﻿ Two Sample T-Test

# Two Sample T-Test Calculator (Pooled-Variance T-test)

## Unknown equal 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 The standard deviations of the groups is unknown, or the sample size is small (less than 31), or both Standard deviation of group1 equals to the standard deviation of group2 Or group1’s sample size equal to group2’s sample size and bigger than 5 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.

 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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