is greater than a specific significance level (for example, P-value = 0.05), one can fail to reject the null hypothesis.
Next, the effect of each factor on the data values is determined. In other words, it is checked if either the row factor or the column factor affects the data in the dataset. This is done by separately stating the null hypothesis and calculating the F statistic for each factor. If the P-value computed from the F statistic of a specific factor is lower than a chosen significance level (for example, P-value = 0.05), then that factor is said to affect the data values in a given dataset significantly.
A two-way ANOVA compares three or more sample means categorized by two factors.
Consider comparing the height of males and females from three age groups. Age is the row factor, and gender is the column factor.
State the null hypothesis that age and gender show no interaction effect on the mean height.
The interaction effect is visualized as two line segments formed by connecting the mean values of each factor.
The line segments of age and gender are roughly parallel, showing that the mean height of males and females is not affected by age and gender simultaneously.
Calculating the F statistic and P-value confirms no interaction effect, showing that age or gender independently affects mean height. We fail to reject the null hypothesis.
Next, check if age or gender affects mean height.
Separately state the null hypothesis, and compute the F statistic and P-values for age and gender.
Since age doesn't substantially affect mean height, we fail to reject the null hypothesis.
Whereas gender substantially affects the mean height. So, the null hypothesis is rejected.
From Chapter 10:
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10.7 : Two-Way ANOVA
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10.1 : What is an ANOVA?
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10.2 : One-Way ANOVA
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10.3 : One-Way ANOVA: Equal Sample Sizes
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10.4 : One-Way ANOVA: Unequal Sample Sizes
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10.5 : Multiple Comparison Tests
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10.6 : Bonferroni Test
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