﻿ F Test

# F Test for Variances Calculator

## Two population variances comparison

Target: To check if the difference between the average (mean) of two groups (populations) is significant, using sample data

Example1: A man of average hight is expected to be 10cm taller than a woman of average hight (d=10)

Example2: The average weight of an apple grown in field 1 is expected to be equal in weight to the average apple grown in field 2 (d=0)

## Assumptions

 The population's distribution is Normal

## Required Sample Data

 S1,SS2 -Sample standard deviation of the population n1,n2 - Sample size of group1 and group2

Enter input data and then press "Calculate test" button to get the results

## Hypotheses

 H0: σ12 ≥ σ22 H0: σ12 = σ22 H0: σ12 ≤ σ22 H1: σ12 < σ22 H1: σ12 ≠ σ22 H1: σ12 > σ22

## Test calculation

If you enter raw data, the tool will run the Shapiro-Wilk normality test and calculate outliers, as part of the test calculation.

### Statistic Data

 α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error) Outliers: Included Excluded It is not recommended to exclude outliers unless you know the reasons
or or enter summarized data ( n, S) in Group1 and Group2 forms

## Enter sample data

Header: You may change groups' name to the real names.
Data: When entering data, press Enter after each value

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

## Enter sample data

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of 3 consecutive columns includes the header, and paste below.

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

### Group l:

 n1: Sample size of group1 S1: Sample Standard deviation of group1 skewness: Normality pval1: Shapiro Wilk test Outliers count: ,based on the Tukey's fences method, k=1.5

### Group 2:

 n2: Sample size of group2 S2: Sample Standard deviation of group2 skewness: Normality pval2: Shapiro Wilk test Outliers count: ,based on the Tukey's fences method, k=1.5
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