One way ANOVA

• Assumptions

1. Homogeneity of variance
2. Dependent variable is measured on ratio/interval scale of measurement
3. Independent variable is measured on nominal scale of measurement
4. Independent variable has at least 3 categories

• 5 Step Hypothesis
  

• Hypothesis

Ho: there is no significant difference in the means of categories of independent variable. That is μ1=μ2=…=μn

Ha: at least one of the means of categories of independent variable differs significantly. That is μ1≠μ2≠…≠μn

• ANOVA Table

• Critical value

F(1-a/2,n_1-1,n_2-1), F(a/2,n_1-1,n_2-1)  

• P-value

2*(1-P(F≤|f|))  

• Decision rule

Reject Ho if F < F(1-a/2,n_1-1,n_2-1)  or F > F(a/2,n_1-1,n_2-1)

• Post Hoc Analysis
  

To determine which of the means are significantly different from one another Post Hoc Analysis is used. Simultaneous comparisons between all pairs of groups can be done here. Turkey Crammer, Bonferroni procedure, Scheffe’s method, Dunnett’s correction are methods of Post Hoc analysis.

The formula for critical range of Turkey Crammer is given by following formula.

A specific pair is said to be significantly different if the absolute difference is greater than the critical range.