hypothesis_testing

hypothesis_testing - 1 HYPOTHESIS TESTING Often a set of...

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1 HYPOTHESIS TESTING Often a set of data is collected, or an experiment carried out, not simply with a view to summarising the results and estimating suitable parameters but rather in order to test an idea. This idea or hypothesis may arise by purely theoretical reasoning, or it may be suggested by the results of earlier experiments. brief overview: The way statistics is used to set up our hypothesis to test is a little strange. First we start with what is called the “Null hypothesis.” This is the assumption that there is no effect of e.g. experimental treatment, difference in conditions etc. We test this against an alternative hypothesis: that is the hypothesis we are attempting to support with our data. Generally we hope that our data shows sufficient differences from the expectations of the null hypothesis to reject it and so accept our alternative hypothesis. E.g. from null hypothesis we expect no effect of drug upon heart rate. Our data shows an increase. If that increase is sufficiently large then we may conclude that no, the null hypothesis was wrong, there is an effect of this drug which does cause an increase in heart rate. (Not always the case we hope for a difference, one may hope that there is no difference.—we can show there is no effect. Eg. tobacco company may wish to show that smoking their cigarettes does not cause an in increase of a certain type of cancer. Rather than hope to reject the null hypothesis, we may hope to be able to “fail to reject” the null hypothesis.) We then use a statistical test to calculate the probability of observing a difference as large as that obtained or larger given the null hypothesis is true . If the probability is less than some specified level then we reject the null hypothesis and accept the alternative. Null hypothesis The notation commonly used to represent the null hypothesis is H o , and that of the alternative hypothesis H a (or H1). However, you do not often see these explicitly written in scientific papers. You do sometimes see “the hypothesis we wish to test is…. .” However during your research it is very useful to state the null hypothesis as you would see it in statistical textbooks Start by assuming there is no effect. What then would you expect? Would write something like: H o : µ d - µ p = 0 where “d” and “p” represent drug and placebo [more often written as above rather than H o : µ d = µ p but they are the same] [note we do not use sample parameters but population parameters.] may be something like: H o : ρ = 0 [no correlation] may be something like: H o : µ = 2 vs. H a : µ 2 If the null hypothesis is rejected then we need an alternative hypothesis to fall back on. (Your expectations or hypothesis being tested.) This dichotomy is denoted: H o : µ d - µ p = 0 vs. H a : µ d - µ p 0 or it might be something like: H o : µ d - µ p = 0 vs. H a : µ d < µ p
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2 Differences between these depends upon your expectations. For instance, if you were developing
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This note was uploaded on 12/22/2010 for the course MATH 1131 taught by Professor Wong during the Spring '10 term at York University.

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hypothesis_testing - 1 HYPOTHESIS TESTING Often a set of...

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