Question

The following data are the results from a between-subjects study. Please use appropriate statistical procedure to examine if factor A is significant. Create ANOVA table, report statistics, and perform post-hoc tests, if necessary.

A1	A2	A3
4	5	11
5	6	6
4	7	9
6	8	9
3	9	10

Answer 1

Using Minitab software, (Stat -> Basic Statistics -> ANOVA -> One way), we got the outputs.

To test whether means due to three levels of factor A are significantly different from each other,

i.e. to test against H₁ : not H₀

The test statistic can be written as

which under H₀ follows a F distribution with df = ( df(Factor A) , df(Error) )

We reject H₀ at 5% level of significance if p-value < 0.05

Here,

The value of the test statistic

and p-value = 0.002

Since p-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there is significant difference in means due to different level of factor A.

Post Hoc Analysis : We have Tukey's test for difference to test which mean is significant from the other.

From Tukey's test output, we can see

p-value for difference of means between (A₂, A₁) and (A₃, A₁​) are less than or equal to 0.05, so we can conclude that mean of A₁ is significantly different from others.