Hypothesis Test

Hypothesis Testing Selecting the appropriate comparison test for a project can be challenging for GB/BB's, especially in the learning stages. It is always best to confirm this with a BB/MBB. There are many more than listed here and a Black Belt should advance their study in these tests and non-parametric tests. One popular source is Juran's Quality Handbook (1999). It is also important to understand the manual computation of these as many of these tests (some can be very mathematically challenging). Many statistical software programs have simplified the work to the point where comprehension and fluency in these tests is convenient to overlook. Parametric Tests are used when: Normally distributed data Non-normal distribution but transformable Sample size is large enough to satisfy the Central Limit Theorem Require that the data be interval or ratio data. Nonparametric Tests are used when: The above critiria are not met or if the distribution is unknown: These test are used when analyzing nominal or ordinal data. Nonparametric test can also analyze interval or ratio data. Table of Comparison of Means using parametric tests Hypothesis Testing Steps 1) Define the Problem 2) State the Objectives 3) Establish the Hypothesis 4) State the Null Hypothesis (Ho) 5) State the Alternative Hypothesis (Ha) 6) Select the appropriate statistical test 7) State the Alpha Risk level 8) State the Beta Risk level 9) Establish the Effect Size 10) Create Sampling Plan, determine sample size Now, the physical part of the test: 11) Gather samples 12) Collect and record data 13) Calculate the test statistic 14) Determine the p-value If p-Value is < than alpha-risk, reject Ho and accept Ha If p-Value is > than alpha-risk, fail to reject the Null, Ho Try to re-run the test (if practical) to further confirm results. The next step is to take the statistical results and translate it to a practical solution. It is also possible to determine the critical value of the test and use to calculated test statistic to determine the results. Either way, using the p-value approach or critical value should provide the same result. Create a Visual Aid of the Test To make the learning process easier, it is recommended that the problem be broken into four smaller steps. Create a table similar to the one below and begin by completing the top two boxes. The bottom-left is the results from the test and then then coverting those numbers into meaning is the practical result that belongs in the bottom-right box. The null hypothesis is refered to as "Ho". The alternate hypothesis is referred to as "Ha". This is the hypothesis being tested or the claim being tested. The null hypothesis is either "rejected" or "failed to reject". Rejecting the null hypothesis means accepting the alternative hypothesis. The null hypothesis is valid until it is proven wrong. This is done by collecting data and using statistics with a specified amount of certainty. The more samples of data usually equates as more evidence and reduces the risk of an improper decision. The null hypothesis is never accepted, it can be "failed to reject" due to lack of evidence, just as a defendant is not proven guilty due to lack of evidence. The defendant is not necessarily innocent but is determined "not guilty". There is simply not enough evidence and the decision is made that no change exists so the defendant started the trial as not guilty and leaves the trial not guilty. Selecting the Hypothesis Test If you have One X and One Y variable and...... If you have >1 X and One Y variable and......