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

    Comparison of Sample Means

    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.

    Hypothesis Test Chart



    The null hypothesis will be 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.

    Hypothesis Testing on TI-83 or TI-84 Calculator








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