Hypothesis means a supposition or an assumption or a claim. Hypothesis testing forms a critical part while conducting Statistical test and is a part of “DMAIC” methodology in Six Sigma, Analyse phase.
Let us look at simple examples where we make assumptions :
- Increase in price will increase the sales revenue of an organization
- Pizza delivery outlet has sample of delivery times for the last one month and would like to compare with the competitors target time of 30 minutes
In all the above cases we make an assumption and with the help of Statistical tests, we arrive at a conclusion whether the assumption is true or false.
So let us see how we can develop the hypothesis and the different criteria used to arrive at conclusion.
There are 2 types of Hypothesis: Null and alternative.
Null Hypothesis : It means No difference, No effect, Zero impact. Null hypothesis is an assumption that there is no difference in two or more populations with reference to their means or variances. It is denoted by Ho.
Thus in the above examples our Ho is :
- Increase in price does not affect the sales revenue of the organization
- Target delivery time of the outlet # 30 minutes
Alternative hypothesis is exactly the opposite of Null hypothesis. The alternative hypothesis is the hypothesis which the belt is trying to prove. It is denoted by Ha or H1. In the above cases the alternative hypothesis is :
- Increase in price affects the sales revenue of the organization
- Target pizza delivery time = 30 minutes
Now we need to test the supposition or prove whether the Null hypothesis is true or the alternative hypothesis.
Following are the steps which will help us arrive at a decision.
Step I : Set up a hypothesis
Step II : Set up a Suitable Significance level
Step III : Setting a test criterion
Step IV : Doing computations
Step V : Decision making
We have seen how to set up a Null and alternative hypothesis.
Step II: Having set up the hypothesis, next step is to test validity of Null against Alternative Hypothesis i.e. Ho vs H1 at a certain level of significance.
The confidence with which an experimenter rejects or accepts Ho depends upon the significance level.
Here we need to look at Type 1 and Type II errors.
Type I error : Rejecting the Null hypothesis when it is true. is the level of significance and is the probability of rejecting the Null hypothesis when it is true and is usually at 5%. When the hypothesis is accepted at 5% level, we are running the risk in the long run of making a wrong decision 5% of the time.
Type II error : Accepting the null hypothesis when it is false. is the probability of accepting the null hypothesis when it is false.
(Type I and Type II error is an extensive topic which can be considered for a separate session).
Step III : Setting a test criterion
After we have decided the Hypothesis and the significance level, we need to understand which is the statistical test to be conducted. One of the most widely used test is the Student t-test. Other tests are F, Chi square etc.
Each test makes assumption about your data and the sample drawn from the population.
Step IV : Doing computations
Depending upon the selection of the test we go ahead and do the computations. There are very good statistical software available and the most commonly used is “Minitab”. We can also perform these tests with the help of Excel. Excel add-in has good features.
The statistical significance of the test result is given by the p value. If the p value is less than alpha (significance level) we reject the Null hypothesis.
Step V : Decision making
The rejection of Ho means the differences are statistically significant and the acceptance means they are due to chance. Depending upon the outcome we then take decision of our sample and the population.
Many frameworks exist for implementing the Six Sigma methodology. Six Sigma Consultants all over the world have developed proprietary methodologies for implementing Six Sigma quality, based on the similar change management philosophies and applications of tools.
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