Applied Statistics Quiz 2 2023 with complete solution questions and answers

What research decisions influence the magnitude of Type I error? The nominal alpha level sets the limit on the magnitude of risk of Type I error. The risk of committing the error is the alpha level. Example: alpha level = .05, the risk of committing error is 5%. How are risk of Type II error and statistical power related? Risk of Type II error is beta and statistical power is (1-beta). So, as risk of Type II error increases, statistical power decreases. Other factors being equal, which type of significance test requires the value of t that is larger (in absolute value) in order to reject HO: a directional or non-directional test? A non-directional test or two-tailed test requires a value of t that is larger in absolute value to reject HO compared to a directional test. What is a null hypothesis? What is an alternative hypothesis? A null hypothesis states one specific value for the unknown population mean m. An alternative or research hypothesis states a range of outcomes/values for the population mean m. Also, the alternative can be directional or non-directional. What is an alpha level? What determines the value of alpha? Alpha level is a theoretical risk of Type I error that is chose by the researcher prior to looking at the results of a study. Usually it corresponds to conventional standards for level of acceptable risk. What is an "exact" p-value? It is the level of marginal significance within a statistical hypothesis test. It is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. What is statistical power? What information is needed to decide what sample size is required to obtain some desired level of power (such as 80%)? Statistical power is the likelihood that a study will detect an effect when there is an effect to be detected. The information needed to evaluate statistical power is: alpha level and population effect size. Using these values, a statistical power table can be used to find out how sample size corresponds to power and that can be used to decide what minimum N should be necessary for a level of power such as .80. EXTRA CREDIT: When a research reports a "p" value, p stands for "probability" or risk. a. What probability does this p refer to? b. Do we typically want p to be large or small? What is the conventional standard for an "acceptably small" p-value? a. The theoretical risk of committing a Type I error. b. We typically prefer p, the risk of Type I error, to be small (usually smaller than .05) c. The usual conventional standard is p < .05 (or sometimes p < .01 or .001)