Hypothesis Testing — p-value, z-test and t-test

A claim is assumed valid

if its counterclaim is highly implausible

In mathematics there are many techniques for proving your statement to be true. These proofs could actually help in making inferences or taking decisions. Proof by induction, Proof by contradiction or statistical proofs are valued. One such technique of making statistical inferences is Hypothesis testing.

Hypothesis testing is a way for you to test the results of a survey/experiment to see if you have meaningful results. The process of hypothesis testing is to draw inferences or some conclusion about the overall population or data by conducting some statistical tests on a sample. You are basically testing whether the results are valid by figuring out that your results have/not happened by chance.

For drawing some inferences, we have to make some assumptions that lead to two terms that are used in the hypothesis testing:-

• Null Hypothesis(H0): It is a fact that is assumed to be true such that there is no change in assumption or no anomaly pattern is observed.
• Alternate Hypothesis(H1): The opposite of Null Hypothesis is Alternate Hypothesis.

Hypothesis testing is actually answering the question

Can the results from a test or survey be repeated?

p-value(α)

An important term one encounters is p-value also called as significance value(α); It is the probability for the Null Hypothesis H0 to be true.

Intuition behind Hypothesis testing

The only hypothesis that needs to be specified in this test and which embodies the counterclaim is referred to as the null hypothesis; that is, the hypothesis to be nullified. A result is said to be statistically significant if it allows us to reject the null hypothesis. The result, being statistically significant, was highly improbable if the null hypothesis is assumed to be true. A rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis. But no specific alternatives need to have been specified.

Generally we select the p-value to be small someway close to 0.05 and we use t-statistics to compare with p-value for accepting or rejecting H0.