# F Test Calculator

The F test calculator compares the equality of two variances..
It also validates the data normality, checks the test power, identify the outliers and generates the R syntax.

Enter summarized data: S₁, n₁, S₂, n₂
Enter raw data directly
Enter raw data from excel

The F test calculator calculates the F test p-value and the effect size. When you enter the raw data, the F test calculator provides also the Shapiro-Wilk normality test result and the outliers.

## F-test

Hypotheses
H0: σ₁² = σ₂²
H1: σ₁² σ₂²
F test formula
${F}_{\mathrm{\left(df₁, df₂\right)}}=\frac{{{S}_{1}}^{2}}{{{S}_{2}}^{2}}$
df₁ = n₁ - 1
df₂ = n₂ - 1
F distribution

The one sample f-test formula is the ratio of the , is similar to the z score formula, but instead of population standard deviation it uses the sample standard deviation (S), and since the statistic is average, it divides S by √n.

### What is a F-test for equality of two variances?

The F-test for equality of two variances, compares the variances of two populations. Under the null hypothesis, it is assumed that the variances are equal.

## How to use the f test calculator?

1. Choose the tails:
The one-tailed test, left or right, is more powerful than the two-tailed test and results in a smaller p-value. You should choose it if only one direction is interesting, but the question of when to use the one-tailed test is controversial.
Two - the alternative hypothesis states that the variance of population-1 either smaller or bigger than the variance of population-2
Left - the alternative hypothesis states that the variance of population-1 smaller than the variance of population-2
Right - the alternative hypothesis states that the variance of population-1 bigger than the variance of population-2
2. Significance level (α): A p-value less than the significance level is statistically significant.
Researchers usually use 0.05, but if the price of a mistake is big, they may use a smaller value like 0.01.
3. Outliers: extreme values. relevant only if you entered raw data.
included - the calculator will calculate the outliers but will include them in the calculation.
Excluded - The calculator will exclude the outliers before calculating the average and the standard deviation.
4. Advanced fields - for sample size
When planning the experiment, you should choose the effect size that the test should identify. You should choose the sample size before conducting the research. We added this field to alert users that didn't calculate the sample size, or did it incorrectly.
If you use the calculator for homework you may ignore these fields.
Effect - If you don't know the required effect size, you may use the 'effect' field. The default is 'Medium', if you change the value, it will change 'effect type' to 'Standardized effect size' and fill the proper value per Cohen's suggestion in the 'effect size' field. (Small:1.02, medium:1.15 , large:1.35 ) The calculator will not use this field when pressing the 'calculate' button.
The ratio of variances represents the effect size, which is the value you aim for the test to identify. To detect a smaller effect size, a larger sample size is required.
5. Rounding - how to round the results?
When a resulting value is larger than one, the tool rounds it, but when a resulting value is less than one the tool displays the significant figures.
6. How to enter data?
Enter summarized data: S₁, n₁, S₂, n₂ - use this option if you already have the sample measures (Usually homework).
a. Enter the names of the groups instead of "Group-1" and "Group-2", this is not mandatory.
c. Enter the sample standard deviations (S₁, S₂).
d. Enter the sample sizes (n₁, n₂).
Enter raw data directly - usually you have the raw data.
a. Enter the names of the groups.
b. Enter the raw data separated by 'comma', 'space', or 'enter'. (*you may copy the data from excel)
Enter raw data from excel - copy the raw data along with the header. This can be done from Excel, Google Sheets, or any tool that separates data with tabs and line feeds. Ensure that you copy the entire block, including the header.
The f-test calculator ignores empty cells and non numeric cells.

## Reference

Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2023) G*Power 3.1 manual. 15 F test: Inequality of two Variances.