Intuition behind Null Hypothesis, Alternative Hypothesis & test of significance

Before understanding Types of Hypothesis we must understand the below concepts.

What is Population: In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker).

What is Sample: A sample is a set of individuals or objects collected or selected from a statistical population by a defined procedure. The elements of a sample are known as sample points, sampling units or observations. Typically, the population is very large, making a census or a complete enumeration of all the individuals in the population either impractical or impossible. The sample usually represents a subset of the population.

Test of Significance:

As the name suggests, tests are performed to check the significance of either 2 samples that we have in hand or between one sample & some given standard theoretical value.

A threshold is set & conclusions are drawn based on whether our significance value is found to be below or above the threshold. 

Here we used two terms, threshold and significance value. Threshold is termed as alpha and in most cases is assumed as 5% and in medical trials or in cases more sensitive is set at 1%, but it is not a fixed value. It can assume different values in different experiments too. And the significance value is the difference amount between two samples we are supposed to test. It is termed as p value. If p value is greater than alpha then null hypothesis is rejected as difference is more than 5%.

Also, in order to perform the tests, we need to take some assumptions. Those assumptions are called hypothesis & hypothesis is categorized into two types.

(i)             Null Hypothesis

(ii)            Alternative Hypothesis

Null Hypothesis: Represented as H0. It says that there is ZERO DIFFRENCE between the two samples that are used for test. If the two samples are say, Observed sample & Theoretical sample then Null Hypothesis assumes that there is no difference at all. The two samples are the same.

 

Alternative Hypothesis: Represented as H1 or HA. This is the exact opposite of Null Hypothesis. So this one says, there actually exists difference between the two samples.

Now, in order to understand these two concepts even better, let me introduce one more term called, “level of significance.” Level of Significance basically quantifies the difference between the two samples.

We discussed about the threshold before. If the “level of significance” or the difference between two samples that we get from our test goes beyond a certain threshold then we accept the Null hypothesis else we reject it.

Let’s understand this with an example.

Say a pharmaceutical company is asking you to test whether their newly introduced drug is any better than their existing drug. You conduct a study & take the results from two samples, one group of people are using the new drug & the other using the old one. Now you perform these tests & came up with a level of significance value. If this value is below 1%, i.e. the difference observed between the two samples is below 1% then we say Null hypothesis holds meaning there is no difference between the two samples. This 1% value is a widely used threshold. There is no rule to use 1 % but mostly 1% or 5% threshold values are used in experiments. And if the difference between the two samples is observed to be more than 1% in this case, then we say Null Hypothesis is rejected & Alternative hypothesis holds.