Data Analysis & Application: ANOVA Case Study

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Table of Contents

Background
Data Analysis Plan
Testing Assumptions
Results & Interpretation
Statistical Conclusions
Application
References

Background

This paper focuses on the analysis of the results for Quiz 3 provided in the dataset Grades.sav. The purpose of this paper is to determine if the number of correct answers to Quiz 3 differed significantly depending on the class section. First, the paper provides a data analysis plan by naming the variables and stating the research question and hypotheses. Second, the paper tests for the assumption of normality using Shapiro-Wilk test. Third, the results of the analysis are provided and interpreted. Fourth, the statistical conclusions are drawn. The paper is concluded with a discussion of the application of the methods for psychology discussed.

Data Analysis Plan

This paper focuses on the analysis of two variables, including the number of correct answers for Quiz 3 named as ‘quiz3’, which was the dependent variable, and class section named as ‘section’, which was an independent variable. The research question this paper attempts to answer is the following:

RQ1: How do the test results for Quiz 3 differ depending on the class section?

The research question will be answered by using ANOVA to test the following hypothesis:

H₀: There are no statistically significant differences in the results for Quiz 3 depending on the class section.
H_A: There are statistically significant differences in the results for Quiz 3 depending on the class section.

Testing Assumptions

The dependent variable was tested for normality using Shapiro-Wilk test in SPSS. The results of the test are provided in Table 1 below.

Table 1. Normality test results

	Kolmogorov-Smirnov^a			Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
quiz3	,131	105	,000	,932	105	,000
a. Lilliefors Significance Correction

According to Shapiro-Wilk test results, the assumption of normality was violated. The significance level of p < 0.001 demonstrates that the null hypothesis of Shapiro-Wilk test should be rejected. Since the null hypothesis of Shapiro-Wilk test is that the population under analysis is normally distributed, it was concluded that the assumption of normality was violated (Field, 2018).

Results & Interpretation

The hypothesis was tested using ANOVA in SPSS. The outputs of the ANOVA tests results, including descriptives, ANOVA table, and multiple comparison table are provided in in Tables 2-4 below.

Table 2. Descriptive statistics

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
	N	Mean	Std. Deviation	Std. Error	Lower Bound	Upper Bound	Minimum	Maximum
1	33	7.33	1.534	.267	6.79	7.88	4	10
2	39	6.72	1.538	.246	6.22	7.22	4	10
3	33	7.79	2.088	.363	7.05	8.53	4	10
Total	105	7.25	1.769	.173	6.91	7.59	4	10

Table 3. ANOVA table

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	20.816	2	10.408	3.484	.034
Within Groups	304.746	102	2.988
Total	325.562	104

Table 4. Multiple comparison table (Tukey)

(I) section	(J) section	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
(I) section	(J) section	Mean Difference (I-J)	Std. Error	Sig.	Lower Bound	Upper Bound
1	2	.615	.409	.293	-.36	1.59
1	3	-.455	.426	.536	-1.47	.56
2	1	-.615	.409	.293	-1.59	.36
2	3	-1.070^*	.409	.027	-2.04	-.10
3	1	.455	.426	.536	-.56	1.47
3	2	1.070^*	.409	.027	.10	2.04
*. The mean difference is significant at the 0.05 level.

The 33 participants in class section 1 answered 7.33 questions correctly on average (SD = 1.534); the 39 participants in class section 2 answered 6.72 questions correctly on average (SD = 1.538), and the 33 participants in class section 3 answered 7.79 questions correctly on average (SD = 1.534). The effect of class section, therefore, was significant, F(2,102) = 3.484, p = 0.034. Post hoc analysis revealed that there was a statistically significant difference in the mean value between the section 2 and section 3 with p = 0.027.

Statistical Conclusions

The analysis demonstrated that the mean number of correct answers for Quiz 3 differed significantly among class sections. In particular, ANOVA test results demonstrated that the mean number of correct answers for Quiz 3 in class section 3 were significantly higher than the mean number of correct answers for Quiz 3 in class section 2.

However, it should be mentioned that the assumption of normality was violated, which implies that the results of the analysis may be biased. However, according to Filed (2018), ANOVA is robust against violations of normality. This implies that the possibility of Type 1 error is only slightly affected by the violation of normality.

Application

My field of study is psychology, and the applications of ANOVA can be vast. For example, ANOVA can be used for comparing the effectiveness of different treatments on the severity of posttraumatic stress disorder symptoms (PTSD). In this case, the severity of PTSD symptoms will be a dependent variable and the type of treatment will be an independent variable. A group of participants with PTSD can be treated using cognitive-behavioral treatment, medications, and a combination of these treatments. ANOVA can be used to compare the severity of PTSD symptoms after the treatment and determine if there were statistically significant differences in the outcomes. The results, can help to select the most effective treatment strategy to addressed the problems of patients.

References

Field, A. (2018). Discovering statistics using SPSS: North American edition (5th ed.). Sage.

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