ML 4202 Chapter 16 Mathematical differences If numbers are not exactly the same they are different Statistical significance If a particular difference is larger enough to be unlikely to have occurred because of chance or sampling error then the difference is statistically significant Managerially important differences One can argue that a difference is important from a managerial perspective only if results or numbers are sufficiently different Hypothesis Testing Hypothesis Assumption or theory that a researcher of manager makes about some characteristic of the population under study Steps in hypothesis testing 1 The hypothesis is specified 2 An appropriate statistical technique is selected to test the hypothesis 3 A decision rule is specified as the bases for determining whether to reject or fail to reject FTR the null hypothesis Ho We do NOT say reject Ho or accept Ha 4 The value of the test statistic is calculated and the test is performed 5 The conclusion is stated from the perspective of the original research problem or question Step One Hypotheses are stated using two basic forms the null hypothesis Ho and the alternative hypothesis Ha o Null hypothesis The hypothesis of status quo no difference no effect Sometimes called the hypothesis of the status quo o Alternative hypothesis tested against the Null and is sometimes called the research hypothesis of interest o The null hypothesis and the alternative hypothesis must be stated in such a way that both cannot be true Step Two Choosing the correct test Step Three Developing a Decision Rule o Decision rule Rule or standard used to determine whether to reject or fail to reject the null hypothesis o The level of significance is either 10 05 or 01 o Ex A researcher wants to test a hypothesis at the 05 level of significance This means that she will reject the null hypothesis if the test indicates that the probability of occurrence of the observed result for example the difference between the sample mean and its expected value because the chance or sampling error is less than 5 Step Four Calculating the Value of the Test Statistic Step Five Stating the Conclusion Stating the Conclusion o Type I Error a error Rejection of the null hypothesis when in fact it is true o This may reached because the researcher may have gathered an incorrect conclusion due to sampling error o The probability of committing a type I error is referred to as the alpha o Type II Error b error Failure to reject the null hypothesis when in a level fact it is false o The value 1 B reflects the probability of making a correct decision in rejecting the null hypothesis when in fact it is false o Never done with 100 certainty o A Type I error is not as serious as a Type II error Tests are either one tailed or two tailed Independent samples Samples in which measurement of a variable in one population has no effect on measurement of the variable in the other Related samples Samples in which measurement of a variable in one population may influence measurement of variable in the other Degrees of freedom Number of observations in a statistical problem that are free to vary The number of observations minus the number of assumptions or constraints necessary to calculate a statistic Chi square test Test of the goodness of fit between the observed distribution and the expected distribution of a variable