PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

Student Name

Capella University

PSY FPX 7864 Quantitative Design and Analysis

Prof. Name:

Date

ANOVA Application and Interpretation

A one-way ANOVA is utilized when “the researcher needs to compare means on a quantitative Y outcome variable between two or more groups” (Warner, 2012, p. 219). This analysis will illustrate the comparison of quiz3 scores across three sections using ANOVA comparisons.

Section 1: Data File Description

The analysis involves two variables: section and quiz3. This will include a comparison of the mean quiz3 scores across the three sections. In the context of a one-way ANOVA, the independent variable is referred to as a component (Warner, 2013). The variable “unit” is measured on a nominal scale, while quiz3 is a quantitative variable that employs interval scales. The sample size (N) for the tests is set at 105.

Section 2: Testing Assumptions

Tests of Normality

a. Lilliefors Significance Correction

The p-value from the Shapiro-Wilk test is .000, indicating a significant deviation from normality. To achieve accurate results, it is recommended that the research includes a larger data set. There are 105 samples in this analysis.

Section 3: Research Question, Hypotheses, and Alpha Level

The descriptive output for the three sections, along with quiz3, is as follows: the first section has a mean score of 7.15 with a standard deviation of 1.278, the second section has a mean score of 6.77 with a standard deviation of 1.495, and the third section has a mean score of 7.94 with a standard deviation of 1.560.

Descriptives

Section 4:

To compare the mean quiz3 scores, a one-way ANOVA will be employed. The degrees of freedom (df) were 2 between groups and 102 within groups, resulting in a total of 104. The number of independent pieces of knowledge on which a statistic is based (Warner, 2012, p. 56). The F-value in the output is 5.932, which serves as the critical value for rejecting the null hypothesis, leading to its rejection in this analysis.

The performance p-value is .000, which is below the conventional threshold of .05. This p-value further supports the decision to reject the null hypothesis. The effect size is calculated by dividing 25.013 by 240.057, yielding a value of .104, indicating a small to medium effect size.

ANOVA Summary Table

Since the ANOVA results indicate that at least one of the sections differs significantly, further examination of the output is necessary. At the 0.05 significance level, the mean difference is noteworthy. The post-hoc (Tukey HSD) results reveal a significant difference in means. The mean difference between Section 3 and Section 2 is 1.170, while the mean difference between Sections 2 and 3 is .788. These findings lend credibility to the assumptions made.

Multiple Comparisons

Dependent Variable: quiz3

*The mean difference is significant at the 0.05 level.

Section 5: Conclusion

The results of the one-way ANOVA indicate that this method is an appropriate tool for providing a valid response to the research question. The test successfully produced output that supported the rejection of the null hypothesis and affirmed the alternative hypothesis, indicating a significant difference in quiz3 mean scores across the three sections. One of the advantages of ANOVA is its ability to evaluate and assess performance across three or more groups. However, a limitation of the test is that if ANOVA indicates a significant difference among groups, a follow-up test is necessary to obtain final results.

References

George, D. (2016). IBM SPSS Statistics 23 Step by Step (14th ed.) [VitalSource Bookshelf version]. Retrieved from https://bookshelf.vitalsource.com/books/9781134793402

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

Warner, R. M. (2012). Applied Statistics: From Bivariate Through Multivariate Techniques (2nd ed.) [VitalSource Bookshelf version]. Retrieved from https://bookshelf.vitalsource.com/books/978148330597