# Descriptive Statistics AnalysisDescribe the Sun Coast data using the descriptive statistics tools discussed in the unit lesson. Establish whether assumptions are met to use parametric statistical proc

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Must be familiar with Excel

Descriptive Statistics Analysis

Describe the Sun Coast data using the descriptive statistics tools discussed in the unit lesson. Establish whether assumptions are met to use parametric statistical procedures. Repeat the tasks below for each tab in the Sun Coast research study data set. Utilize the Unit IV Scholarly Activity template

here

.

You will utilize Microsoft Excel ToolPak. The links to the ToolPak are

here

in the Course Project Guidance document.

Here are some of the items you will cover.

- Produce a frequency distribution table and histogram.
- Generate descriptive statistics table, including measures of central tendency (mean, median, and mode), kurtosis, and skewness.
- Describe the dependent variable measurement scale as nominal, ordinal, interval, or ratio.
- Analyze, evaluate, and discuss the above descriptive statistics in relation to assumptions required for parametric testing. Confirm whether the assumptions are met or are not met.

The title and reference pages do not count toward the page requirement for this assignment. This assignment should be no less than

five pages in length,

follow APA-style formatting and guidelines, and use references and citations as necessary.

Descriptive Statistics AnalysisDescribe the Sun Coast data using the descriptive statistics tools discussed in the unit lesson. Establish whether assumptions are met to use parametric statistical proc

