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 A

DDBA 8307 Week 4 Assignment Exemplar – One-Way ANOVA1

John Doe2

DDBA 8307-63

Dr. Jane Doe4

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 Question5

Is there a statistically significant difference in weekly widgets produced among day shift, night shift, and swing shift employees?

Hypotheses6

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.

Results7

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

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 A 1

Figure 1. Box-plot comparing number of weekly widgets produced by work shift.

Inferential Results8

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 shift9, 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)10 was evaluated with no violation noted. The results were significant,11 F(2, 432) = 4.641, p =.0112. The measure of effect size measured by η2 was .0213, indicating that 2% of the variance in widgets produced is accounted for by work shift. Post hoc analysis14, 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.

Table 2

ANOVA Summary Table for the Impact of Work Shift on Widgets Produced

Source	df	SS	MS	F	η2	p
Between-group		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.

References

Type references here in proper APA format.

Appendix – One-Way ANOVA SPSS Output15

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.

1 Footnotes within the narrative are depicted by bold yellow superscripts; the footnotes will not be in your final submission.

2 Type your name here.

3 Type in DDBA section number (e.g. DDBA 8307 – 6).

4 Enter faculty name here.

5 Quantitative research questions can be presented in a variety of formats; however, you will be safe using this format.

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

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.

8 All values required for the APA write-up are derived from the SPSS output.

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).

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.