Student name

Capella University

RSCH-FPX7864 Quantitative Design and Analysis

Professor Name

Submission Date

Data Analysis Plan

The common type of analysis that is applied in the various fields such as nursing, medical, and natural sciences to quantify the difference in means between groups is the analysis of variance (ANOVA). The test may be applicable either clinically or educationally, to either test the effectiveness of the intervention, or determine whether there are any differences in the average performance between groups.

ANOVA for Quiz Comparison

As Thango (2022) observed, ANOVA is specifically employed in the determination of the presence of statistically significant differences between three or more groups. Moreover, the test ascertains the presence of variability between the groups that can lead to more differences than those found in the groups. In the analysis, the most important aspect to be compared is the Quiz 3 marks of the learners in the three class sections. The categorical variable is the variable of class section, which is defined as a group of learners who belong to a certain section. Although the variable under consideration is the “Quiz 3 marks,” it is a continuous variable which is used to measure the performance of students. As such, the researchers would be able to test the means to answer whether there is any significant difference between the quiz scores of sections taking the same course.

• Research Question

Is there a significant difference in the mean Quiz 3 scores among the three groups of learners?

• Null Hypothesis (Ho)

There is no significant difference in the mean Quiz 3 scores among the three groups of learners.

• Alternate Hypothesis (H₁)

There is a significant difference in the mean Quiz 3 scores among the three groups of learners.

Testing Assumptions

The establishment of homogeneity of variance is a crucial aspect of the assumptions verification before the ANOVA is used. The test that is normally employed to determine the statistical equality of variances among groups is Levene (Zhou et al., 2023). The test was also statistically significant in the analysis; F(2, 102) = 2.89, p =.006. The p-value obtained is lower than 0.05, and the null hypothesis was rejected, which proves that there is no difference in variance among the groups. The case of homogeneity of variance is undermined by the analysis. In addition to that, the test will be significant to support the assumption before conducting the ANOVA since the violation implies that the inferences made after the analysis will not be valid. Where homogeneity of variance is not possible, a different approach can be adopted, like ANOVA, in testing unequal variances.

Results and Interpretation

Statistical interpretation is impossible without descriptive analysis, in which the data can be summarized by providing a measure of central tendency (mean and dispersion of data in the form of standard deviation). A descriptive statistical analysis was used to examine the performance of learners on the Quiz 3 marks in three classes. The descriptive statistical analysis gave insight into the average scores of each group and the extent of variance of the scores in each section. The statistical findings are given below:

Group 1: M = 7.237, SD= 1.153

Group 2: M = 6.333, SD= 1.611

Group 3: M = 7.939, SD= 1.560

The ANOVA was conducted to examine the differences in Quiz 3 scores between the three sections of the school classes. The results of ANOVA demonstrated a statistically significant result because F(2, 102) = 10.951, p =.000; the p-value is lower than.001, which is strong evidence to reject the null hypothesis (Choi, 2023). Analysis implies that the assumption of the equality of means was violated, and at least one of the sections of the classes had a significant difference between the means Quiz 3 score and the other sections. Additionally, the findings also indicate that ANOVA findings indicate that there is more between-group as compared to within-group variation, a fact that validates the fact that the performance of the students in the three sections was significantly different in some aspects.

Since a statistically significant difference between the Quiz 3 scores of the three groups in the ANOVA study led to the discovery, a post hoc analysis was conducted to explore the differences between the groups in particular. The statistical technique used should be post hoc analysis as a way of making comparisons of multiple means of groups (Aslam and Albassam, 2020). The post hoc tests are the Scheffe test and the Tukey HSD test. Under the next instance, the HSD test created by Tukey was conducted to compare the mean scores between two groups. Since the Tukey HSD has been used, the analysis has been used to draw all possible comparisons between the groups, assuming that the variances are equal as well as the sample sizes.