Running head: INSERT TITLE HERE 0 Sun Coast Remediation Course Project Guidance Background To help make a connection between business research and its use in the real world, this course will use an iterative course project. Throughout the term, you will serve as the health and safety director for Sun Coast Remediation (Sun Coast). Sun Coast provides remediation services to business and governmental organizations. Most of their contracts involve working within contamination sites where they remove toxic substances from soil and water. In addition to the toxicity of the air, water, and soil their employees come into contact with, the work environment is physically demanding and potentially contributory to injuries involving musculoskeletal systems, vision, and hearing. Sun Coast genuinely cares about the health, safety, and well-being of their 5,500 employees, but they are also concerned about worker-compensation costs and potential long-term litigation from injuries and illness related to employment. Health and Safety Director Task Sun Coast hired you last month to replace the previous health and safety director, who left to pursue other opportunities. This is a critical position within the company because there are many health and safety-related issues due to the nature of the work. Throughout the term you will use your knowledge of research methods to bring the proposal to fruition. You will conduct a literature review, develop research questions and hypotheses, create the research design, test data, interpret data, and present the findings. Each unit will accomplish one of these tasks. It has already been decided that the business problems will be best addressed using a quantitative research methodology. You will not collect any data for this project. All data will be provided for you. Statistical Tools You will conduct the data analysis using Microsoft Excel Toolpak. See the links below for more information. https://support.office.com/en-us/article/load-the-analysis-toolpak-in-excel-6a63e598-cd6d-42e3-9317-6b40ba1a66b4 https://www.excel-easy.com/data-analysis/analysis-toolpak.html Sun Coast Remediation Course Project Sections Since this is a quantitative research study, there are specific steps that should be followed. The following is a template that will help you develop your project. (It is also provided as a separate template in Unit VII.) Use this information to guide your completion of the course project. See the templates provided in each unit to properly format your assignments in proper APA style. Insert Title Here Insert Your Name Here Insert University Here Table of Contents Include the table of contents here. There is a tool for creating a table of contents on the References tab of the Microsoft Word tool bar at the top of the screen. Executive Summary The executive summary will go here. The paragraphs are not indented. It is formatted like an abstract. Sun Coast Remediation Course Project Introduction Senior leadership at Sun Coast has identified several areas for concern that they believe could be solved using business research methods. The previous director was tasked with conducting research to help provide information to make decisions about these issues. Although data were collected, the project was never completed. Senior leadership is interested in seeing the project through to fruition. The following is the completion of that project, and includes statement of the dilemmas, literature review, purpose statements, research methodology, design, and methods, research questions and hypotheses, data analysis, and findings. Statement of the Problems/Dilemmas There were six business dilemmas identified. Particulate Matter (PM) There is a concern that job-site particle pollution is adversely impacting employee health. Although respirators are required in certain environments, particulate matter (PM) varies in size depending on the project and job site. PM between 10 and 2.5 microns can float in the air for minutes to hours (e.g. asbestos, mold spores, pollen, cement dust, fly ash), while PM less than 2.5 microns can float in the air for hours to weeks (e.g. bacteria, viruses, oil smoke, smog, soot). Due to the smaller size of PM less than 2.5 microns, it is potentially more harmful than PM between 10 and 2.5 since the conditions are more suitable for inhalation. PM less than 2.5 are also able to be inhaled into the deeper regions of the lungs, potentially causing more deleterious health effects. It would be helpful to understand if there is a relationship between PM size and employee health. Air quality data have been collected from 103 job sites, which is reflected in PM size. Data is also available for average annual sick days per employee per job-site. Safety Training Effectiveness Health and Safety training is conducted for each new contract that is awarded to Sun Coast. Data for training expenditures and lost-time hours were collected from 223 contracts. It would be valuable to know if training has been successful in reducing lost-time hours and, if so, how to predict lost-time hours from training expenditures. Sound-Level Exposure Sun Coast’s contracts generally involve work in noisy environments due to a variety of heavy equipment being used for both remediation and the clients’ ongoing operations on the job sites. Standard ear-plugs are adequate to protect employee hearing if the decibel levels are less than 120 decibels (dB). For environments with noise-levels exceeding 120 dB, more advanced and expensive hearing protection is required, such as ear-muffs. Data have been collected for the primary variables that are believed to contribute to excessive noise. It would be important if these data could be used to predict the dB levels of work environments before placing employees on site. New Employee Training All new Sun Coast employees participate in general health and safety training. The training program was revamped and implemented six months ago. Data is available for two Groups; a) Group A employees who participated in the previous training program, and b) Group B employees who participated in the revised training program. It is necessary to know if the revised training program is more effective than the prior training program. Lead Exposure Employees working on job sites to remediate lead must be monitored. Lead levels in blood are measured as micrograms of lead per deciliter