Data Analysis Plan

Using the JASP software for this experiment analyzes two variables: “Section” and “Quiz3.” The independent variable “Section” is definite, thus separating the class into three groups: 1, 2, and 3, respectively. The dependent variable, “Quiz3,” is regarded as a continuous variable because it pertains to the scores of students in terms of correct answers. To analyze whether the average scores of Quiz3 differ among the different sections, this paper will use one-way ANOVA.RSCH 7864 Assessment 4 : ANOVA Application and Interpretation The central research question investigates if the average scores of Quiz3 show any discernible variation among the three sections.

The null hypothesis is that the mean scores for Quiz3 are the same in all three sections.

The alternative hypothesis is that the mean Quiz3 score for at least one section is appreciably distinct from the rest.

Testing Assumptions

Assumption Checks

The table below shows whether the assumption of equal variances required for ANOVA is satisfied by Levene’s assessment for variance equality. The test outcomes show that Levene’s F-statistic is 2.690, and the corresponding p-value is 0.073. Since this p-value is greater than 0.05, the null hypothesis cannot be rejected. This means the variances are equal in the groups. In other words, the presumption of equal variances is met. Therefore, the homogeneity of variances assumption is not breached, and ANOVA analysis can be continued.

Results & Interpretations

Descriptives

The summary statistics for Quiz 3 across each section are as follows: Section 1: Mean is 7.242, while the standard deviation is 1.173. For Section 2, the mean score is 6.179 with a standard deviation of 1.537. The mean score in Section 3 is 7.545, which is conducted by a standard deviation of 1.734. These statistics therefore show the variance in performance from the three sections. To establish if the differences are statistically significant, an ANOVA is carried out. The ANOVA indicates that the mean scores of Quiz 3 are significantly different in the sections. The F value is calculated to be 8.354, and the corresponding p-value is less than 0.001. Because the p-value is below the threshold of 0.05, the null hypothesis, stating that there is no difference between the sections, is rejected. This would mean that the section variable affects the performance during Quiz 3 to a considerable extent.

The homogeneity of variances was assumed to be tenable as indicated by the results of Levene’s test, thus that enabled the standard ANOVA analysis followed by Tukey’s post hoc test. The post hoc comparisons indicate that Section 1 did have a better score as compared with that of Section 2 with a mean difference of 1.063 (p = 0.010). However, there was no significant difference between Sections 1 and 3 (p = 0.692), whereas a significant difference was found between Sections 2 and 3 (p < 0.001). Thus, it can be concluded that Section 1 had significantly better performance than Section 2, and the performance of Sections 1 and 3 was not significantly different. The clear difference in performance for Section 2 compared to the other two sections indicates a significant difference in quiz results between the groups.

Statistical Conclusions

With all these considered, it must be accepted that the test does have restrictions associated with performing ANOVA. The very fundamental restrictions include violating normality as well as non-equal variances that may easily lower the applicability of a resultant conclusion due to the unreliability established through the sample obtained. Its low sample size would also ensure its general applicability to fewer cases. This also increases the chances of Type I errors, where a true null hypothesis may be rejected. Furthermore, although post hoc tests are useful in identifying group differences, they do not always clarify which specific groups contribute to the overall findings, thus requiring caution when interpreting the outcomes. These limitations highlight the need for careful consideration when trying to conclude the data.

Applications

A potential independent variable that could be introduced into the nursing field for performing a one-way ANOVA is the type of educational program provided to patients managing chronic conditions such as diabetes. The independent variable in this case would be categorized into three groups: a basic educational program, an advanced educational program, and a comprehensive combined program. The dependent variable will be the control of blood sugar, and that will be quantified in terms of average number of days spent by the patient within the limits of normal level of blood sugar. This is a highly critical analysis since the determination of the education program most useful for improvement in blood sugar control is sure to indicate which interventions have the capability of improving the patient’s outcome while reducing the chances of complications resulting from diabetes. The most suitable educational approach as determined can influence the quality of care and provide better patient outcomes for healthcare.