• Pairwise Comparison: Session 1-2

The results of the Tukey HSD test indicate that the comparison between Groups 1 and 2 has a p-value of less than 0.05, which is an indicator of the presence of a statistically significant difference in the Quiz 3 scores of the groups. It has been analyzed that group 1 surpassed group 2 in the field of academic performance at a statistically significant level in relation to group 2. Results indicate a statistically significant difference in the outcome of learners in group 1 and learners in the second group.

• Pairwise Comparison: Group 1-3

The comparison between group 1 and group 3 gave a p-value that was bigger than 0.05, indicating that there was no statistical difference between the Quiz 3 performance of the two groups. Thus, the Group 1 learners did not differ in performance from the Group 3, and this does not correlate with the evidence of a significant gap in quiz performance in the group.

• Pairwise Comparison: Group 2-3

The p-value generated by the final pairwise test between Group 2 and Group 3 was less than 0.05, indicating that there was a difference between the performance on Quiz 3. The results indicated that Group 2 students performed better than Group 3 students, had a better mean score. In summary, the post hoc analysis provided further insight into the ANOVA results. The results showed a large difference between G 1 and G 2, G 2 and G 3, but not between G 1 and G 3.

Statistical Conclusion

The statistical evaluation showed the performance of learners on Quiz 3 of three different classes. These comparisons help determine whether instructional differences influence student achievement across groups. The homogeneity of variance test used by Levene was F(2,102) = 2.898, p = 060, which means that the outcome was not significant and allows us to believe that the hypothesis of equal variance is met (Thango, 2022). Based on this, the null hypothesis of equal group variances was accepted, which made one of the assumptions that were necessary before carrying out the ANOVA test.

The results of the ANOVA test are as follows: F (2,102) = 10.951, p =.001, statistically significant differences among the scores in Quiz 3 among the three groups of learners. Applying the results of ANOVA, the null hypothesis, indicating a lack of difference between the means of groups, was rejected, and it was seen that one group was significantly different compared to the other two groups. The post hoc test of Tukey was conducted to identify the particular groups that were dissimilar. The pair-wise comparison has revealed that there is a significant difference between Groups 1 and 2, and between Groups 2 and 3. Nevertheless, Groups 1 and 3 had no substantial differences; therefore, the analyses were more aware of the performance of the students in the entire class section.

Limitation

ANOVA is an effective statistical test, but the test is limited. The fact that ANOVA fails to take into consideration context, including differences in teaching styles, which may perhaps establish the student performance in any of the three groups of classes, is one of the constraints. The other weakness is that ANOVA assumes a normal distribution, which is not always so in real life in the educational context (Knief and Forstmeier, 2021). In case of non-normally distributed data, there is a possibility of data influencing the validity and reliability of the results. One more drawback of ANOVA and post hoc comparisons is that the larger the number of post hoc comparisons, the higher the risk of Type I error that the results of statistical significance can be obtained. Therefore, the results of the analysis can be considered false or misleading, which is why precautions should be taken when interpreting the results in the course of conducting ANOVA, especially in cases of a lot of comparisons with the use of post hoc tests.

Application

ANOVA is a powerful statistical instrument and is widely applied in nursing practices in the case of establishing the effectiveness of various nursing interventions on three or more populations of patients. Moreover, the ANOVA provides an approximation of the total impact of the various interventions of nurses on the outcome measure, including patient satisfaction (Alharbi et al. 2022). As an illustration, ANOVA might be employed to determine the level of satisfaction among patients who had undergone various nursing interventions. As an example, they can use the test to evaluate the effect on patient satisfaction who went through three nursing interventions, such as behavioral therapy, nurse-led education, and medication management (Pouresmail et al. 2023).

In the next case, patient satisfaction was the dependent variable, and the independent variable was the nursing intervention. The findings of ANOVA enabled the researchers to identify the nursing intervention that influenced the level of satisfaction and therefore informed clinical decision-making. Thus, the ANOVA analysis can be especially valuable in cases when the healthcare workforce should employ the most effective techniques to enhance the experiences of patients. Besides, analysis applies to the improvement of the quality of care by managers of health institutions to raise patients’ satisfaction rates.