Difference Between Paired T-Test and Unpaired T-Test

We live in a day and age where information can be mathematically determined with the aid of statistics. However, the study of statistics, as it seems, isn’t simply that of facts and numbers.


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Statistical inference consists of the use of statistics to create decisions concerning the parameters of a population, based on random sampling. The implementation of statistical inference involves hypothesis testing and talks about how this procedure is employed by statisticians to just accept or reject the assumption of a population parameter. U

Key Takeaways

  1. A paired t-test is a statistical method used to compare the means of two related samples, such as measurements taken from the same individuals at different times or under different conditions.
  2. An unpaired t-test, also known as an independent samples t-test, compares the means of two unrelated samples, such as measurements from two groups of individuals.
  3. The choice between a paired and unpaired t-test depends on the nature of the data and the research question, with paired t-tests used for related samples and unpaired t-tests for independent samples.

Paired T-Test vs Unpaired T-Test

The difference between the two statistical terms Paired T-test and Unpaired T-test is that in Paired T-Tests, you compare the differences between the paired measurements that have been deliberately matched whereas, in Unpaired T-Tests, you measure the difference between the means of two samples that do not have a natural pairing.

Paired t test vs Unpaired t test

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Comparison Table

Parameter of comparisonPaired T-TestUnpaired T-Test
MeaningPaired T-Test, also known as repeated samples T-Test, determines the distinction between the two means of the same subject.Unpaired T-Tests, also known as independent T-Tests or student’s T-Test, is determining the two means groups of different/unrelated subjects.
Homogeneity of variancesUnder Paired T-Test the variance of the two mean groups are not equal.Under Unpaired T-Test the variance of the two mean groups are equal.
Effects/impactsPaired T-tests deal with very minor errors since the test is done only between two similar groups.Unpaired T-Tests have slightly more errors in comparison with paired T-Tests since the experimenter would be affected by variations between two different subjects.
OutcomePaired T-Tests need not collect massive amounts of sample data for comparison this successively saves money and time.Since Unpaired T-Tests have to compare the means of two independent subjects this lands up being a slightly more costlier and time-consuming process.


What is Paired T-Test?

A Paired T-Test, additionally referred to as correlated pair t-test/paired sample t-test/dependent t-test, is a statistical procedure that runs a test on dependent variables. A paired test is done on similar subjects before the allocation of data and two tests are done before and after a treatment.


The two hypotheses under paired t-test.

  1. The null hypothesis (H0): no significant difference between specified populations, H0: μ1 = μ2
  2. The alternative hypothesis (H1): there is a statistically significant difference between the two population means caused by rejecting the null hypothesis. H1: μ 1 ≠ μ2


The paired sample t-test makes the subsequent assumptions:

  1. The differences between the similar pairs follow a normal probability distribution.
  2. The observations ought to be sampled independently and identically distributed.
  3.  A Paired t-test is measured on a gradual level with the help of ratios or intervals. Since T-Tests are based on a normal distribution, the data needs to be continuous and not discrete
  4. The independent variables should comprise of two dependent/similar groups.
paired t test

What is Unpaired T-Test?

An unpaired t-test, also known as an independent sample t-test/two-sample t-test, is a statistical method that determines whether or not there is a significant distinction between the means of two unrelated independent groups. For example: when you want to compare the average sleep cycle of individuals grouped by gender: male and female groups.

Hypothesis for the independent t-test:

The null hypothesis for the independent t-test is that the population means from the two different groups are equal:

H0:  μ1=  μ2

Alternative hypothesis is accepted once the null hypothesis is rejected, which means that the population means are not equal

H1:  μ1 ≠  μ2

To reject or accept the null hypothesis, a significance level is critical. This particular value is 0.05.


  1. The first assumption concerns the scale of measurement- the data collected ought to follow a continuous or ordinal scale.
  2. The data should be collected from a randomly selected portion of the total population.
  3. The data should result in a normal, bell-shaped distribution curve. The significance level can be specified when a normal distribution is assumed.
  4. A massive sample size ought to be used.
  5. The variance and standard deviations should be equal for the dependent variables.
unpaired t test

Main Differences Between Paired T-Test and Unpaired T-Test

  1. Paired T-Tests means comparing the difference between the two mean groups of dependent subjects. For example: the IQ of 5 students before and after training.
  2. The variance of Paired T-Tests is said to be equal. Since the variance is equal standard deviation also is equal for the two mean groups.
  3. Paired T-Tests has less random errors since Paired T-Tests mainly deal with finding the variations between two mean groups of similar subjects the experimenter need not focus on the individual differences.
  4. Paired T-Tests saves heaps of time and money for the experimenter as he need not find large amounts of sample data to calculate the two similar mean groups. Unpaired T-Tests are slightly costlier and time-consuming process as the experimenter would have to find a lot of data to analyze the two independent mean groups.

  1. https://libguides.library.kent.edu/SPSS/PairedSamplestTest
  2. https://libguides.library.kent.edu/SPSS/IndependentTTest
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