Synthesis Of Statistical Findings Derived From ANOVA
Submit a synthesis of statistical findings derived from ANOVA that follows the Week 4 Assignment Template. Your paper must include the following:
- A description and justification for using the one-way ANOVA
- A properly formatted research question
- A properly formatted H0(null) and H1 (alternate) hypothesis
- An APA-formatted “Results” section for the one-way ANOVA
- Identification of the statistical test
- Identification of independent and dependent variables, including the identification of the number of levels for the independent variable
- Identification of data assumptions and assessment outcome
- Inferential results in correct APA statistical notation format
- A properly formatted box plot
- A discussion on how you would extend the one-way ANOVA to a two-way ANOVA using the variables in the Week 4 Data File for One-way ANOVA.sav dataset.
- Properly APA-formatted references
- Appendix containing SPSS output (see Week 4 Assignment Exemplar)7
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Order Paper NowDDBA 8307 Week 4 Assignment Exemplar – One-Way ANOVA[footnoteRef:1] [1: Footnotes within the narrative are depicted by bold yellow superscripts; the footnotes will not be in your final submission.]
John Doe[footnoteRef:2] [2: Type your name here.]
DDBA 8307-6[footnoteRef:3] [3: Type in DDBA section number (e.g. DDBA 8307 – 6). ]
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Dr. Jane Doe[footnoteRef:4] [4: Enter faculty name here.]
One-Way Analysis of Variance (ANOVA)
You will describe and defend using the one-way ANOVA for your analysis. Use at least two outside resources—that is, resources not provided in the course resources, readings, etc. These citations will be presented in the References section. This exercise will give you practice for addressing Rubric Item 2.13b, which states, “Describes and defends, in detail, the statistical analyses that the student will conduct….” This section should be no more than two paragraphs.
Research Question[footnoteRef:5] [5: Quantitative research questions can be presented in a variety of formats; however, you will be safe using this format. ]
Is there a statistically significant difference in weekly widgets produced among day shift, night shift, and swing shift employees?
Hypotheses[footnoteRef:6] [6: Two hypotheses, the null (H0) and alternative (H1), are to be stated for each research question. See p. 39 in the Research Handbook for more detailed examples. See more on hypotheses at http://www.socialresearchmethods.net/kb/hypothes.php ]
Null Hypothesis (H0): There is not a statistically significant difference in weekly widgets produced among day shift, night shift, and swing shift employees.
Alternative Hypothesis (H1): There is a statistically significant difference in weekly widgets produced among day shift, night shift, and swing shift employees.
Results[footnoteRef:7] [7: DBA Rubric Item 3.2d: Reports inferential statistical analyses results, organized by research question, in proper APA statistical notation/format. Includes the alpha level chosen for the test, test value, p (significance level) values, effect size, degrees of freedom, confidence intervals (when appropriate), etc. ]
In this subheading, I will present descriptive statistics, discuss testing of the assumptions, present inferential statistic results, and conclude with a concise summary.
Descriptive Statistics
A total of 435 employees participated in the study. The assumption of equality variances (Levene’s test, p = .475) was evaluated with no violation noted. Table 1 contains descriptive statistics for the study variables. Figure 1 depicts a box plot.
Table 1
Work Shift M SD Day Shift 21.36 4.55 Night Shift 22.10 4.15 Swing Shift 22.96 4.49 Figure 1. Box-plot comparing number of weekly widgets produced by work shift.
Inferential Results[footnoteRef:8] [8: All values required for the APA write-up are derived from the SPSS output.]
