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Unformatted text preview: Chapter 14 Test of Significance In this chapter we put together the few skills and techniques we have learnt so far into a formal method for testing hypothesis, which is the classical way of doing statistical inference. Assume that as a new employee at the national tax department you propose a new tax code that you claim is revenue-neutral (i.e. tax revenue will remain the same) but if adopted will save on adminstration costs. To show this you collect a sample of 100 forms in the treasury department, and applying your new tax rule, find that the sample average came to- 2190 Baht with a sample standard deviation of 7200 Baht. The question then is whether this drop in tax revenue of- 2190 really represents a drop in overall tax revenue or can be attributed to chance error. We shall break the hypothesis testing process into three essential steps, namely, 1) setting up the hypothesis, 2) calculating the test statistic, and 3) concluding. 14.1 Setting up the hypothesis We set up the null and alternative hypothesis as follows: H : Average = 0 H a : Average > 1 2 CHAPTER 14. TEST OF SIGNIFICANCE The null hypothesis H expresses the idea that an observed difference is merely due to chance. That is, for our example, the actual change in revenue collected is zero - there is no change. Usually the null is something that the researcher intends to disprove. The alternative hypothesis H a then is what the researcher sets out to prove given evidence from his or her sample. So, somewhat counter-intuitively, the null hypothesis is the “alternative” explanation for the findings, in terms of chance error. 14.2 The test statistic A test statistic is used to measure the difference between the data (from the sample) and what is expected as stated in the null hypothesis. TS = observed- expected SE Judging at the numerator, we observe that if the observed value is much different from the expected value, the difference will be large and so will the test statistic. More specifically, the test statistic tells us how many standard errors away an observed value is from its expected value, and a large test statistic therefore means that the sample evidence is much different from what is expected as depicted by the null. This suggests that one should not accept the null hypothesis. The next section formalizes this using the p-value and the “critical value” methods....
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- Spring '10