    Chapter 5: Analysing the Data Part II : Inferential Statistics # Step 1: Stating the statistical hypotheses

The first step in the process is to set up the decision making process. This involves identifying the null and alternative hypotheses and deciding on an appropriate significance level. Associated with these decisions are issues to do with Type I and Type II errors, one or two-tailed tests, and power. A very important issue to be aware of here is the problem of multiple tests of significance.

There are generally two forms of a statistical hypothesis: null (typically represented as H0) and an alternative (typically symbolised as H1 - this is the research hypothesis - the one we are really interested in showing support for!). Since our interest is in making an inference from sample information to population parameter(s), hypotheses are usually formally stated in terms of the population parameters about which the inference is to be made. We use two forms of hypotheses to set the stage for a logical decision. If we amass enough evidence to reject one hypothesis, the only other state of affairs which can exist is covered by the remaining hypothesis. Thus, the two hypotheses (null and alternative) are set up to be mutually exclusive and exhaustive of the possibilities.

Some example of statistical hypotheses encountered in inferential statistics:

 Statistic used for Estimation Null Form (Ho) Alternate Form (H1) 1. Mean ( ) Ho: µ = 100 H1: µ 100 2. Correlation (r) Ho: = 0 H1: > 100 3. Two Means ( 1, 2) Ho: µ1 = µ2 H1: µ1 µ2 4. Variance (s2) Ho: 2 = 10 H1: 2 < 10

The importance of this step in the hypothesis testing procedure is that the mathematics behind any statistical test you are likely to come across has as its basis the testing of a specific hypothesis. You should always check that what your test is designed to test is suitable for what you want it for. The actual reporting of statistical analysis does not require that the statistical hypotheses for a particular test be reported, they are for your own clarity and understanding of what the test actually tests. Note the difference between statistical hypotheses and research hypotheses.

To summarise, we set up statistical hypotheses in two forms Ð null and alternative Ð such that, if we have sufficient sample evidence, we can reject the null hypothesis in favour of the alternative. If we donÕt obtain sufficient evidence we must fail to reject the null hypothesis. Note, I said, "fail to reject" rather than "accept" the null hypothesis Ð this was deliberate. You still may not believe or accept that the null hypothesis is true. It may be that you just haven't found sufficient evidence against it. Either way our "proof" is only indirect and never absolutely certain. Since we never have absolute proof that one hypothesis is more viable than the other, we must consider the types of errors we could potentially make in deciding (i.e., concluding) which hypothesis the evidence supports. In the end, the researcher has the final say in concluding which hypothesis has sufficient support. Such a decision can be incorrect in two possible ways relative to the real state of affairs in the world.

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