﻿ Two Sample T-Test (Welch's T-test)

# Two Sample T-Test Calculator (Welch's T-test)

## Unknown unequal standard deviation

### Expected difference between two populations' mean

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 Standard deviation of group1 dosn't equal to the standard deviation of group2 Expected difference d between the populations' average is known

## Required Sample Data

 x1, x2 - Sample average of group1 and group2 S1,S2 -Sample standard deviation of group1 and group2 n1,n2 - Sample size of group1 and group2

## Hypotheses

 H0: μ1 ≥ μ2+d H0: μ1 = μ2+d H0: μ1 ≤ μ2+d H1: μ1 < μ2+d H1: μ1 ≠ μ2+d H1: μ1 > μ2+d

## 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

 d: Expected difference between the populations' averages, μ1-μ2 (when μ1 = μ2, fill zero) α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (maximum type1 Error) Outliers: Included Excluded It is not recommended to exclude outliers unless you know the reasons
or or enter summarized data (x, n, σ, 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 2 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:

 x1: Sample average of group1 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

The difference between the expected SD and the sample SD

### Group 2:

 x2: Sample average of group2 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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