Statistical power analysis

**Order Instructions:**

This paper will be a continues paper and the writer must have a very good understanding of using the software mentioned in this paper. It is critical that the writer stay consistent with all of this paper most importantly reading all instructions and properly following directions to complete each section of the paper. This particular paper consist of 3 main parts to complete and the writer must clearly respond to this 3 main points listed in APA 6th edition. I will email the main dataset mentioned in the questions which will enable the writer to complete this paper. The writer must thoroughly analyze the data as require using the proper means.

For this assignment you use SPSS (PASW) software and learn to properly manipulate data according the APA requirements. This is an important skill and will be a major factor in future assignments in this course, your doctoral studies and dissertation. It is strongly encouraged that you review Chapter 5 of the APA Publication Manual to understand table and figure requirements before starting.

Follow the directions for using SPSS (PASW) in this assignment:

You will then write a 3-4 page paper in which you present your table and an analysis of your findings. Keep in mind that you cannot draw conclusions without further testing. Instead identify notable trends, patterns, relationships, associations, etc. Your paper must meet the following requirements:

• Include an opening including thesis statement, body and conclusion.

• Include a properly stated research question

• Include a properly formatted null and alternative hypotheses

• Follow APA (American Psychological Association) style and include in-text citations and a separate references page

• Software

• IBM SPSS Statistics Standard GradPack (current version). Available in Windows and Macintosh versions.

Course Text(s)

• Green, S. B., & Salkind, N. J. (2014). Using SPSS for Windows and Macintosh: Analyzing and understanding data (7th ed.). Upper Saddle River, NJ: Pearson.

o Units 1 and 2, pp. 1–50

? Lesson 1, “Starting SPSS”

? Lesson 2, “The SPSS Main Menus and Toolbar”

? Lesson 3, “Using SPSS Help”

? Lesson 4, “A Brief SPSS Tour”

? Lesson 5, “Defining Variables”

? Lesson 6, “Entering and Editing Data”

? Lesson 7, “Inserting and Deleting Cases and Variables”

? Lesson 8, “Selecting, Copying, Cutting, and Pasting Data”

? Lesson 9, “Printing and Exiting an SPSS Data File”

? Lesson 10, “Exporting and Importing SPSS Data”

? Lesson 11, “Validating SPSS Data”

This text includes a series of step-by-step tutorials for using SPSS statistical software to enter data; generate statistics, charts, and graphs; and format SPSS output in APA style. Tutorials include screenshots as well as real-world examples of the statistics in question.

Datasets

• Pearson Education. (2010). Datasets to accompany Using SPSS for Windows and Macintosh by Green and Salkind [Data file]. Retrieved from http://www.prenhall.com/greensalkind/GreenSalkind.zip copy and paste to retrieve.

Please Note: The SPSS maximum variable data length is 1,500 variables.

Note: You will need a file-compression program, such as WinZip, to unzip this file.

• Main Dataset

Articles

• Corner, P. D. (2002). An integrative model for teaching quantitative research design. Journal of Management Education, 26(6), 671–6 92.

Retrieved from ABI/INFORM Global database.

This article highlights the quantitative research reasoning and process that typifies the stages in a quantitative study. It likens each stage—f ormulating a problem statement, crafting a hypothesis, collecting data, analyzing data, and interpreting findings—to a corresponding step in its proposed integrative model.

Readings

• American Psychological Association. (2010). Publication manual of the American Psychological Association (6th ed.). Washington: Author.

This text is the preferred style manual for business researchers and provides guidance on the formatting and presentation of research conducted with statistical software.

• Boslaugh, S., & Watters, P. A. (2008). Research design. In Statistics in a nutshell. Sebastopol, CA: O’Reilly Media. Retrieved from http://proquest.safaribooksonline.com/book/-/9781449361129

This text teaches the beginning statistician when and how to apply different statistical tests. Written as a resource for those without an extensive statistical background, it includes descriptions, illustrations, and solved examples.

Note: The link above takes you to a preview version of the chapter from the publisher and only includes samples of the pages rather than the full text. Click on the “Next” and “Previous” buttons in the upper right of the page to navigate the chapter.

