Paired vs Unpaired t-test: comparison chart and examples customer experience

Paired vs Unpaired t-test: comparison chart and examples

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In today’s world, the value is statistics is simply and undeniably unmatched. We have an abundance of data coming from huge populations and you have to draw conclusions based on the parameters by using random sampling. Although, with importance comes difficulties and statistical methods used for such evaluations are not that simple to perform. It includes hypothesis formulation, testing and then based on the statistical process we decide to either accept or reject the hypothesis. 

Two of such statistical hypothesis testing techniques are paired t-test and unpaired t-test. The key difference between both of them is that in paired t-test you compare the paired measures that match deliberately. Whereas in unpaired t-test you compare the means of two samples that have no natural pairing. 

But just this isn’t enough to thoroughly understand both paired t-test and unpaired t-test. Hence, this article will see the difference between paired and unpaired t-test with a comparison chart.

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Difference between paired and unpaired t-tests

Feature 

Paired t-test

Unpaired t-test

Definition 

A statistical test that compares the means and standard deviations of two related samples 

A statistical test that compares the means and standard deviations of two unrelated or independent samples

Also known as

Dependent t-test

Independent t-test

Hypothesis 

  • Null hypothesis H0: no significant difference between the means of two related groups
  • Alternative hypothesis H1: there is a significant difference between the means of two related groups
  • Null hypothesis H0: no significant difference between the means of two unrelated groups
  • Alternative hypothesis H1: there is a significant difference between the means of two unrelated groups

Variance

Does not assume equal variance between groups

Assumes equal variance between groups, in case of unequal variance use Welch’s test

Assumptions 

  • The dependent variable is normally distributed
  • Independently sampled observations
  • Dependent variable measured in ratios or intervals 
  • Independent variables have two related or matched groups
  • The dependent variable is normally distributed
  • Independently sampled observations
  • Dependent variable measured in ratios or intervals 
  • The variance of data is the same between groups
  • The same standard deviation for groups
  • Independent variables have two unrelated or independent groups

When to use

When an item or a group is to be tested twice

When comparing mean between two independent groups with equal variance

Example scenarios

  • Effect of a drug on the same sample of people
  • Different courses for the same subject on a group of students
  • Standard exam results for a group of students before and after prelims
  • Effect of drug on ½ of the patients assigned to a treatment group and other ½ assigned to a control group
  • Measuring the level of glucose for two independent groups like men and women
  • Comparing the time taken by trains following different routes and New York City as a destination

Pros

  • Requires small sample size
  • Two groups have the same sample with the same abilities
  • If an individual drops the study it won’t affect the sample size of the other group
  • As the samples are assigned randomly, the chances of the individual getting the same test are reduced and hence minimizes the effects of the potential of order with the test

Cons 

  • If one individual drops from the study, both the groups lose one sample as the individual share both the groups
  • The order in which the treatment is assigned can affect the performance of the individual. He may get more used to the process and might end up performing better in the second test
  • Requires a larger sample size
  • The sample of two groups may differ in abilities, hence providing biased results

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Working of paired and unpaired t-test with an example

For this comparison, we will take an example: a doctor wants to see how a group of people respond to the same drug. Let’s take a look at the data:

To perform a paired t-test: the doctor will let the group of patients take drug #1 for one month and then measure the recovery. Then have them use drug #2 and then again measure the recovery equally.

Paired vs Unpaired t-test: comparison chart and examples customer experience

Since each patient takes both the drugs, the doctor will take paired t-test and compare the mean of two tables to find out which drug is more effective.

To perform an unpaired t-test: the doctor will take 20 patients and randomly split them into two groups and make them take drug #1 and drug #2 separately. 

Paired vs Unpaired t-test: comparison chart and examples customer experience

Since the patient in the two groups is totally different and independent, the doctor will use an unpaired t-test to see which of the group has the higher mean and determine which drug will be more effective.

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Paired vs Unpaired t-test: comparison chart and examples customer experience

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