# Selecting the Correct Hypothesis Test

Hypothesis testing is a very detailed subject. Understanding how to correctly conduct these tests is beyond the scope of this manual or the Six Sigma methodology itself. However, since the Six Sigma project team is expected to be applying these tests to uncover facts and these facts will then be used to base decisions on, a basic understanding is important.

One of the most basic decisions that one has to make while conducting a hypothesis test is what type of hypothesis test should be conducted. This article will explain the decision criteria on which this decision needs to be based.

One Tailed vs Two Tailed: Firstly one must decide whether the test has to be one tailed or two tailed. The statistical definitions of one tailed and two tailed tests are quite difficult. Hence, explanation by an example should serve the purpose.

Let us assume that we are comparing the differences between the Average Handling Times (AHT’s) of two different call centres. A two tailed test will check if there is any significant statistical difference in the samples being measured. This means that if one of the samples is significantly higher or significantly lower than the other, a difference will be shown. Hence in a two tailed test we are concerned about differences arising on both sides.

However, in the case of one tailed test we will first have to decide whether we want to compare for upper tail test or lower tailed test. The upper tailed test will check if one of the samples is significantly higher than the other. If the sample has a lower value, the null hypothesis will be selected and no difference will be shown. The exact opposite of this is the lower tailed test where null hypothesis will be rejected only if one sample is markedly lower than the other.

### Decision Criteria

Apart from this there are three simple decision criteria upon which the selection of the correct hypothesis test is based. They are as follows:

The Number of Groups Being Tested: There are different hypothesis tests available if the statistical difference has to be checked for three samples and that of two samples. Clarifying the number of different samples will be the first step in selecting the correct test.

Whether the Y’s are Discrete or Continuous: There are different hypothesis tests available for discrete and continuous variables.

Population Parameter Being Compared: There are different hypothesis tests available for means, medians, standard deviations and even population parameters. Depending on what is being evaluated for difference, different tests may have to be used.

Listing down the different tests and explaining the difference between them is beyond the scope of this manual.

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