# What role do t-tests play in Pharmaceutical Processes? When can we apply it?

First of all, I would like to set the concept of hypothesis testing then we will move step by step to the agenda of this post. Hypothesis testing, what is it? It is a method of drawing inference or conclusion about the sample based on a population as a whole. In simpler words, the process of collecting samples from a population and to determine whether the results are statistically significant or not.

You might be wondering “Why we use t-test specifically and why not other tests?” Because in most of the process scenarios, we do not know the population parameters like mean or standard deviation and hence the only option is t-test.

Suppose in a **pharmaceutical company**, they manufacture lakhs of tablets per day – in such case, it is difficult to know the population parameters like mean and standard deviation. So we apply sample t-tests.

### Types of t-test

There are various types of t-test namely one sample t-test, two sample t-test and paired sample t-tests.

We will discuss **“when can we apply one sample t-test, two sample t-test and paired sample t-tests?”**

**One sample t-test**– We use one sample t-test when we have one sample group. By doing so, we would be able to find whether the mean is significantly different or not with regards to our target specification.

For e.g. in a pharmaceutical company, QA officer collects samples of 10 tablets to measure the dissolution rate of a drug. Here, we can find whether the mean of a dissolution rate is significant to our target dissolution rate or not.

Reference

H_{0} = Target mean value, x bar = Sample mean value

From the above diagram, we can conclude that the mean of the dissolution rate is significantly different than the target value.

**Two sample t-test**– We use two sample t-test when we have two independent sample groups. By doing so, we would be able to find whether the means are significantly different or not with regards to our target specification. And we would be able to compare which one is good.

For e.g. in a pharmaceutical company, QA officer collects a two sample groups (A and B) each of 10 tablets to measure the dissolution rate of a drug. We can compare which of these types have a better dissolution rate and hence we able to choose the best one.

Reference

⊕ = Mean value

With the help of the above diagram, we can compare the groups and select the group which has a better mean value.

**Paired sample t-test**– We use paired sample t-test when we have two dependent sample data of the same subject i.e. to measure the effect on a particular group before and after the treatment (say).

For e.g. during a clinical trial, we choose 8 patients and measure their weight before the drug treatment. And again, after the two months, we again measure their weight. By doing so, we can check whether the drug is effective or not. Here we will have two sets of data –

Before treatment

After treatment

It is also called a **dependent sample t-test**, why it is called so? With reference to the above example, let’s make it clear that the data are collected from the same observations (same patients). Here the patient’s weight is dependent on drug treatment.

Reference

As we can see, there are two data groups – Before treatment and After treatment.

We can visualize the differences whether the drug is effective or not based on their weights.