Hypothesis testing: Basic principles

During the problem-solving process, especially in Six Sigma projects, we are put in a position to statistically prove relationships between various process outputs and parameters that are suspected to influence them. The causal relationship is based in statistics on what is called hypothesis testing.

For example: we want to improve the hardness of a metal part and the potential factor is the cooling rate.

Hypothesis testing is a formal procedure for investigating and proving the causal relationship. We start from potential factors and demonstrate this link using various statistical tests. Hypothesis testing is often used by scientists to test specific predictions, called hypotheses, that arise from various theories.

The steps in testing the hypothesis are:

1. Issuing the null hypothesis (H0) and the alternative (Ha) - The null hypothesis is considered a hypothesis of unchanging, without differences or dependencies. The null hypothesis is always considered true. In our example - H0: Cooling speed does not affect hardness. Ha: Cooling speed influences hardness.

2. Data collection - We collect data with which we can demonstrate or not what we set out to do. In our example about the hardness of the treated parts and about the cooling rates used to treat each part.

3. Performing a statistical test. The statistical test is used depending on the type of data. We can list Test of Equal Variance, ANOVA, Moods Median test, T-Test,, Chi-Square test or Regression. In this case, regression is used to test the hypothesis.

4. The decision whether to reject the null hypothesis or not. In statistical tests the parameter that shows us whether or not to reject the null hypothesis is called P-value. In the chosen example if the P-value is less than 0.05, H0 is rejected and Ha is true: the cooling rate influences the hardness.

5. Presentation of results and conclusions. Based on the results, it is concluded that the cooling rate has a decisive influence on the hardness. The obtained equation can be used to find out what cooling speed to use to obtain the hardness required by the customer.

Testing the hypotheses is like a lawsuit, where the defendant is presumed innocent (Ho) and the prosecution must provide evidence to prove that Ho is not true.

As a Six Sigma practitioner, you are "prosecutors": you must provide evidence "beyond a shadow of a doubt." If you fail to reject the null hypothesis then it turns out that the chosen influencing factor is not true - we started from the potential cause but it did not become the root cause.