Websites

• Trochim, W. (2006). Web center for social research methods: Selecting statistics. Retrieved from http://www.socialresearchmethods.net/

This site is an online textbook that addresses the topics of a typical graduate course in social research methods, including sampling, measurement, validity, types of designs, and analysis. Learners can navigate the textbook using a graphical research road map or simple table of contents. The textbook addresses the entire research process as well as the statistical aspects of research and is not software-specific. From the main page, click on the ” Selecting Statistics” link.

**SAMPLE ANSWER**

**Introduction**

The main purpose of this paper is to analyze the dataset aiming to establish trends, patterns relationship, and association and establishing whether there exists a relationship between different variables. Thus, the basis of this paper will be to understand the raw data after analysis (Kraemer, 2015). The output of the analysis will help in noticing different spread and distribution of data. To achieve this SPSS for Windows software will be used to analyze the data provided, notably all the tables and figures will be formatted in American Psychological Association (APA) formatting style. Through this, a masterpiece work will be achieved and some inference drawn about the sample population.

The research will be guided by the following **research question**: **is there a significant difference in injury rate at different working sites when different genders are managing or at a different risk factor?**

The stated research questions will act a blueprint and foundation for all analysis that will be carried out (Kraemer, 2015). The research will be based on **the hypothesis**:

** H _{0}: there is no significance difference in injury rate at different working sites when different genders are managing or at different risk factor. **

**H _{1}: there is a significance difference in injury rate at different working sites when different genders are managing or at different risk factor. **

**Thus, the purpose of this paper is to make an inference reject or fail to reject the set claim. To achieve this, a number of analyses will be carried out at 95% level of significance. **

**Data analysis**

The following tables show the frequency distribution of sites, the gender of the supervisors, and risk factor.

Table 1: Site frequency distribution |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | Boston | 15 | 29.4 | 29.4 | 29.4 |

Phoenix | 19 | 37.3 | 37.3 | 66.7 | |

Seattle | 17 | 33.3 | 33.3 | 100.0 | |

Total | 51 | 100.0 | 100.0 |

Table 2: SupervisorGender frequency distribution |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | Female | 27 | 52.9 | 52.9 | 52.9 |

Male | 24 | 47.1 | 47.1 | 100.0 | |

Total | 51 | 100.0 | 100.0 |

*Table 1* shows that most of the supervisors involved in the research come from Phoenix with a 37.3%, followed by 33.3% from Seattle, and Boston had the least supervisors in the sample. Also, the sample consists 52.9% females and 47.1% males, which is illustrated in *Table 2*.

To answer the research question whether there exists a relationship between genders of the supervisor, the number of employees, the number of working hours, a risk factor with injury rate, a one-way ANOVA was performed (Gelman, 2014). The results are shown in *Table 4.*

Table 4: ANOVA table summary. |
||||||

Sum of Squares | df | Mean Square | F | Sig. | ||

NumEmps | Between Groups | 2263.147 | 33 | 68.580 | 2.136 | .050 |

Within Groups | 545.833 | 17 | 32.108 | |||

Total | 2808.980 | 50 | ||||

Hours_Worked | Between Groups | 9791279435.294 | 33 | 296705437.433 | 2.136 | .050 |

Within Groups | 2361493333.333 | 17 | 138911372.549 | |||

Total | 12152772768.627 | 50 | ||||

SupervisorGender | Between Groups | 7.973 | 33 | .242 | .868 | .648 |

Within Groups | 4.733 | 17 | .278 | |||

Total | 12.706 | 50 | ||||

Risk | Between Groups | 168.286 | 33 | 5.100 | 2.545 | .022 |

Within Groups | 34.067 | 17 | 2.004 | |||

Total | 202.353 | 50 |

The decision here is to reject the null hypothesis when sig. < The critical value (α = 0.05). Since the sig. Value of number of employees, hours worked, supervisors gender are greater or equal to 0.05 we fail to reject the null hypothesis that they have no significance difference (Andraszewicz, 2014). In that matter, we conclude that they show no significant difference at the 95% level of significance. Nevertheless, risk factor shows significance difference since its p-value is less than the critical level.

To measure the nature of the association between these factors with injury rate, a correlation analysis was done on the data set. The results obtained were as follows.

