Hypothesis Testing

Hypothesis testing is a data-driven study to verify the validity of a claim made about a population based on observed data. This claim, or theory, is called a hypothesis.
Steps involved in doing hypothesis testing:
- Select the appropriate Hypothesis Test based on the data type
- State Null (H0) and Alternate Hypothesis (Ha)
- Calculate Test Statistics/P-Value
- Interpret the results (Fail to reject Null (Accept Null) or Reject Null

Null Hypothesis (H0):
- There is NO significant (statistical) difference between the two or more groups selected for the study.
- Ex: The cycle time for Vendor A is the same as Vendor B while carrying out the same process. It is represented asμCT(A) = μCT(B)
Alternative Hypothesis (Ha):
- There is A significant (statistical) difference between the two or more groups selected for the study.
- Ex: The cycle time for Vendor A is not the same as Vendor B while carrying out the same process. It can be represented as μCT(A) ≠ μCT(B) or μCT(A) > μCT(B) or μCT(A) < μCT(B)

There are situations under which one can choose Hypothesis Testing. The major ones are as below.
- Sometimes we cannot decide if there are any significant differences between groups graphically or by using calculated test statistics. A formal statistical hypothesis test to decide objectively whether there is a difference.
- To improve processes, we need to identify factors that impact the central tendency or spread or proportions. Hypothesis tests provide the answer.
- Once the improvements are made in order to validate the improvements made Hypothesis testing can be used.

Null Hypothesis (Ho ):
- Usually describes a status quo. The one you assume to be true unless otherwise proven. The one you reject or fail to reject based upon evidence
- Signs used in Minitab:=
Alternative Hypothesis (Ha ):
- Usually describes a difference
- Signs used in Minitab: ≠ or < or >
Note that we are not proving the hypothesis to be true or false. We will reject or fail to reject the null hypothesis based on the evidence from our samples. Failing to reject the null hypothesis implies that the data does not provide sufficient evidence to conclude that a difference exists. On the other hand, rejection of the null hypothesis implies that the sample data provide sufficient evidence to say that a difference exists.

Guilty Vs Innocent
- The Indian justice system can be used to illustrate the conceptof hypothesis testing.
- In India, we assume innocence until one is proven guilty. This corresponds to the null hypothesis.
- It requires strong evidence, “beyond a reasonable doubt,” to convict the defendant. This corresponds to rejecting the null hypothesis and accepting the alternative hypothesis. More specifically, we have significant evidence to supportthat a difference exists.
- Ho: Person is not guilty;Ha: Person is guilty