Two way ANOVA with replication

• 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)