# Introduction

This article will demonstrate how QLazDOE software can manage simple comparative studies with matched pairs of experimental material, which is called **paired t-test (one-sample t-test)**.

Example used for this demonstration is from the book "Design and Analysis of Experiments" by Douglas C. Montgomery, which you can purchase from: https://www.wiley.com/en-hr/Design+and+Analysis+of+Experiments,+10th+Edition-p-9781119492443

# Problem Statement

There is a hardness testing machine that presses a rod with a pointed tip into a metal specimen with a known force. By measuring the depth of the depression caused by the tip, the hardness of the specimen is determined. It is suspected that one tip produces different mean hardness readings than the other. Our task is to determine whether two tips produce same results or not.

We will use 10 material specimens, dividing each specimen into two parts, then randomly assigning one tip to one-half of each specimen and the other tip to the remaining half. The order in which the tips are tested for a particular specimen would be randomly selected.

Strictly speaking, we should consider 10 material specimens as 10 treatments, but for the sake of easier definition of the problem in QLazDOE software, we will consider 10 material specimens as 10 replicates and will imagine that there is only one level for each tip. Although scientifically not correct, this will be a useful trick for easier design of experiment.

Therefore, for the purpose of designing experiment, we will refer to the two tips as **two factors, **each having only** 1 level**. Since there are 10 measurements for each tip/specimen combination, we will consider this experiment to be **replicated**, with **10 replicates**.

Finally, we will compare the means using** one-sided, paired t-test (a single-sample t-test)**, in order to examine whether two tips can be considered equal or different in respect to producing results for material hardness.

# Definition of Factors and Levels

First we need to insert and define new DOE project, entering project name, description and problem statement.

Now we need to provide definition of factors and levels for this project. We will treat this problem as **full-factorial** experiment with two** factors** (two tips) having **1 level.**

Click on the button or corresponding menu item "Create new Factors and Levels Definition File", for creating and opening new factors & levels definition file.

This action will create and open file for definition of factors and their levels, where we can enter and save our definition of two factors with one level. We can enter any value for level value, let's enter zero (0).

We can also click button or corresponding menu item "Determine Number of Factors and Levels", in order to get information about number of factors and levels into the project record.