WHat is F statistic and how to interpret it?
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# WHat is F statistic and how to interpret it?

WHat is F statistic and how to interpret it

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## Recipe Objective

F-statistic is the ratio of two variances. It is named after Sir R. Fisher. It considers both between group variability as well as within group variability. Large F signifies greater dispersion. ​

F-test is used when you want to get the following insight: ​

1. Whether the two samples coming from populations have equal variances.
2. Wheteher a new process reduces the variance of existing process

Hypothesis testing with ANOVA includes the following: ​

1. Null Hypothesis: There is no difference in the sample variances
2. Alternate Hypothesis: The sample variances are not equal

In this recipe, we learn how to perform F-test in R. ​

## STEP 1: Defining two groups with numeric values

``` group1 = c(33, 18, 22, 35, 46, 55, 20, 27, 34, 15) group2 = c(14, 15, 25, 27, 40, 45, 34, 60, 55, 58) ```

## STEP 2: Carrying out F-test

``` var.test(group1,group2) ```
```F test to compare two variances

data:  group1 and group2
F = 0.55868, num df = 9, denom df = 9, p-value = 0.3988
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.1387681 2.2492399
sample estimates:
ratio of variances
0.5586794
```

Result: After checking the p-value of the F-statistic, we see that it's higher than 0.05. This means that we accept the null hypothesis i.e. There is no difference in the two group variances

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