Question

There are many statistical approaches that researchers use to evaluate a hypothesis. One of the most popular ones is the p-value approach. In this approach, the null hypothesis is rejected in favor of the alternative, which is sometimes called the research hypothesis, when the p-value is less than α (which is the significance level -tolerance level if you wish) . The p-value is the the probability of observing a sample as extreme (or even more extreme) as the one found by the researcher under the null (i.e. assuming that the null is true). Once the sample is collected and the test statistic is found, the p-value is found from the table or software. That is the null is rejected if the p-values <α  . The alpha value again is a tolerance level, which is set in advance. In other words, it is the probability of type one error ...i.e how much tolerance the researcher is welling to take (in saying that the alternative is true when in fact the null is true hypothesis- i.e. rejecting a true null hypothesis) and this is set before collecting the data. The most common α is 0.05. Recently (in fact it is March, 2016)  the ASA, American Statistical Association, passed a new guidelines for the use of the p-value  and encouraged using other approaches. The critical value approach, the boundaries of the rejection region are found based on the alpha and the distribution before even collection the data .....Once the data is (should say are) collected and analyzed the test statistic is computed (it is either a z-statistic, t- statistics, chi-square, etc). The the decision rule is to reject the null hypothesis in favor of the alternative if the computed test statistic is located in the rejection region (that is found earlier based on alpha), otherwise we accepted the null (well we don't say accept the null, instead we say fail to reject...because we can never say the defendant is innocent but we say not guilty).

Discuss the advantages and disadvantageous of the p-value approach compared to the critical-value approach.

Answer 1