Four major steps in performing hypothesis test.
Step 1: State the Hypothesis. State the null and alternative hypothesis. Based on the convention, the null hypothesis always contains an equal sign. For example, taking cold medicine and taking a placebo will get you better after catching a cold in the same amount of time. That is the null hypothesis. The alternative hypothesis becomes: Taking medicine will allow you to recover faster.
Step 2: Collect data. For example, we need two groups of people—group 1 will take the medicine and group 2 will take the placebo. Please note: we should sample our patients in similar conditions (such as age group) to avoid bias in the data.
Step 3: Perform Statistical Test. We need to take a sufficient amount of samples so that legitimate test results can be obtained. Given the sample data, we will perform statistical analysis and draw a conclusion on the hypothesis. Step 4: Statistical Importance and Practical Importance. If the effect (such as taking medicine or placebo) is important but the statistical analysis results are not clear, we should take more data to affirm the results. If the effect is not important to the process, we should not waste time on the investigation. We need to focus on more effective parameters for process improvement.
Four major steps
Sample size affects the confidence interval and hypothesis test. In this slide, we use the process average estimate to illustrate the inter-relationships among the confidence level, confidence interval and the sample sizes. The value 1.96 and the confidence interval (𝜀) are obtained from a 95% confidence level. We need the known population standard deviation to compute the minimum number of samples taken for the hypothesis test. Given the same condition but increasing the confidence level to 99%, the number of samples increase to a larger number (more than 31%) given in the formula. We also note that in some applications, the population standard deviation may not be known. In this case, we will use sample to estimate the population standard deviation. We often increase the samples to further verify the population standard deviation estimates.