Two Sample T-Test Calculator (Pooled-Variance)

Unknown equal standard deviation

Expected difference between two populations' mean

tails: the default is two tailed test
Pooled variance t test

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

t statistic

T-student distribution

t distribution two tailed t distribution two tailed t 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.

d: Expected difference between the populations' averages, μ12 (when μ1 = μ2, fill zero)
α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (maximum type1 Error)
Outliers: 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
validation message