﻿ Two Sample Z-Test

# Two Sample Z-Test Calculator

## Known 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

 Normal distribution σ1,σ2 - The standard deviations of both populations are known ( so either σ1=σ2 or ϭ1≠ϭ2 ) Expected difference d between the populations's average is known

## Required Sample Data

 x1, x2 - Sample average 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 (if we expect the two populations' averages to be equal d should be zero) 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 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 identify standardized effect size - the change divided by the standard deviation effect ratio - the effect size is a ratio from the expected mean
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

## 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 σ1: Standard deviation of group1 S1: Sample Standard deviation of group1, S1 is NOT mandatory, but will help to validate σ1 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 σ2: Standard deviation of group2 S2: Sample Standard deviation of group2, S2 is NOT mandatory, but will help to validate σ2 skewness: Normality pval2: Shapiro Wilk test Outliers count: ,based on the Tukey's fences method, k=1.5
validation message