# Paired T-Test Calculator

## Test calculation

If you enter raw data, the tool will run the Shapiro-Wilk normality test and calculate outliers, as part of the paired-t test calculation.

The default is two tailed test.
Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error)
It is not recommended to exclude outliers unless you know the reasons
The test is expected to identify this effect. If one exists, H0 will be rejected. standardized effects examples( 0.1 - small effect, 0.3 - medium effect, 0.5 - large effect). more
Expected difference, usually zero
Enter raw data directly
Enter summarized data
Enter raw data from excel

## 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)

 Before After

The tool will not count empty cells or non-numeric cells.

## 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.
Copy the data,

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

### Results

The population's name
Average of differences
Sample size, number of pairs
The standard deviation of the differences
Shapiro Wilk test
count: ,based on the Tukey's fences method, k=1.5
validation message

## Information

Hypotheses
H0: μd = μ0
H1: μd < > μ0
Test statistic
T-student distribution
Target: the test compares the means of the same items in two different conditions or any others connection between the two samples when there is a one to one connection between the samples. The test uses the t distribution. more

Two-tailed test example:
Treatment is given to 50 people to reduce the cholesterol level. The expected reduction is 10mg/dL. The researcher takes two measures for each person before and after the treatment. The average reduction of the cholesterol level is 12mg/dL. (xd= 12mg/dL n=50). The standard deviation of the reduction is 2.2mg/dL. Sd=2.2mg/dL μ0=10mg/dL In this case, the researcher would like to know if μ0 is correct.
Both results are interesting, if the reduction is larger than the expected or if it is lower.

Right-tailed example.
Does the treatment for pattern hair loss effective?
Measurment: hair density, hairs per square cm.
Check the same person before and after 6 months treatment.

H0: the base assumption - identical results before and after the treatment.
H1: the opposite of base assumption - after treatment gets a larger density.