# ANOVA - Single Factor (One-Way)

This example shows you how to perform a single factor ANOVA (analysis of variance).
A single factor or one-way ANOVA is used to test the null hypothesis that the means of several populations of data are all equal.

H0: μ_{1} = μ_{2} = μ_{3} = .......

H1: at least one of the means is different.

In this example the fuel consumption of five car makes are examined. Five drivers measured how much the cars with a different type consumed petrol. Input Data:

We would like to know wether all kind of cars use equal average quantity of fuel at 95%-confidence level or not.

To perform a single factor ANOVA, execute the following steps.

1. Select Anova and click OK.

2. In the Type Box select One-way.

3. Click in the Input Range box and select the range B2:F7.

4. Click in the Output Range box and select cell H1.

5. Alpha = 0,05.

6. Select Grouped by Colunms and Labels in first row.

7. Click OK.

### Result:

Conclusion: if F > F crit, we reject the null hypothesis. This is the case, 22,561 > 2,866. Therefore, we reject the null hypothesis. The means of the five populations are not all equal. At least one of the means is different, it means the average fuel consumption of at least a model is different from the others.

However, the ANOVA does not tell you where the difference lies. In order to determine this we need a t-Test to test each pair of means
.