## Experimental Design

 Getting Started General Instructions | Introduction to Your Study | Experimental Design | Stating a Hypothesis Descriptive Statistics Histograms | Central Tendency | Standard Deviation | Confidence Intervals Comparing Two Samples Samples and Populations | Choosing a T-Test | Independent T-Test | P-Values and T-Tables Important Concepts The Normal Distribution | Z Scores | Probability Distributions Levels You are currently on Experimental Design at level 1. Level 1 | Level 2 | Level 3 Next Topic Introduction to Your Study | Stating a Hypothesis

### Explanation

Introducing Experimental Design
Many experiments compare two sets of measurements of the same variable. There are many ways of setting up an experiment to produce such data, but when we talk about experimental design, we are referring to a specific aspect of the experiment: whether or not the two sets of measurements can be sensibly paired off with each other.
• If you can pair off each measurement from one sample with a natural partner from the other sample, then you have a paired design. This may be because you are measuring something twice under different conditions (sometimes called a repeated measures design) or because the two things you are measuring are naturally related;
• If there is no sensible way of pairing off the values from the two samples, then you have an independent design.

Examples
Here are two examples to make it clearer.

• Comparing the running speeds of horses and zebra would be an independent design as there is no sensible way to pair off each horse with each zebra;
• Comparing the running speed of horses for a week of eating one type of feed with the same horses for a week on a different type of feed would be a paired design as you can pair off measurements from the same horse.

Which Design Do You Have?
If you have carried out an experiment which has produced two samples of data that you want to compare, you will need to know which type of experimental design you are dealing with so that you can choose the right analysis method. How this choice is made is covered later, but for now we will look at how to identify the experimental design type that you have.

The type of design that you have is often obvious. If you have measured the same students twice, then you can pair the first measurement from each student with the second measurement from that same student. Meaurements may be related in other ways too. Perhaps you are comparing the strength in people's left hand with that in their right. You are not measuring the same hand twice, but it is obvious how the two measurements should be paired off.

On a practical note, when collecting data in a paired design, it makes sense to record the paired measurements in the same row of the table where you are recording your data. Most computer software will expect paired measurements to be on the same row in a table too. If you can't think how to line up the two sets of measurements in this way, you probably have an independent design!

When choosing your design, you should think about the purpose of the experiment and your hypothesis. Think about the hand strength example above. If your null hypothesis is that there is no difference between the strength of a person's left hand and the same person's right hand, then you have a paired design. If your null hypothesis is that the average left hand is no different in strength from the average right hand, then you have an independent design, as you are not pairing off the hands.

### Exploration

Here are a few self test questions you can answer to check you have understood the concept of experimental design:

In which type of experimental design are the same students measured more than once?
Imagine you are comparing the height of boys and girls at age 12. You pick 50 random boys and 50 random girls. What type of experimental design do you have?
Imagine now that you want to see if brothers are taller than their twin sisters. What type of design would you have?

### Application

In your experiment, you have measured dailyreading from students and you are looking to see if there is a difference between the case when smstreatment is sms2 and the case when smstreatment is sms1.