# Paired vs Unpaired T-Test: Difference and Comparison

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

A paired t-test is a statistical test used to compare the means of two related samples; in this, samples are paired or matched in some way. The paired t-test is used when there is a natural pairing between two samples. An unpaired t-test is a statistical test used to compare the means of two independent samples. The unpaired t-test is used when there is no natural pairing between the two samples.

## 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.

Hypothesis:

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

Assumptions:

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.

## 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.

Assumptions:

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.

## 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.

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