Statistics Tutorial

Paired t-test

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Getting StartedGeneral Instructions | Introduction to Your Study | Experimental Design | Stating a Hypothesis
Descriptive StatisticsHistograms | Central Tendency | Standard Deviation | Confidence Intervals
Comparing Two SamplesSamples and Populations | Choosing a T-Test | Paired T-Test | P-Values and T-Tables
Important ConceptsThe Normal Distribution | Z Scores | Probability Distributions
LevelsYou are currently on Paired T-Test at level 1. Level 1 | Level 2 | Level 3
Next Topic Choosing a T-Test | P-Values and T-Tables

Explanation

What a Paired T-Test Does
A paired t-test compares two samples in cases where each value in one sample has a natural partner in the other. The concept of paired samples is covered in more detail in the pages on choosing a t-test.

What a Paired T-Test Measures
A paired t-test looks at the difference between paired values in two samples, takes into account the variation of values within each sample, and produces a single number known as a t-value.

You can find out how likely it is that two samples from the same population (i.e where there should be no difference) would produce a t-value as big, or bigger, than yours. This value is called a p-value. So, a t-test measures how different two samples are (the t-value) and tells you how likely it is that such a difference would appear in two samples from the same population (the p-value). P-values and t-values are covered in more detail in the next topic.

How to use a Paired T-Test
This level assumes that you will use a software package to perform a t-test. If you want to know how to do it by hand, read level two.

Software can perform the calculations to produce t-values and p-values, but it is your responsibility to do the following:

  • Pick the right kind of t-test, in this case, a paired t-test and the right direction of test (one or two tailed). See the pages on choosing a t-test for more on this;
  • Ensure the distribution of your data is suitable for a t-test. See the pages on the normal distribution for more on this;
  • Know how to interpret the results of doing a t-test. See the pages on t-values and p-values for more on this.

One final practical point: each value in one sample is paired with a single value in the other. When you enter your data into a computer for analysis by a software package, make sure the paired values are lined up. This usually means having data in two columns where each row represents a single pair. The fact that values are paired is very important.

Exploration

For each of the following examples, answer Yes or No to say whether or not you would use a paired t-test.

Example ScenarioUse a Paired T-Test?
Comparing the average height of men and women   Help
Comparing the weight of slimmers before and after a diet   Help
Testing whether height and weight are related   Help
Testing patients given a drug with those given a placebo   Help

Application

Your data contains samples under two conditions:
  • When is pre-test, the mean of is 13.766666666667
  • When is post-test, the mean of is 17.233333333333

The mean difference between in each of the two samples is -3.47.
Which of these averages is most useful for comparing pairs of values?   Help
There is a difference between the values in the two samples. What can you conclude from this fact?   Help

How can we tell whether the difference is due to sampling error or a true effect?
  Help
Performing a t-test on your data produces a p-value of p<0.021 and a t-value of -2.13.
Which of these values tells you the probability of the difference between your samples being due to sampling error?   Help

Choosing a T-Test | P-Values and T-Tables