ANOVA Application and Interpretation

**QUESTION**

Complete an SPSS data analysis report using ANOVA for assigned variables.

You’re starting to learn some important information about your data, but you still want to know more. It’s time for a one-way analysis of variance (ANOVA). Unlike t-tests, which only allow for comparisons of two groups, ANOVA will allow you to examine potential group differences for variables with multiple levels.

Instructions

Complete this assessment using the Data Analysis and Application Template [DOC] (also known as the DAA Template).

• Refer to IBM SPSS Step-By-Step Guide: One-Way ANOVA [PDF] for additional information on using SPSS for this assessment.

• Review the Copy/Export Output Instructions [PDF] for help copying SPSS output into your DAA Template.

• Use the Data Set Instructions [PDF] for information on the data set

• Refer to the Course Study Guide [PDF] for information on analyses and interpretation.

The grades.sav file is a sample SPSS data set. The data represent a teacher’s recording of student demographics and performance on quizzes and a final exam across three sections of the course. Each section consists of 35 students (N = 105). There are 21 variables in grades.sav.

This assessment is on ANOVA. You will analyze the following variables in the grades.sav data set:

SPSS Variables and Definitions

SPSS Variable Definition

Section Class section

Quiz3 Quiz 3: number of correct answers

Step 1: The Data Analysis Plan

In Step 1:

• Name the variables used in this analysis and whether they are categorical or continuous.

• State a research question, null hypothesis, and alternate hypothesis for the ANOVA.

Step 2: Testing Assumptions

Test for one of the assumptions of ANOVA—normality.

• Create SPSS output showing the Shapiro-Wilk test of normality. Run the Shapiro-Wilk test on the dependent variable test for the entire sample. Do not split the data up by gender before running the normality test.

• Paste the table in the DAA.

• Interpret the Shapiro-Wilk test and how you determined whether the assumption of normality was met or violated.

Step 3: Results and Interpretation

In Step 3:

• Paste the following SPSS tables into the document:

o Descriptives table.

o ANOVA table.

o Multiple Comparison table.

• Report the means and standard deviations of quiz3 for each group of the section variable.

• Report the results of the F test and interpret the statistical results against the null hypothesis and state whether it is accepted or rejected.

• Interpret the post-hoc tests (multiple comparisons), if the F is significant.

Step 4: Statistical Conclusions

In Step 4:

• Provide a brief summary of your analysis and the conclusions drawn about this ANOVA.

• Analyze the limitations of the statistical test and/or possible alternative explanations for your results.

Step 5: Application

In Step 5:

• Analyze how you might use the ANOVA in your field of study.

• Name an independent variable (IV) (the IV should have three or more groups or categories) and dependent variable (DV) that would work for such an analysis and why studying it may be important to the field or practice.

Submit your DAA Template as an attached Word document in the assessment area.

Software

The following statistical analysis software is required to complete your assessments in this course:

• IBM SPSS Statistics Standard or Premium GradPack, version 24 or higher, for PC or Mac.

You have access to the more robust IBM SPSS Statistics Premium GradPack.

Please refer to the Statistical Software page on Campus for general information on SPSS software, including the most recent version made available to Capella learners.

Make sure that your SPSS software is downloaded and installed with fully activated licensing on your computer and running properly within your operating system (PC or Mac). If you need help with these steps, refer to the SPSS Installation Helper.

Competencies Measured

By successfully completing this assessment, you will demonstrate your proficiency in the course competencies through the following assessment scoring guide criteria:

• Competency 1: Analyze the computation, application, strengths, and limitations of various statistical tests.

o Analyze statistical assumptions.

• Competency 2: Analyze the decision-making process of data analysis.

o Articulate the data analysis plan.

• Competency 3: Apply knowledge of hypothesis testing.

o Interpret statistical results and hypotheses.

• Competency 4: Interpret the results of statistical analyses.

o Explain statistical conclusions, the limitations of the test, and possible alternative explanations.

• Competency 6: Apply the results of statistical analyses (your own or others’) to your field of interest or career.

o Analyze the potential applications of the test in the field and their implications.

• Competency 7: Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study.

o Communicate in a manner that is scholarly and professional, and adheres to APA style and formatting.

ANOVA Application and Interpretation Scoring Guide

CRITERIA NON-PERFORMANCE BASIC PROFICIENT DISTINGUISHED

Articulate the data analysis plan. Does not articulate the data analysis plan. Insufficiently articulates the data analysis plan or contains some errors of logic or application. Articulates the data analysis plan. Names the two variables; specifies as categorical or continuous. States a research question, null hypothesis, and alternate hypothesis. Has one or two errors. Accurately articulates the data analysis plan. Names the two variables; specifies as categorical or continuous. States a research question, null hypothesis, and alternate hypothesis. There are no errors.

Analyze statistical assumptions. Does not include output or analyze the normality assumption. Attempts to analyze statistical assumptions, but includes incorrect output or contains multiple errors of logic or application. Analyzes statistical assumptions. Includes correct output for the Shapiro-Wilk test with one or two errors of interpretation. Accurately analyzes statistical assumptions. Includes correct output for the Shapiro-Wilk test with no errors of interpretation.

Interpret statistical results and hypotheses. Does not include output or interpret statistical results and hypotheses. Attempts to interpret statistical results and hypotheses but includes incorrect output or contains multiple errors of logic or application. Interprets statistical results and hypotheses. Pastes the correct output; reports means and SDs for each group; reports the F-test and interprets against the null hypothesis; if significant, interprets post-hoc tests. Has one or two errors. Accurately interprets statistical results and hypotheses. Pastes the correct output; reports means and SDs for each group; reports the F-test and interprets against the null hypothesis; if significant, interprets post-hoc tests. There are no errors.