of blood (μg/dL). A base-line is taken pre-exposure, then post-exposure at regular intervals, and at the conclusion of the remediation. Data are available for 49 employees who recently concluded a two-year-long lead remediation project. It is necessary to determine if blood lead levels have increased. Return-On-Investment Sun Coast would like to know if all lines of service provide the same return-on-investment. Return-on-investment data is available for air monitoring, soil remediation, water reclamation, and health and safety training. If return-on-investment is not the same for all lines of service, it would be helpful to know were differences exist. Literature Review Include this information here. Important Note: Students should refer to the information presented in Unit I and the Unit I assignment to complete this section of the project. Research Objectives Include this information here. Students should compose short, direct, statements about the objectives of the study. Important Note: Students should refer to the problems/dilemmas Sun Coast is facing and to the information presented in Unit II and the Unit II assignment to complete this section of the project. Delete this. Research Questions and Hypotheses Students should state the research questions and hypotheses. Each problem/dilemma that they are researching should have one research question and a null and alternative hypothesis. In total, there should be six research questions and 12 hypotheses, as shown below. Important Note: Students should refer to the information presented in Unit II and the Unit II assignment to complete this section of the project. Delete this before you begin. RQ1 H01 HA1 RQ2 H02 HA2 Continue with the remaining research questions and hypotheses. Research Methodology, Design, and Methods Students should detail the research design they have selected and why it is an appropriate research approach for addressing the business dilemmas. The following subheadings can be used to include all required information. Delete this statement. Research Methodology Explain the research methodology chosen for this research project and provide rationale for why it is appropriate given the problems/dilemmas. Research Design Students should explain whether the research design is exploratory, explanatory, or descriptive. Provide rationale for the choice. Research Methods Describe the research methods that will be used for this research study. They may include survey, observation, experimentation, descriptive, correlation, or causal-comparative. Data Collection Methods Students should specify how the data were collected to test the hypotheses. Data collection methods include, but are not limited to, survey, observation, and records analysis. Sampling Design Students should briefly describe the type of sampling design that was most likely used for the data that were collected. Choices include, but are not limited to, random sample, convenience sample, etc. Explain your rationale for your sampling design selection(s). Data Analysis Procedures Students should specify which statistical procedures were used to test each set of hypotheses from among correlation, regression, t test, and ANOVA. They should explain why each procedure was the most appropriate choice. Data Analysis Student narrative should restate the null and alternative hypotheses for each of the six business dilemmas, indicate the p-value of the results, and explicitly accept or reject the null and alternative hypotheses. Exceptional submissions will explain if assumptions for parametric testing were met. Students should provide the Excel Toolpak results of their statistical analyses. At a minimum, histograms, descriptive statistics, and the statistical tests should be cut and pasted from Excel directly into the final project document. For the regression hypotheses, the students should display and discuss the predictive regression equation. Correlation Analysis Descriptive statistics and assumption testing. Include this information here. Delete these statements before you begin. Hypothesis testing. Include this information here. Delete these statements before you begin. Simple Regression Analysis Descriptive statistics and assumption testing. Include this information here. Delete these statements before you begin. Hypothesis testing. Include this information here. Delete these statements before you begin. Multiple Regression Analysis Descriptive statistics and assumption testing. Include this information here. Delete these statements before you begin. Hypothesis testing. Include this information here. Delete these statements before you begin. Independent Samples t Test Descriptive statistics and assumption testing. Include this information here. Delete these statements before you begin. Hypothesis testing. Include this information here. Delete these statements before you begin. Paired Samples t Test Descriptive statistics and assumption testing. Include this information here. Delete these statements before you begin. Hypothesis testing. Include this information here. Delete these statements before you begin. One-Way ANOVA Descriptive statistics and assumption testing. Include this information here. Delete these statements before you begin. Hypothesis testing. Include this information here. Delete these statements before you begin. Findings Students should discuss the findings in the context of Sun Coast’s problems/dilemmas and the associated research questions. The following are some key points that students should make based on the statistical results. Important Note: Students should refer to the information presented in Unit VII and the Unit II assignment to complete this section of the project. RQ1 Is there a relationship between particulate matter size and employee sick days? RQ2 Is there a predictive relationship between safety training expenditure and lost time hours? Continue to provide findings in association with the research questions. Recommendations Include this information here with paragraphs. Delete this statement before you begin your assignment. Conclusion Include this information here with paragraphs. Delete this statement before you begin your assignment. References Include references here using hanging indentations, and delete these statements and example reference. Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Thousand Oaks, CA: Sage. Appendices

