Deciding Between ANOVA or SEM Essay

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ANOVA Study

It seems that our challenge for finding an applicable question for using ANOVA is at least partly an artifact of not having access to more data, such as other performance measures, with which comparisons can be constructed. It might be interesting to analyze the mean scores of students in the course of interest with their mean scores from the courses they took just before enrolling in the current course. Alternately, the mean scores of final grades from students currently enrolled in the course and students enrolled last term could be analyzed. The second option would likely be easier to implement since the course instructor would have easy access to both sets of data. An additional independent variable to examine would be the number of concurrent courses that students in the select course were taking during the term.

Since the students enrolled this term and last term are two independent groups, this requirement for conducting an analysis of variance is met. The research questions and the hypotheses for this analysis would be as follows:

RQ2: Is there a relationship between the number of courses a student enrolls in during a single term and their final grade in the select course?

H0: the final grade in the select course is not related to the number of courses a student enrolls in during a single term

H1: the grade in the select course is related to the number of courses a student enrolls in during a single term

The final grade in the select course is the dependent variable and the number of concurrent course a student is enrolled in is the independent variable.

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Quantitative interval data is yielded from these measures, which also meets a requirement for ANOVA. ANOVA can exhibit type 1 and type 2 errors, which would be considered as follows:

A type 1 error means that the null hypothesis would be inaccurately rejected, which creates a false positive -- we have essentially rejected what is true. That is to say that we would incorrectly assume that there is a relationship between the number of courses a student is enrolled in and their final grade in the select course -- this would be considered an error of the first kind, which can be addressed by using an alpha of 0.05 or lower. A type 2 error means that the null hypothesis would not be rejected, which creates a false negative. That is to say that the assumption would be made that there is no relationship between the number of course a student concurrently enrolls in and their final grade in the select course. This is an error of the second kind and it can be ameliorated by decreasing alpha to 0.01, but we need to appreciate that as the probably of committing one type of error decreases, the probability of committing the other type of error increases......

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