# ANOVA (Analysis of Variance)

Share Now ANOVA is a statistical method that stands for analysis of variance and it is used to analyze the differences among group means and between groups.

In “T Hypothesis testing” we can analyze variance between two groups only but with the help of ANOVA we can check null hypothesis between two or more than two groups.

The logic behind this analysis has to do with how much variance there is in the population.

For Example:Suppose Multinational Motor Company wants to examine the safety of midsize cars, SUV’s, and pickup trucks. They collectted the 15 observations of each types. Now they want to test, whether the mean pressure applied to the driver’s head during a crash test is equal for each category of Vehicles.

Use α = 5% (Upto how much percent of error you can tolerate).

Here we will use single factor or one-way ANOVA to test the null hypothesis, it determines whether two or more groups have the same mean.

H0: μ1 = μ2 = μ3

Let’s perform the ANOVA now,

1. Click on the Data tab then click Data Analysis button.
2. Select Anova: Single Factor and click OK.
3. Click in the Input Range box and select the range C10: E25.
4. Select Grouped by Columns Radio button because data is in columns form.
5. Click Check Box Label’s in the first row because we have labels in the data.
6. Click in the Output Range box and select cell G10 then click OK.

Excel will generate a Summary table and ANOVA table. P value in ANOVA table helps us to interpret the null hypothesis.

Let’s check the significance of P Value

1. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. (here alpha = 0.05).

2. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

3. p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions. 