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.
Application of t – test to check the drug dissolution rate
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 12 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 (target = 365 C).
- Reference
Ho=Target mean value, x bar=Sample mean value
Since our p-value is 0.019 which is less than our alpha value of 0.05, 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. 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 12 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
Since our p-value is 0.3 which is greater than our alpha value of 0.05, we can conclude that the mean of the dissolution rate is not significantly different. But there is a difference in the variance part (individual value plot).
- 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 20 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.
Since our p-value is 0.007 which is less than alpha value of 0.05, we can conclude there is a significant difference between the treatments.
We can visualise the differences whether the drug is effective or not based on their weights.
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