# Paired T-Test Calculator

Dependent T test

## 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.

Enter raw data directly
Enter raw data from excel
Enter summarized data

## 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 ignores 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

### Measurements

count: outliers ,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

## R Code

The following R code should produce the same results:

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.