Reply WK 4 DQ 2 VT
Topic 4 DQ 2
To Set the Criteria for the Decision (step 2 in hypothesis testing) we must identify the critical value and the rejection region. What information do you need to set the criteria?
Determining the critical region which will yield results sufficient to reject the null hypothesis and avoid a Type II error is an important part of the hypothesis test (Gravetter et al., 2021). In order to determine this region, it is important to know the initial population mean and standard variation, as well as the expected sample number and the expected effect size (Gravetter et al., 2021). By using the expected effect size, one can simulate the alternative hypothesis distribution (what it would look like if the effect were real) and see where it falls in relation to the original distribution (which would stay the same if the null hypothesis were true). Whatever portion of the alternative distribution falls past the z-score of +- 1.96 would represent the proportion of samples that would be sufficient evidence of a treatment effect (Gravetter et al., 2021).
With the information referenced above, one could find the exact point on the distribution that would mark the critical point of when sample values would cross the alpha level threshold. This value is called M critical and is calculated using the null hypothesis mean, the z score of the alpha level and the standard deviation for the sample distribution (standard error value) (Gravetter et al., 2021). Once the critical point is determined, the z-score for THAT point is computed, and the corresponding proportion on the unit normal table represents the probability or power of the test.
How do you determine when to use a one-tailed test? When do you use a two-tailed test?
A one tailed test is only used when there is evidence supporting a directional prediction, such as prior research (Gravetter et al., 2021). If the researchers are confident that the effect can only increase or only decrease the mean, they may use a one tailed test. The one tailed test uses the same alpha level, but as the proportion of the distribution is not split between the two sides, the z-value associated with the critical region is 1.65 and will only occur on one side of the distribution (Gravetter et al., 2021). This can potentially increase the power of the hypothesis test because there is a larger critical region, but it also makes it more likely that a Type I error will occur, where a treatment effect is detected when there is none (Gravetter et al., 2021). In other words, the evidence could be misleading.
A two tailed test is considered more rigorous, as the alpha level split between two tails makes the z-score boundary for the critical regions + or – 1.96 z (Gravetter et al., 2021). In situations where the treatment effect is unknown, or there is a possibility that it may either increase or decrease the mean, it is important to use a two tailed test in order to detect all effects. Additionally, when a researchers wants to decrease their likelihood of getting a Type I error, they may use a two tailed test to make the critical region smaller (Gravetter et al., 2021). Ironically, this may potentially increase Type II error, because there is a possibility that a treatment effect may be missed because it is too small to be detected. In this scenario, it would be important that the researcher increase the power of their hypothesis in other ways, such as increasing the sample size.