Table 5: Correlations |
|||||||

number of employees | number of hours at work | injury rate | supervisors gender | risk factor | site | ||

number of employees | Pearson Correlation | 1 | 1.000^{**} |
-.636^{**} |
.236 | .351^{*} |
.130 |

Sig. (2-tailed) | .000 | .000 | .096 | .012 | .363 | ||

N | 51 | 51 | 51 | 51 | 51 | 51 | |

number of hours at work | Pearson Correlation | 1.000^{**} |
1 | -.636^{**} |
.236 | .351^{*} |
.130 |

Sig. (2-tailed) | .000 | .000 | .096 | .012 | .363 | ||

N | 51 | 51 | 51 | 51 | 51 | 51 | |

injury rate | Pearson Correlation | -.636^{**} |
-.636^{**} |
1 | -.090 | -.433^{**} |
-.074 |

Sig. (2-tailed) | .000 | .000 | .532 | .001 | .606 | ||

N | 51 | 51 | 51 | 51 | 51 | 51 | |

supervisors gender | Pearson Correlation | .236 | .236 | -.090 | 1 | .096 | -.047 |

Sig. (2-tailed) | .096 | .096 | .532 | .501 | .745 | ||

N | 51 | 51 | 51 | 51 | 51 | 51 | |

risk factor | Pearson Correlation | .351^{*} |
.351^{*} |
-.433^{**} |
.096 | 1 | .272 |

Sig. (2-tailed) | .012 | .012 | .001 | .501 | .054 | ||

N | 51 | 51 | 51 | 51 | 51 | 51 | |

Site | Pearson Correlation | .130 | .130 | -.074 | -.047 | .272 | 1 |

Sig. (2-tailed) | .363 | .363 | .606 | .745 | .054 | ||

N | 51 | 51 | 51 | 51 | 51 | 51 | |

**. Correlation is significant at the 0.01 level (2-tailed). | |||||||

*. Correlation is significant at the 0.05 level (2-tailed). |

As illustrated, there exists a moderate negative correlation between injury rate and risk, number of employees, and number of working hours (Murphy, 2014). However, a weak negative correlation of -0.090) between injury rate and gender of supervisor exists and -0.073986 between injury rate and site (Andraszewicz, 2014).

A model that can predict injury rate using risk, supervisor gender, hours worked, and site as the predictors in the model was as follows;

Injury rate = 53.053735 + 2.559949*(supervisor gender) – 0.000642 * (hours worked) – 2.256611 * (risk) + 1.628766*(site). Nevertheless, the F-table that was obtained after the regression analysis is as tabulated below.

Table 6: ANOVA^{a} |
||||||

Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | 7093.819 | 4 | 1773.455 | 9.980 | .000^{b} |

Residual | 8174.037 | 46 | 177.696 | |||

Total | 15267.856 | 50 | ||||

a. Dependent Variable: InjuryRate | ||||||

b. Predictors: (Constant), Site, SupervisorGender, Hours_Worked, Risk |

The decision rule is to reject the null hypothesis when |F_{ calculated}|> F_{ tabulated. }In this case, F_{ calculated} = 9.980 > F_{ 0.05 (3, 47) }= 2.61, thus we reject the null hypothesis (Kass, 2014). This means in agreement with (Kraemer, 2015) that there exists a significant difference between these variables.

**Conclusion**

To sum up all, the primary objective of the research has been achieved, since an inference has been made about the sample population. The analysis has led to the rejection of the null hypothesis, thus concluding that there is a significance difference in injury rate at different working sites, when different genders are managing or at different risk factor. Hence, in a comprehensive way the questions that were posed at the beginning have been fully answered.

**References**

Kass, R. E., Eden, U. T., & Brown, E. N. (2014). Analysis of Variance. In *Analysis of Neural Data* (pp. 361-389). Springer New York.

Kraemer, H. C., & Blasey, C. (2015). *How many subjects?: Statistical power analysis in research*. Sage Publications.

Andraszewicz, S., Scheibehenne, B., Rieskamp, J., Grasman, R., Verhagen, J., & Wagenmakers, E. J. (2014). An introduction to Bayesian hypothesis testing for management research. *Journal of Management*, 0149206314560412.

Murphy, K. R., Myors, B., & Wolach, A. (2014). *Statistical power analysis: A simple and general model for traditional and modern hypothesis tests*. Routledge.

Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014). *Bayesian data analysis* (Vol. 2). London: Chapman & Hall/CRC.

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