RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation
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RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

Name

Capella University

RSCH FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Data Analysis Plan

Based on grades, an ANOVA was run on a single factor. The variables to be examined in this analysis are Section, the class section, and Quiz 3, specifically the quantity of correctly answered questions on Quiz 3. The independent variable in this section is a categorical one. The dependent variable is the continuous quiz #3.

Research Question: Is there a statistically significant difference between the mean scores of different student groups on Quiz 3?

The null hypothesis of the study is that the mean scores of the student subgroups on Quiz 3 do not differ in a way that is statistically significant. An alternative hypothesis posits that there will be a significant difference in the mean score of one student group on Quiz 3 compared to the scores of the other student groups.

Testing Assumptions

Assumption Checks

Test for Equality of Variances (Levene’s)

Test

F

df1

df2

p

Levene’s 2.898 2.000 102.000 0.060

Here, the test statistic (F) is 2.898 with degrees of freedom of 2 and 102, respectively, and a p-value of 0.060. If the p-value is less than or equal to the significance threshold—typically 0.05— we reject the null hypothesis that the variances are equal and conclude that the assumption of homogeneity has been broken. However, we are unable to reject the null hypothesis and determine that the homogeneity assumption has not been violated if the p-value is greater than the significance level. In this case, the p-value exceeds the significance threshold of 0.05 at 0.060. This means that we are unable to rule out the null hypothesis and declare the homogeneity assumption to be true.

Results & Interpretation

Descriptives

N

Mean

SD

SE

Coefficient of variation

Section 1 3 7.273 1.153 0.201 0.159
Section 2 3 6.333 1.611 0.258 0.254
Section 3 3 7.939 1.560 0.272 0.196

ANOVA – quiz3

Cases

Sum of Squares

df

Mean Square

F

p

Section 47.042 2 23.521 10.951 < .001
Residuals 219.091 102 2.148

Post Hoc Tests

Standard Post Hoc Comparisons – section

Comparison

Mean Difference

SE

t

p (tukey)

1 vs 2 0.939 0.347 2.710 0.021
1 vs 3 -0.667 0.361 -1.848 0.159
2 vs 3 -1.606 0.347 -4.633 < .001

Note. P-value adjusted for comparing a family of 3

The descriptive table indicates that each section’s quiz 3 average was firm. The standard deviation (SD= 1.153) and mean (M= 7.273) of Section 1 were recorded. Section 2 had M= 6.333 and SD= 1.611. The data in Section 3 displayed M= 7.939 and SD= 1.560. The mean scores from quiz #3 were linked to the three student sections in the ANOVA table. When comparing the mean of quiz 3 to the three student selections, the ANOVA table revealed a significant difference, F (2,102) =10.951, p< .001, indicating that there was a significant difference in mean quiz scores among the student sections. However, post hoc tests showed no significant difference (p > 0.05) due to insufficient statistical significance between section 1 and section 3.

Application

In the field of applied behavior analysis (ABA), the ANOVA statistical test can be used to compare multiple independent factors to a single dependent variable. One example of how the ANOVA might be used is to compare strategies for decreasing aggressive behavior. The strategies used to reduce aggressive behavior would be the independent variable. These strategies could include things like requesting a break, getting access to a preferred object or activity, or neutrally rerouting hostile behavior while rewarding positive behavior.

RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

The dependent variable would be the patient’s hostile behavior. Since patients with autism frequently communicate through aggression, it is critical for the field of ABA to investigate how different treatment approaches can lessen aggressive behavior. A patient’s quality of life and interactions with others around them are improved when we, as professionals, can assist them in expressing their needs or goals without using violence.

References

Andrade, C. (2019). The P value and statistical significance: misunderstandings, explanations, challenges, and alternatives. Indian Journal of Psychological Medicine, 41(3), 210–215. https://doi.org/10.4103/ijpsym.ijpsym_193_19

RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

Midway, S. R., Robertson, M., Flinn, S., & Kaller, M. D. (2020). Comparing multiple comparisons: practical guidance for choosing the best multiple comparisons test. PeerJ, 8, e10387. https://doi.org/10.7717/peerj.10387