Question

Problem 3: A researcher has compiled data on a balanced Two-Way ANOVA design, but on her way to making her presentation, her data was ripped to shreds by an enormous rabid dog (fortunately she was otherwise unharmed). Help her give her presentation!

Use what you know about ANOVA to complete the table and fill in the missing information that the dog tore up.

Source	SS	df	MS	F
A	228	2		3
B	936		312
AxB			71
Err
Tot	2046	23

How many levels of treatment A are there? How many levels of treatment B? How many replicates are there?

Write the p-value or critical value next to each of the F-statistics and indicate the ones that are significant at the .05 level.

Interpret the results of the ANOVA (in a brief paragraph).

Answer 1

A researcher has compiled data on a balanced Two-Way ANOVA design, but on her way to making her presentation, her data was ripped to shreds by an enormous rabid dog (fortunately she was otherwise unharmed)

The Balanced Two-Way ANOVA

Source of variation	SS	df	MSE	F	P -value
A	228	2	114	3	0.0878
B	936	3	312	8.21	0.0031
AxB	426	6	71	1.87	0.1677
Error	456	12	38	---	----
Total	2046	23	---	---	---

Levels of treatment A are 3

Levels of treatment B are 4

replicates are 2

Interpritation

This is an analysis of variance table. Each term in the model, plus the model as a whole, is tested for its ability to account for variation in the dependent variable. Note that variable labels are not displayed in this table. The P value A is grater than 0.05.Therefore factor  A is statistically insignificant.

This is an analysis of variance table. Each term in the model, plus the model as a whole, is tested for its ability to account for variation in the dependent variable. The P value for B is less than 0.05. Therefor factor B is statistically significant

This is an analysis of variance table interaction between the two factors, A and B The P value for interaction between the two factors  A and B is grater than 0.05. Therefore the interaction between the two factors A and B is statistically insignificant means they are not affeected on the model.