in other wordsthe -value of the test is the smallest level of significance that would lead to the rejection of in generala statistical test involves the following steps formulate an appropriate statistical model for the data give the null ( and alternative ( hypotheses in terms of the parameters of the model determine the test statistic ( function of the data only determine the (approximatedistribution of the test statistic under calculate the outcome of the test statistic calculate the -value or the critical regiongiven preselected significance level accept or reject the actual choice of an appropriate test statistic is akin to selecting good estimator for the unknown parameter th the test statistic should summarize the information about th and make it possible to distinguish between the alternative hypotheses example (hypothesis testingwe are given outcomes xm and yn of two simulation studies obtained via independent runswith and the sample means and standard deviations are sx and sy thusthe {xi are outcomes of iid random variables {xi }the {yi are outcomes of iid random variables {yi }and the {xi and {yi are independent we wish to assess whether the expectations ux exi and uy eyi are the same or not going through the steps abovewe have the model is already specified above ux uy versus ux uy for similar reasons as in example take - tq / / by the central limit theoremthe statistic hasunder approximately standard normal distribution (assuming the variances are finiteq the outcome of is ( ) / / - as this is two-sided testthe -value is ph [ - - because the -value is extremely smallthere is overwhelming evidence that the two expectations are not the same