Hypothesis testing and p values

About the author

Aparna Mishra

Linkedin: https://www.linkedin.com/in/aparna-mishra-a934b6212

Hypothesis testing ,p-values and the statistics involved is one of the most commonly asked topics in interviews , hence its always better to be prepared with the minute mathematical details as well as real life examples/ business scenarios to be used as examples to express your point better . This post aims to help you do the same .Lets begin!

What is a Hypothesis?

A Hypothesis is a statement that can be tested either by experiment or observation, provided we have past data. For eg – We can make a statement like “ Cristiano Ronaldo is the best footballer “ , and we can test the statement based on all the data of the past football matches.

Steps involved in Hypothesis testing :

• Formulating a Hypothesis.
• Finding the right test for Hypothesis.( Outcomes of tests refer to the population parameter rather than sample statistics ).
• Executing the test.
• Making a decision on the basis of the test.

What cannot be a Hypothesis?

Not a Hypothesis if the statement cannot be tested and we have no data regarding it.

There are two Hypothesis:

• Null Hypothesis – denoted by- H₀
• Alternate Hypothesis – denoted by- H₁

The Null Hypothesis is the statement we are trying to reject. Therefore, the Null Hypothesis is the present state of affairs while the Alternate Hypothesis is our personal opinion.

Null Hypothesis

A Null Hypothesis is the hypothesis that is to be tested for rejection after assuming it to be true. The concept of Null Hypothesis is similar to “Innocent until proven guilty”. So, is considered True until it is rejected.

Alternate Hypothesis :

Alternate Hypothesis is the opposite of Null Hypothesis. Whatever we assume our Null Hypothesis to be , the Alternate Hypothesis is the complement of that assumption.

Simple and Composite Hypothesis :

Simple Hypothesis is when the Hypothesis statement has an exact value of the parameter.

Example – A textile company claiming that it exports its products and makes $ 10,000 per month.

Composite Hypothesis is when we have a range of values in the Hypothesis statement.

For example – the average height of girls in the class is greater than 5 feet.

Two Tailed Test :

One Tailed Test :

If the Alternate Hypothesis gives the alternate in only one direction for the parameter specified in the Null Hypothesis, it is called a One-tailed test.

Critical region :

Also called the Rejection Region. It is the set of values for the test statistic for which the Null Hypothesis is rejected which means if the observed test statistic is in the critical region then we reject the Null Hypothesis and accept the Alternative Hypothesis.

Confidence Interval :

Type I and Type II error :

Type I error :

Type II error :

P- value :

The p-value is the smallest level of significance at which a null hypothesis can be rejected and this is the reason why many tests give p-value and is more preferred since it gives us more information than the critical value.

The smaller the p-value, the stronger the evidence that we should reject the null hypothesis.

• If p > .10 → “not significant”
• If p ≤ .10 → “marginally significant”
• If p ≤ .05 → “significant”
• If p ≤ .01 → “highly significant.”