Hypothesis Testing

What is Hypothesis testing ?

Hypothesis testing is used in the statistics to make some strong comment about the population using the sample data i.e. the mean height of two population is equal or not, the coin is biased towards heads or not.

Let’s take an example of mean heights of two population of two different cities.It’s an impossible task to ask each and every person of two cities about their heights and calculate their mean.So how we can tell that the mean of both the population is same or not?

What is Resampling and Permutation method?

We use the resampling and permutation method to know about the population.Let’s assume we have sample of two cities C1 & C2 with 50–50 data of heights in each set.Calculate the mean of both C1 & C2 and subtract the mean of C1 & C2. Let’s assume we get the value of difference is 5 cm.

x = |mean(C1)-mean(C2)| = 5 cm

Let’s perform the resampling and permutation.Jumble both the set C1 & C2. We get the new set S = {C1+C2}. We again choose 50–50 data randomly from S in two set S1 & S2. Again calculate the mean of S1 & S2 and subtract them and note down the difference. Perform this method k times so that we get k such mean differences(Choosing the data randomly very important). But before performing the resampling we need to create null hypothesis. But what is null hypothesis? Hypothesis testing has two types: 1- Null hypothesis 2- Alternative hypothesis

Null hypothesis is denoted by h0 and alternative hypothesis is denoted by h1.We need to set our null hypothesis as the hypothesis of no difference because it easy to create simulation.And the opposite of null hypothesis is alternative hypothesis. So here our null hypothesis is that “There is no difference in population mean.” and alternative is that there is difference in population mean.We have one more thing i.e. significance value on which we reject or select our null hypothesis.The less is significane values, more the chance of getting the accuracy increases .Here we assume our significance level as .05 means if our p-value is less than .05 or 5% we will reject the null hypothesis else we accept the null hypothesis.

Let’s arrange the k means difference is increasing order.Then find the place where the x ≥ 5 cm and calculate the probability for it.Let’s assume we get the probability 0.2 or 20%. How can we write in the equation form ? This is as follows -

P(x ≥ 5 |H0 ) = 0.2

Here 0.2 > .05 hence we accept the null hypothesis i.e. the mean of both the population is same.We can read the above equation in English as “the probability of getting x ≥ 5 given that the null hypothesis is true is 0.2”.

Let’s assume another case where we get probability 0.03. As we compare this value with 0.05 , we get that 0.03 is less than 0.05 hence we reject the null hypothesis.In english we can read this as “The probability of getting x ≥ 5cm given that the null hypothesis is true is 0.03 which very low hence we can reject the null hypothesis. Because our observation can’t be false hence it’s possible that we choose the wrong hypothesis so we need to reject them and choose the alternative of it.This is how we can perform hypothesis testing and give our decision over population.

That’s all about hypothesis , resampling and permutation folks.

Thanks for reading.

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