The lecture material focuses on the explanation of how to perform the ANOVA and chi-square tests. Concerning the ANOVA difference of mean test, it emphasizes setting up a data table for the ANOVA single factor difference of means test. It, however, gives an overview of setting up the data table for performing the two types of ANOVA two-factor tests. As such, it provides one with adequate information that was not handled in the previous lecture on the setup of the data table, analyses, and interpretation of results. The lecture is also keen to introduce the two types of chi-square test that were earlier not mention. That is the chi-square goodness of fit tests and the contingency table analysis. It is clear on how to perform both analysis and their significance in research as discussed by Weaver et al., (2017) .
The ANOVA on the differences by grade on the performance rating is discussed below. The first step is setting up the null and the alternate hypothesis, as stated below.
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H0 All mean performance ratings are equal across different grades
H1 At least one mean performance rating in the different grades differs from the rest
After the set up of the hypothesis, the next step is the setting up of the alpha value to 0.05 and then the rejection rule. Thus, the null hypothesis is rejected if the p-value is less than the set alpha value (p-value < 0.05).Figure 1 below shows the table of the performance rating for a single factor ANOVA. Data in the table is sorted, as shown in figure 1, to facilitate testing.
Figure 1: Data Set Up For ANOVA Single-Factor of Difference of Means Test
The ANOVA single-factor test is selected by choosing it in the data analysis tools. The test is then performed through an appropriate selection of the data, labels, and output cells, as shown in figure 2.
Figure 2: Running the Test in the Data Analysis Tool for ANOVA Single-Factor of Difference of Means Test
After performing the test, the rounded value of the p-value is 0.570. Therefore since P> 0.05, we reject the null hypothesis. It leads to the conclusion that at least one mean performance rating differs from the other grades. The result of the test is shown in figure 3 below.
Figure 3: The Output Table for ANOVA Single-Factor of Difference of Means Test
References
Weaver, K., Morales, V., Dunn, S., Godde, K., & Weaver, P. (2017). An introduction to statistical analysis in research (pp. 227-355). John Wiley & Sons.