Explain statistical conclusions, the limitations of the test, and possible alternative explanations. Does not explain statistical conclusions, the limitations of the test, and possible alternative explanations. Insufficiently explains statistical conclusions, the limitations of the test, or possible alternative explanations or contains multiple errors of logic or application. Explains statistical conclusions, the limitations of the test, and possible alternative explanations with one or two errors. Accurately explains statistical conclusions, the limitations of the test, and possible alternative explanations with no errors.

Analyze the potential applications of the test in the field and their implications. Does not analyze the potential applications of the test in the field and their implications. Incorrectly analyzes potential applications of the test in the field and their implications with multiple errors of logical or application. Analyzes the potential applications of the test in the field and their implications with one or two errors or omissions. Thoroughly analyzes the potential applications of the test in the field and their implications with no errors or omissions.

Communicate in a manner that is scholarly and professional, and adheres to APA style and formatting. Does not communicate in a manner that is scholarly or professional, or adhere to APA style and formatting. Inconsistently communicates in a manner that is somewhat scholarly and professional, and adheres to APA style and formatting. Communicates in a manner that is scholarly and professional, and adheres to APA style and formatting. Exhibits strict and nearly flawless adherence to organizational, professional, and scholarly writing standards, including APA style and formatting.

ANOVA Application and Interpretation

**ANSWER**

ANOVA Application and Interpretation

Learner Name

Capella University

Data Analysis Plan

Variable Type

Quiz3 Continuous

Section Categorical

Research question.

Is there a difference in the score of quiz3 among the different sections?

Hypothesis

H0: There’s no difference in mean among the quiz3 score in different sections.

H1: At least one group have a statistically significant difference in mean from the group mean.

Testing Assumptions

The Shapiro-Wilk test is used to assess weather the variable data or sample data was drawn from a normally distributed data set, (Hanusz et al, 2016)

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

quiz3 .143 105 .000 .948 105 .000

a. Lilliefors Significance Correction

The Shapiro-wilk test results produced a p-value=0.000< 0.05 and therefore we can make a statistical conclusion that the data came from a population with a distribution that significantly deviated from the normal distribution. Exploring the Q-Q plot of the variables data, the variable data exhibits normality characters. With the patterns, we could be able to use the data to test for the ANOVA. Results and Interpretation Descriptive quiz3 N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound 1 33 7.27 1.153 .201 6.86 7.68 5 10 2 39 6.33 1.611 .258 5.81 6.86 2 10 3 33 7.94 1.560 .272 7.39 8.49 6 10 Total 105 7.13 1.600 .156 6.82 7.44 2 10 The mean score for quiz3 is 7.13, with a standard deviation of 1.6. the maximum score on quiz3 is 10 while the minimum score is 2. Section 2 had a bigger sample size of 39 with the lowest sample mean of 6.33. ANOVA quiz3 Sum of Squares df Mean Square F Sig. Between Groups 47.042 2 23.521 10.951 .000 Within Groups 219.091 102 2.148 Total 266.133 104 The one-way ANOVA test was performed to determine if the three different sections produce different scores for quiz 3. The result from the ANOVA test revealed that there was a statistically significant difference in the mean of the quiz3 score among the sections, (F (2,102) =10.951, p=0.000<0.05). Multiple Comparisons Dependent Variable: quiz3 Tukey HSD (I) section (J) section Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound 1 2 .939* .347 .021 .11 1.76 3 -.667 .361 .159 -1.52 .19 2 1 -.939* .347 .021 -1.76 -.11 3 -1.606* .347 .000 -2.43 -.78 3 1 .667 .361 .159 -.19 1.52 2 1.606* .347 .000 .78 2.43 *. The mean difference is significant at the 0.05 level. The Turkey test for multiple comparison, found out that the mean score was significantly different between section 1 and 3 (p=0.00) as well as between group 1 and 2 (0.021), the two combinations produced p-values less than 0.05. Statistical Conclusions The data analysis revealed that there was at least one section whose score was not the same as the score in other sections, performing the Turkey test revealed that the groups with the different mean of quiz3 score when group 1 and 2 are compared as well as when group when group 1 and 3 are compared. Mathematically, it can be deduced that the mean score of section 1 is significantly different from those of section 2 and section 3. Rejecting the null hypothesis was in order and making the conclusion that at least one section`s mean score of quiz3 was different from the mean score of the other section. Though the one-way ANOVA test is used to is instrumental in comparing mean among 2 and above groups, it is limited in a way that the comparisons can only be done on one dependent variable at a time. In addition, the ANOVA test only show that there is a difference in the group but not which groups is different from the other. Without the post-hoc test, I will not be possible to know the exact groups that have mean difference. Application Since the main use of ANOVA is to test the difference among multiple groups, this test is applicable in the medical industry to asses which medication works better for a particular disease. This use is most appropriate when there are more than two medications that can be used to cure a single illness, (Abate, 2013). An example is when finding the best vaccine for the corona virus, there are a number of vaccines in the market, that is; Moderna, AstraZeneca, Johnson and Johnson. Taking these three vaccines, to find out which one is most preferred for a target group of people, they are tested against the vaccines at random, thee result recorded and an ANOVA test used to determine the difference in the effect. References Abate, K. S. (2013). The effect of podcast lectures on nursing students’ knowledge retention and application. Nursing Education Perspectives, 34(3), 182-185. Hanusz, Z., Tarasinska, J., & Zielinski, W. (2016). Shapiro-Wilk test with known mean. REVSTAT-Statistical Journal, 14(1), 89-100. ANOVA Application and Interpretation