# Two way ANOVA with replication

Share

- Definition of Two way ANOVA with Replication

A replication study involves repeating a study using the same methods but with different subjects and experimenters. Main focus of two way ANOVA with replication is test for significance of interaction between treatments.

For example I want to test each of three blends of fertilizers on one sample of each of four types of crops. Each combination of blend and crop has a sample of size 5. Here I consider three set of hypothesis statement given below.

Null Hypothesis, Ho1: there is no significant difference between mean of three blends. V/s Alternative Hypothesis, H11: there is significant difference between mean of three blends.

Null Hypothesis, Ho2: there is no significant difference between mean of four types of crops. V/s Alternative Hypothesis, H12: there is significant difference between mean of four types of crops.

Null Hypothesis, Ho3: there is no significant interaction effect between blends and type of crop. V/s Alternative Hypothesis, H13: there is significant interaction effect between blends and type of crop.

- 5 Step Hypothesis

- Hypothesis

Null Hypothesis, Ho1: there is no significant difference between mean of levels of treatment A. v/s Alternative Hypothesis, H11: there is significant difference between mean of levels of treatment A.

Null Hypothesis, Ho2: there is no significant difference between mean of levels of treatment B. v/s Alternative Hypothesis, H12: there is significant difference between mean of levels of treatment B.

Null Hypothesis, Ho3: there is no significant interaction effect between treatment A and B. V/s Alternative Hypothesis, H13: there is significant interaction effect between treatment A and B.

- ANOVA Table

- Critical value

F(1-a/2,n1-1,n2-1), F(a/2,n1-1,n2-1)

- P-value

2*(1-P(F≤|f|))

- Decision rule

Reject Ho if F < F(1-a/2,n1-1,n2-1) or F > F(a/2,n1-1,n2-1)

Developed by Versioning Solutions.