Basic Definitions of Hypothesis Testing

Null and Alternative Hypothesis

In hypothesis testing, the null hypothesis (denoted by Ho) is a neutral statement, is tested against an Alternative hypothesis (denoted by H1). The conclusion of a hypothesis testing is that I either reject the Null Hypothesis or fail to reject the null hypothesis. If the direction of claim is mentioned it is one tailed hypothesis or directional hypothesis. If the direction of claim is not mentioned it is a two-tailed hypothesis or non-directional hypothesis.

Alpha

Alpha is the Probability of Type I which is also known as level of significance. It’s generally taken as 1%, 5% or 10%. With alpha equal to 5% I am 95% confident about my results. 

Type I and Type II error

In hypothesis testing, there can be 2 types of errors, type I and type II. Type I error is the rejection of null hypothesis when it is actually true. While Type II error is not rejecting the null hypothesis when it is actually false. The probability of Type I error is alpha, while the probability of Type II error is known as beta. Wrongly rejecting a null hypothesis is considered more serious as compared to wrongly accepting it.

Critical Region

The critical region is defined as a region of outcome set where the null hypothesis is rejected. Alpha, the probability of type I error is also known as the size of the critical region. The decision rule is based on p-value approach or critical value approach. The critical value approach is based on the concept that if the value of test statistic lies in between the critical region (W) then I reject the null. Otherwise, if the value of test statistic falls in the complement of the critical region I fail to reject the null. 

P-value

P-value is the probability that null hypothesis is true. The decision rule is based on p-value approach or critical value approach. If the p-value is less than alpha, I reject the null hypothesis at alpha% level of significance. Else if the p-value is greater than alpha, I fail to reject the null hypothesis at alpha% level of significance. With p-value being 0.06, I can say that there is 6% chance that null hypothesis is true. 

Can you prove of disapprove a Null hypothesis?

In hypothesis testing, the null hypothesis is never proved or established, but is possibly disproved. Testing of hypothesis begins with assuming that null hypothesis is true, but it is up to the experimenter to prove it false. If the researcher proves it to be false, then the null hypothesis is rejected. But if the researcher cannot prove that the null hypothesis is false, it does not mean the null will be accepted as true because we had initially set out with the assumption that the null is true. This is why we either reject the null hypothesis or fail to reject the null hypothesis, but never accept it.

Consider the example, null hypothesis Ho: The person is innocent vs. alternative hypothesis Ha: The person is not innocent (is guilty) Now, it is up to the prosecution to build a case to prove guilt beyond a reasonable doubt. It should be noted here that a jury can never prove a person to be innocent. The defendant can only be declared not guilty. i.e., the jury has failed to reject the null hypothesis, but it has not accepted it.