Paired T-Test Calculator

Paired sample T test

tails: the default is two tailed test
video tutorial

Target: To check if the assumed μ0 is statistically correct, based on a sample average and sample standard deviation

Example1: A farmer calculated last year the average of the apples' weight in his apple orchard μ0 equals 17 kg, based on big sample
Current year he checked a small sample of apples and the sample average x equals 18 kg
Was the average of the apple's weight changed this year?

Assumptions

Normal Distribution The population's distribution is Normal
standard deviation The standard deviations of the population is unknown
mean Population expected mean is known

Required Sample Data

average Sample average of the population
variance Sample standard deviation of the population
sample size Sample size of the population

Hypotheses

H0: μd ≥ μ0 H0: μd = μ0 H0: μd ≤ μ0
H1: μd < μ0 H1: μd ≠ μ0 H1: μd > 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 correct (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.
The number of observations must be identical in both groups. (difference = right - left)

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 3 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:

xd: Average of differences
μ0: Expected difference, usually zero
n: Sample size, number of pairs
Sd: The standard deviation of the differences
validation message

Results

skewness:
Normality pval: Shapiro Wilk test
Outliersd count: ,based on the Tukey's fences method, k=1.5