# Paired t-Test

## Contents

### Overview

The Paired t-test is a statistical procedure used to determine whether the mean between two paired samples are statistically different.

Any Hypothesis test in statistics requires the definition of a null hypothesis and an alternate hypothesis. The goal of the test is to aid the analyst in deciding which one of the two hypothesis is true. The table below shows a common set of choices for the null and alternate hypothesis for a paired t-test:

Null hypothesis Alternate hypothesis
Mean of the differences equal to zero Mean of the differences not equal to zero
Mean of the differences equal to zero Mean of the differences < 0
Mean of the differences equal to zero Mean of the differences > 0

Before running a statistical test, the analyst must choose a significance level, or the probability of rejecting the null hypothesis given that it were true (i.e. the probability of making a wrong decision). An alpha value of 0.05 (5%) is usually adopted but a different value may be used depending on the field of the study. If the p-value obtained at the end of the test is less than the selected significance level, the Null Hypothesis should be rejected in favour of the Alternate Hypothesis.

More details on the Two-Sample t-Test can be found here:

### Practical Example

Suppose a scientist, working for a pharmaceutical company, wants to prove the efficacy of a new treatment for high blood pressure. He designs a clinical trial with 30 patients who have been administered with the new medication and he measures the blood pressure, for each patient, before and after the treatment.

The scientist performs then a paired t-test and obtains the following results:

 Null hypothesis Mean of the differences equal to zero Mean of the differences not equal to zero 1.933 mmHg 0.002

Being the p-value less than the adopted significance level of 0.01, the scientist should reject the null hypothesis and conclude that there is a statistically significant difference between the blood pressure measured before and after the treatment.

### Within Grapheme

To perform a Paired t-Test in Grapheme, click on Create New Analysis from the toolbar of the Statistical Analysis View. Assign a name to the panel and select “Paired T-Test” from the list. Click on Next.

Select the Source Table from the ones available in the Tables view for the First Observation Series, select the view of the table and the column containing the first sample you want to analyse. Then select the Source Table, the view and the column for the Second Observation Series. Click on Next.

Move to the "Configuration" tab and check the condition (or alternate hypothesis) you want to verify. If you want Grapheme to evaluate the confidence interval range, check the setting Compute Confidence Interval and insert the probability value to be used for its evaluation. Click on Finish.

##### Remarks
• All the data available in the panel are updated on the fly, so that any change in the table values, is immediately reflected by the panel tables and charts. Automatic update can be temporary suspended, by clicking on the lock button in the main panel toolbar.
• All the data contained in each table, can be copied to the clipboard for further reporting by clicking on the button available in the toolbar.
• Each chart can be exported as Image by clicking on the “Save as Image” button available in the toolbar