Two Sample test
The twosample 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 crosschecks 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 TwoSample Test to perform if the means of two independent sets differ. This twosample test calculates values possible to contain the distinction between the population means. The twosample ttest 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 twosample test:

one variable defines the two groups

and the second variable defines the measurement of interest
There are two types of Two Sample tests!
 Two Sample T Hypothesis Test (Equal Variance)

The variance of two populations are equal

Two Sample T Hypothesis Test (Unequal Variance)

The variance of two populations are NOT equal
Two Sample T Hypothesis Test (Equal Variance) formula
 Where n1 and n2 are sample sizes

x̅1 and x̅2 are means of sample sizes

Sp is the pooled standard deviation
Two Sample T Hypothesis Test (Unequal Variance) formula

Where n1 and n2 are sample sizes

S12 & S22 are variances of sample 1 and sample 2

x̅1 and x̅2 are means of sample sizes
Twosample ttests answer the following questions:

Is process 1 equivalent to process 2?

Is the new process better than the current one?

There should be some predetermined threshold amount between the new

process and the current process.
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