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# WHat is F statistic and how to interpret it?

# WHat is F statistic and how to interpret it?

WHat is F statistic and how to interpret it

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:

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

Hypothesis testing with ANOVA includes the following:

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

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

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

```
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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