# Two Sample test

The two-sample test is widely utilised to determine while two population means are similar. It is mostly used hypothesis tests in Six Sigma work. The application is used to test whether any of the new processes or treatments is better than a present treatment or process. It cross-checks whether the implementation of a new sales tool increases sales than before. This test is done when the two small samples (n< 30) are taken from two different populations and compared. By the use of the Two-Sample Test to perform if the means of two independent sets differ. This two-sample test calculates values possible to contain the distinction between the population means. The two-sample t-test is useful to calculate the hypothesis and confidence level of the difference among the population means while the standard deviation is unidentified as well as samples sketched free from each other.

## Assumption of Two Sample test includes:-

• A random selection of the sample is done from the two population
• Samples are independent of each other
• The count of sizes must be less than 30
• The samples collected are normally distributed

## Two variables are required to perform the two-sample test:-

• one variable defines the two groups
• and the second variable defines the measurement of interest

### There are two types of Two Sample tests!

1. Two Sample T Hypothesis Test (Equal Variance)
2. The variance of two populations are equal
3. Two Sample T Hypothesis Test (Unequal Variance)
4. The variance of two populations are NOT equal

### Two Sample T Hypothesis Test (Equal Variance) formula

1. Where n1 and n2 are sample sizes
2. x̅1 and x̅2 are means of sample sizes
3. Sp is the pooled standard deviation

### Two Sample T Hypothesis Test (Unequal Variance) formula

1. Where n1 and n2 are sample sizes
2. S12 & S22 are variances of sample 1 and sample 2
3. x̅1 and x̅2 are means of sample sizes

## Two-sample t-tests answer the following questions:-

1. Is process 1 equivalent to process 2?
2. Is the new process better than the current one?
3. There should be some pre-determined threshold amount between the new
4. process and the current process.

## Advantages of the two-sample test

The biggest advantage of this test is that it helps in comparing the averages of two different groups that are not connected in any aspect. It is considered to be very handy if the observation is related to a single group that has no connection to the observation that is of the other group. The other advantage of the test is that it gives the conclusion that there is no significance level difference between the two different groups of the procedure. It is very essential to know the advantages of the test that is being used by you. The degrees of freedom in the test are something that makes it more advantageous.

## Objectives of the two-sample test

It is said that in the space of the test statistic, a two-sample test is a tailed test that is carried on the data of two different samples that are entirely received independently from the different populations. The main objective of the test is to see if the obtained difference between the two populations is significant in the context of the summary statistics. It is a very popular test that is used by researchers to get the closest solutions. It is always suggested to follow the exact procedure of the test to get the accuracy in the result while eliminating the standard error.

## What makes one and two sample tests different?

It is clear that the paired t tests are used in the context of the evaluation of one group that differs from the value that is known, or the two groups that are different from one another, and lastly if there is any significant point that makes them different from each other in the measurements that are paired. There will be a numbers of observations received through the test. Undoubtedly, the test compares several aspects of the samples. There are a lot of cases where the situation arises of reject the null hypothesis in the process.

## What problem makes use of a two-sample test?

It is observed that the following test is used to test the alternative hypothesis that controls the sample and along with that it is also used for the samples that have been recovered from the distribution that is from the similar unknown variance and mean. It is seen that the inference in the circumstance is related to the fact that what if the mean and variance are the same in the distribution? It is a fact that there is going to be a big data set in the process which sometimes gets complex and, in that case, this test is used. Make sure to use the test in the set manner so that it can provide you the most accurate outcomes.

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