Two Sample Z-Test Calculator

Known standard deviation

Expected difference between two populations' mean

tails: the default is two tailed test
Two sample z-test

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 Normal distribution
standard deviation σ12 - The standard deviations of both populations are known ( so either σ12 or ϭ1≠ϭ2 )
difference d Expected difference d between the populations's average is known

Required Sample Data

average x1, x2 - Sample average of group1 and group2
sample size 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 statistic

Z statistic

Normal Distribution

Normal distribution two tailed Normal distribution two tailed Normal distribution two tailed

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, μ12 (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: It is not recommended to exclude outliers unless you know the reasons
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