Role of Statistical Decision Making in Process Improvement

I have been associated with teaching and training in process improvement. Statistical tools and techniques play a very important role in the understanding of a process and assessing its performance with respect to the quality characteristic under study. Many of the organizations are looking for individuals trained in six sigma methodology for continuous process improvement. Many individuals not necessarily having statistical background are seeking six sigma training for their career growth.

In my experience, I find the students get confused with the formulation of the null and alternative hypothesis. With all the computing power and software at hand, we can leave all the complex computations to the facilities available to us. However, the formulation of hypothesis and interpretation of the output has to be clear, in order to utilize the computing power for our benefit. In this blog, I am addressing the concept of hypothesis formulation and their interpretation in different situations.

In the following section it is assumed that we are using Excel Add-in for data analysis, SPSS, SAS, R, or any other software for data analysis. One of the common hypotheses that we test is regarding the mean of the population. The testing of the hypothesis regarding mean could be for one population, two populations or more than two populations.

The test statistics used are z, t (for one or two population) and F tests (for more than two populations) which follow standard normal, student t, and F distribution respectively.

Z and t tests are for one or two population whereas we conduct Analysis of Variance (ANOVA) for 3 or more population comparison. The following steps are to be noted in the test of the hypothesis:

1. The equality sign is always with the null hypothesis. The alternative hypothesis is complementary to null hypothesis. The null and alternative hypotheses contain the full parameter space.
2. The level of significance (α) i.e. the probability of type I error, is pre decided. Conventionally 0.05 or 0.01.
3. Based on the sample data we get the value of test statistic and the significance probability (p) for the test statistic based on the distribution of the test statistic.
4. The decision is always with respect to the null hypothesis.
5. Our sample data either supports the null hypothesis or it does not support the null hypothesis. There isn’t any other option as the null and alternative hypotheses contain the full parameter space.
6. The interpretation is based on the significance probability given in the computer output.
7. We compare p with α. The rule is:

• if p < α then reject the null hypothesis.
• Thus in test of hypothesis we either reject null hypothesis or fail to reject null hypothesis.
• Rejection of null hypothesis means that the data is supporting alternative hypothesis. Whereas if we fail to reject null hypothesis, it implies that the data is supporting null hypothesis.
• Having understood the mechanism of test of hypothesis, one can understand the problem situation better and conclude in terms of the language of the problem that he/ she is interested in.

-by Dr. Sadhana Ghosh