One Sample T-Test Calculator

Unknown standard deviation

tails: the default is two tailed test
video tutorial


Hypotheses

H0: μ ≥ μ0 H0: μ = μ0 H0: μ ≤ μ0
H1: μ < μ0 H1: μ ≠ μ0 H1: μ > μ0

Test statistic

t statistic

T-student distribution

t distribution left tailed t distribution two tailed t distribution right 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

α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correcrt (Type1 Error)
Outliers: It is not recommended to exclude outliers unless you know the reasons
or or enter summarized data (x, n, μ0, S) in Group form

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 column includes the header, and paste below.


It is okay to leave empty cells, empty cells or non numeric cells won't be counted

Group:

x: Sample average
μ0: Assumed population mean
n: Sample size
S: Sample standard deviation
skewness:
Normality pval: Shapiro Wilk test
Outliers count: ,based on the Tukey's fences method, k=1.5
validateion message