﻿Two Sample T-Test

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

## 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: IncludedExcluded It is not recommended to exclude outliers unless you know the reasons effect ratio:effect size (unstandardized):standardized effect size: The power is expected to identify the effect. If one exists, H0 will be rejected. effect size - the change the test is expected to identifystandardized effect size - the change divided by the standard deviationeffect ratio - the effect size is a ratio from the average of the averages
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

validation message