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Data Science Tutorials

How to compare variances in R?, The F-test is used to see if two populations (A and B) have the same variances.

## When should the F-test be used?

A comparison of two variations is useful in a variety of situations, including:

1. When you wish to examine if the variances of two samples are equal, you can use a two-sample t-test.
2. When comparing the variability of a new measurement method to that of an older one. Is the measure’s variability reduced by the new method?

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Hypotheses are based on statistics and research inquiries

1. whether group A’s variance (σ2A) is the same as group B’s variance (σ2B)?
2. whether group A (group σ2A) has a lower variance than group B (group σ2B)?
3. Does group A (group σ2A) has a higher variance than group B (group σ2B)?

In statistics, the analogous null hypothesis (H0) is defined as follows:

```H0:σ2A=σ2B
H0:σ2A≤σ2B
H0:σ2A≥σ2B```

The following are the relevant alternative hypothesis (Ha):

```Ha:σ2A≠σ2B (different)
Ha:σ2A>σ2B (greater)
Ha:σ2A<σ2B (less)```

Note that:

Two-tailed tests are used to test hypotheses 1.

One-tailed tests are used to test hypotheses 2 and 3.

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The F-test necessitates that the two samples be normally distributed.

## How to compare variances in R

To compare two variances, use the R function var.test() as follows:

### Method 1

```var.test(values ~ groups, data,
alternative = "two.sided")```

### Method 2

`var.test(x, y, alternative = "two.sided")`

x,y: numeric vectors

alternative: a different hypothesis “two.sided” (default), “greater” or “less” are the only values that can be used.

`data <- ToothGrowth`

To get a sense of how the data looks, we use the sample_n() function in the dplyr package to display a random sample of 10 rows.

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```library("dplyr")
sample_n(data, 10)
len supp dose
1  25.5   VC  2.0
2  14.5   VC  1.0
3  14.5   OJ  1.0
4   9.7   OJ  0.5
5  16.5   VC  1.0
6  27.3   OJ  2.0
7   9.4   OJ  0.5
8  22.5   VC  1.0
9  11.2   VC  0.5
10  8.2   OJ  0.5```

In the column “supp,” we want to see if the two groups OJ and VC have the same variances.

F-test assumptions are checked with a preliminary test.

The F-test is extremely sensitive to deviations from the standard assumption. Before applying the F-test, make sure the data is normally distributed.

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To see if the normal assumption holds, apply the Shapiro-Wilk test. The Q-Q plot (quantile-quantile plot) can also be used to visually analyze the normality of a variable.

The correlation between a particular sample and the normal distribution is depicted in a Q-Q plot.

If you’re not sure about the normality of your data, try Levene’s or Fligner-Killeen tests, which are less sensitive to deviations from the norm.

## Compute F-test

```res.ftest <- var.test(len ~ supp, data = data)
res.ftest```

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F test to compare two variances

```data:  len by supp
F = 0.6386, num df = 29, denom df = 29, p-value = 0.2331
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.3039488 1.3416857
sample estimates:
ratio of variances
0.6385951```

The F-test has a p-value of 0.2331, which is higher than the significance level of 0.05. Finally, no significance difference exists between the two variances.

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