A one-way ANOVA, a = .05, was conducted to assess whether there was a statistically significant difference in weekly widgets produced among day shift, night shift[footnoteRef:9], and swing shift employees. The independent variable was work shift, with three levels: day shift, night shift, and swing shift. The dependent variable was the number of weekly widgets produced. The assumption of equality variances (Levene’s statistic = .746, p = .475)[footnoteRef:10] was evaluated with no violation noted. The results were significant,[footnoteRef:11] F(2, 432) = 4.641, p =.01[footnoteRef:12]. The measure of effect size measured by η2 was .02[footnoteRef:13], indicating that 2% of the variance in widgets produced is accounted for by work shift. Post hoc analysis[footnoteRef:14], using Tukey’s HSD test, indicated that the mean number of widgets for the day shift (M = 21.36, SD = 4.55) was significantly different from the swing shift (M = 22.96, SD = 4.49). The night shift (M = 22.10, SD = 4.15) did not differ significantly from the day shift or swing shift. Table 2 depicts the ANOVA summary. Figure 1 depicts a box-plot comparing weekly numbers of widgets produced by work shift. [9: Note the one-way ANOVA can assess group difference between more than two groups, unlike the independent-samples t-test, which is used when there are only two groups being compared.] [10: Values derived from SPSS output.] [11: Remember, your results might not be significant; this would be evidenced by p > .05. ] [12: This is the correct format for reporting ANOVA results. However, it is important to understand the parameters. F indicates an ANOVA test was conducted; (2, 432) = the degrees of freedom for between (df = 2) and within groups (df = 432). respectively; (df) are an indication of the number of groups being compared and the sample size. The df (2) is the number of groups minus one, in this case 3 – 1 = 2, whereas (df) = 432 can give an indication of the sample size—the total sample should be very close to this value; 9.1 = the calculated F statistic; p = .01 indicated there was a significant difference among the three groups, as p < .05. Remember, p values ≤ .05 are statistically significant.] [13: η2 is calculated as follows: SS between groups/Total sum of squares (derived from SPSS output—see Table 2).] [14: Post hoc (after the fact) analysis must be conducted when there is a statistically significant (p ≤. 05) omnibus finding. The post hoc test will identify where the specific pairwise differences are (see “multiple comparisons” table in SPSS output). ]
Table 2
ANOVA Summary Table for the Impact of Work Shift on Widgets Produced
Source df SS MS F η2 p Between-group 2 179.07 89.54 4.461 0.00 .01 Within-group 432 8,333.95 19.23 Total 434 8,513.02 Extend One-Way ANOVA to Two-Way ANOVA
Type text here. As you are aware, quantitative DBA Doctoral Studies require the use of at least two independent variables. Discuss briefly how you could extend the one-way ANOVA to a two-way ANOVA. Identify and discuss a second hypothetical independent variable and the number of levels to the second independent variable.
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References
Type references here in proper APA format.
Appendix – One-Way ANOVA SPSS Output[footnoteRef:15] [15: You will copy and paste the appropriate SPSS output into the Assignment. See the document titled “Copying and Pasting SPSS Output Into Word,” located in the Week 2 Resources. ]
Descriptives Total Optimism N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound Day Shift 147 21.36 4.551 .375 20.62 22.10 7 30 Night Shift 153 22.10 4.147 .335 21.44 22.77 10 30 Swing Shift 135 22.96 4.485 .386 22.19 23.72 8 30 Total 435 22.12 4.429 .212 21.70 22.53 7 30 Test of Homogeneity of Variances Total Optimism Levene Statistic df1 df2 Sig. .746 2 432 .475 ANOVA Total Optimism Sum of Squares df Mean Square F Sig. Between Groups 179.069 2 89.535 4.641 .010 Within Groups 8,333.951 432 19.292 Total 8,513.021 434 Post Hoc Tests
Multiple Comparisons Dependent Variable: Total Optimism Tukey HSD (I) age 3 groups (J) age 3 groups Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Day Shift Night Shift -.744 .507 .308 -1.94 .45 Swing Shift -1.595* .524 .007 -2.83 -.36 Night shift Day Shift .744 .507 .308 -.45 1.94 Swing shift -.851 .519 .230 -2.07 .37 Swing Shift Day Shift 1.595* .524 .007 .36 2.83 Night Shift .851 .519 .230 -.37 2.07 *. The mean difference is significant at the 0.05 level.
