### Assumptions

• The dependent variable should be interval or ratio.

• The population in which samples are drawn should be normally distributed.

• Sample cases should be independent of each other.

• Variance between the groups should be approximately equal.

### One-Way ANOVA (It uses F-Statistic)

One way ANOVA is a statistical technique that is used to compare the means of more than two groups based on a single treatment factor. OR we can say that it assess the effects of one independent variable on a single dependent variable.

**Examples:**

The owner is interested to know the average daily sale of new brand at three metro cities.

The vice chancellor is interested to know the average CGPA of three institutes.

Ho: The average sale of the new brand of gasoline is same in all three metro cities.

**Note:** Reject the null hypothesis if the sig value corresponding to F-statistic is less than 0.05.

Rejection of the null hypothesis in ANOVA only tells us that all population means are not equal. But if we are interested to know the difference between (group1 and group2) or (group 2 and group 3) then we will also apply Post-Hoc multiple comparison.

**Procedure:** One-Way ANOVA can be applied by using Univariate GLM which is used to assess the effects of several independent variables on a single dependent variable.

### Two-Way ANOVA

This is used to know the effects of two independent variables on the same dependent variable. For example Educational background (factor A having two categories Arts and Science) and experience (Factor B having two categories of low and high) affect the salary level.

Hypothesis

1. There is no difference in the means of factor A

2. There is no difference in means of factor B

3. There is no interaction between factors A and B

**Note:** Reject the null hypothesis if P value corresponding to F statistic is less than 0.05 at 5% confidence interval.

### Difference between One-Way and Two-Way ANNOVA

The difference is that where one-way ANOVA only generates one F-value, two-way ANOVA generates three F-values: one to test the main effects of each factor, and a third to test the interaction effect (i.e., the combined effect of the two factors). Factorial ANOVA yields the same information that two one-way ANOVA’s would, but it does so in one analysis

**Written By**

**Syed Asif Shah**