Question

1. In your own words, what is one-way analysis of variance used for?

2. In your own words, what is the main difference between one-way analysis of variance and two-way analysis of variance

Answer 1

Question number 1

One way analysis of variance, ie. ANOVA, is a statistical technique, that is used to compare the means of two or more samples, with the help of F distribution.

Typically however, the one way ANOVA is used to compare the means of three or more samples, because comparison of two sample means can be easily done by the t test.

The one way ANOVA tests the null hypothesis, which claims that samples in all groups are drawn from populations with the same mean values. An F-statistic is produced in the testing, which is equal to the ratio of the variance calculated among the means to the variance within the samples. If the group means are drawn from populations with the same mean values, the variance between the group means should be lower than the variance of the samples, following the central limit theorem.

A high F value means that we have enough evidence to reject the null hypothesis, ie. the means are equal.

This is the way in which one way ANOVA operates.

Question number 2.

The main difference between one way ANOVA and two way ANOVA is

(1) The number of factors or independent variables in one way ANOVA is one, whereas in the case of two-way ANOVA there are two independent variables., ie.One-way ANOVA compares three or more levels (conditions) of one factor. On the other hand, two-way ANOVA compares the effect of multiple levels of two factors.