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Hello Class, the following are my thoughts on the criteria needed to identify the critical region and how to decide to utilize a one-tailed vs a two-tailed test.
As the textbook states, the purpose behind stage two is to set the criteria for making a decision on the hypothesis, which is done by creating a critical region based on the decided upon alpha level. The alpha level, or level of significance, is a probability point value that helps researchers determine unlikely outcomes while conducting a hypothesis test (Gravetter et al., 2021). For example, if a researcher utilizes an alpha value of .05, they are separating the most unlikely 5% of scores, or sample means, from the most likely values that will be obtained. These .05, or 5%, of scores will be compared against a unit normal table to create the critical region, which will be used to determine if the recorded sample means will be enough to reject the null hypothesis. If scores fall in these critical regions, the null hypothesis will likely be rejected and if they do not, the null hypothesis will likely not be rejected (Gravetter et al., 2021). Additionally, researchers also need to know the population mean, standard deviation and effect size. These will be used to determine the distribution and plot the critical regions which will provide the researcher with a visual representation of where scores need to fall in order to reject the null hypothesis (Gravetter et al., 2021).
The next important decision for the researcher to make is the use of a one-tailed test or two-tailed test. Within most traditional studies, researchers utilize a two-tailed test, meaning that the critical region will be split in half and applied to either side of the distribution of scores. Utilizing the example above, 2.5% would be applied to one side of the distribution and 2.5% to the other. This would create two smaller zones, one positive and one negative, that would signify unlikely values. On the other hand, researchers can utilize a one-tailed test. To utilize a one tailed test, a researcher would need to make a direct statement regarding the directionality of the measured effect. For example, a researcher would need to state that a treatment will either positively impact scores, or negatively impact scores (Gravetter at al., 2021). If, for example, a research decides to state the alpha as a .05, and states that the scores will positively increase scores, the 5% critical zone will be applied to just one side of the distribution, creating a larger single critical region, or tail (Gravetter et al., 2021).
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