Descriptive Statistics AnalysisDescribe the Sun Coast data using the descriptive statistics tools discussed in the unit lesson. Establish whether assumptions are met to use parametric statistical proc

MBA 5652, Research Methods 1 Cou rse Learning Outcomes for Unit IV Upon completion of this unit, students should be able to: 6. Differentiate between various research -based tools commonly used in businesses. 6.1 Describe various forms of descriptive statistics, including frequency distribution tables, histograms, descriptive statistics tables, K olmogorov -Smirnov tests, m easurement scales, and measures of central tendency. 7. Test data for a business research project. 7.1 Establish whether assumptions are met to use parametric statistical procedures by applying descriptive statistics. Course/Unit Learning Outcomes Learning Activity 6.1 Unit Lesson Video: Kolmogorov -Smirnov Test of Normality in Excel Video: Parametric and Nonparametric Statistical Tests Video: Checking that Data Is Normally Distributed Using Excel Video: 3. Choosing Between Parametric & Non -Parametric Tests Article: “Difference Between Para metric and Nonparametric” Article: “Deciphering the Dilemma of Parametric and Nonparametric Tests” Unit IV Scholarly Activity 7.1 Unit Lesson Unit IV Scholarly Activity Reading Assignment In order to access the following resources, click the links below: Fields, H. (2018). Difference between parametric and nonparametric . Retrieved from http://www.differencebetween.net/science/difference -between -parametric -and -nonparametric/ Dominguez, V. (2016, April 16). Make a h istogram using Excel’s histogram tool in the Data Analysis ToolPak [Video file]. Retrieved from https://www.youtube.com/watch?v=xekiDJzajYk Click here for a transcript of the video. Grande, T. (2017 , August 19 ). Kolmogorov -Smirnov test of normality in Excel [Video file ]. Retrieved from https://www.youtube.com/watch?v=cltWQsmBg0k Click here for a transcript of the video. Grande, T. ( 2015 , July 30 ). Parametric and nonparametric statistical tests [Video file ]. Retrieved from https://www.youtube.com/watch?v=pW EWHKnwg_0 Click here for a transcript of the video. UNIT IV STUDY GUIDE Data Analysis: Descriptive Statistics MBA 5652, Research Methods 2 UNIT x STUDY GUIDE Title Macarty, M. (2015, September 21). Get descriptive s tatistics in Excel with Data Analysis Toolpak [Video file]. Retrieved from https://www.youtube.com/watch?v=h -RzBhBzJOQ Click here for a transcript of the video. Oxford Academic (Oxford University Press). (2016 , November 17 ). Checking that data is norm ally distributed using Excel [Video file] . Retrieved from https://www.youtube.com/watch?v=EG8AF2B_dps Click here for a transcript of the video. Rana, R., Singhal, R., & Dua, P. (2016). Deciphering the dilemma of parametric and nonparametric tests. Journal of the Practice of Cardiovascular Sciences , 2(2), 95. Retrieved from http://link.galegroup.com.libraryresources.columbiasouthern.edu/apps/doc/A488649197/AONE?u=ora n95108&sid=AONE&xid=c54ea f34 The Roslin Institute – Training. (2016 , May 9 ). 3. Choosing between parametric & non -parametric tests [Video file]. Retrieved from https://www.youtube.com/watch?v=_1mH6CnXKfM Click here for a transcript of the video. Unit Lesson Data Analysis: Descriptive Statistics The course is now entering the data analysis stage of research design. This is where the methodological fork in the road goes decisively down the quantitative path. The first topic of discussion under data analysis will be what is referred to as descriptiv e statistics. As the name suggests, the researcher describes the data that are collected. During this stage, the data are described both visually and statistically. Data may be visually displayed to reveal distribution of data, trends, anomalies, outliers, etc. Visual displays of data may take the form of graphs, histograms, tables, plots, and other diagrams. This stage is done before any statistical procedures are used to test the research hypotheses. This begs the question of why the researcher should not simply jump in and immediately start testing their hypotheses using statistical analysis. The following explains the importance of descriptive statistics to test data to ensure assumptions are met before using a parametric test. MBA 5652, Research Methods 3 UNIT x STUDY GUIDE Title Assumptions : The Importan ce of Describing Data There are various benefits of describing the data. One of the most important benefits is to determine if the data meet the assumptions that are required for the use of parametric statistical procedures. Parametric procedures include, but are not limited to , correlation, regression, t test , and ANOVA. Parametric tests have different assumptions that must be met depending on which test is being considered, but most parametric tests require that the assumption of normality be met. Normality refers to a normal distribution of data which, when graphed as frequencies, resembles a bell shape (as in the image to the right) . Other common assumptions that must be met, depending on the statistical procedure used, include sample size, levels – of-measurement, homogeneity of variance, independence, absence of outliers, linea rity, etc. (Field, 2005). It is crit ical that the researcher understands the assumptions for any parametric statistical procedure being considered to determine if they are met before employing the pro ced ure in a research study. An I nternet search for any parametric test will quickly return results that list required assumptions. If the assumptions are not met, parametric statistical procedures cannot be used. To use them would result in invalid results. Fortunately, there are corresponding non -parametric tests that can be used when the data do not meet assumptions for parametric tests. Non -parametric tests also have assumptions that must be met, but they are fewer and less rigid. An example of a parametri c procedure for correlation would be Pearson’s correlation coefficient (Pearson’s r), while a corresponding non -parametric test for correlation would be Spearman’s rank correlation coefficient (Spearman’s rho) . An example of a causal -comparative parametric procedure would be ANOVA, while a corresponding non -parametric causal -comparative test would be Kruskal -Wallis. Since non -parametric tests do not require that as many assumptions are met, some students wonder why non -parametric tests are not always used. The reason is that parametric tests are superior to and more powerful than non -parametric tests and should be used if the assumptions are met. A parametric test is more likely to find a true effect when one exists, therefore rejecting the null hypothesis, than a non -pa rametric test (Norusis, 2008). In other words, a parametric test is less like ly to commit a Type II error. Norusis (2008) recommends that researchers conduct both parametric and non -parametric tests if they are unsure as to which is most appr opriate to use. If the test results are the same, there is nothing more to worry about. If the test results are statistically significant for the parametric test, and non -significant for the non -parametric test, the researcher should take a closer look at whether the assumptions were met or not . Assumption of Normality Assumptions are evaluated both visually and statistically. As mentioned previously, a normal distribution of data is the most commonly required assumption for parametric statistical tests. The following will explain how the assumption of normality can be described and tested. A normal distribution of data exhibits the characteristics of a bell -shaped curve, as shown below. In a perfect normal curve, the frequency distribution is symmetrical about the center ; the mean, median, and mode are all 80 70 60 50 40 30 20 10 Bell Curve 10 20 30 40 50 60 70 80 90 100 Normal distribution gr aph with a bell curve MBA 5652, Research Methods 4 UNIT x STUDY GUIDE Title equal ; and the tails of the curve approach but do not touch the x-axis (Salkind, 2009). T hese are all preliminary indicators that a curve may represent a normal distribution, but there are additional factors to consider. Distribution curves can be short and wide, t all and thin, and anywhere in between. As shown below, each of the colored bell -shaped curves has a mean (μ) of zero. Their standard deviations (σ) , however, or the me asure of how widely the data disperses around the mean, are different for each curve. The orange curve has a relatively small standard deviation because the data is closely clustered around the mean. The red curve has a relatively large standard deviation because the data is loosely clustered around the mean. Kurtosis describes the tallness of the curve s. A platykurtic curve is short and squatty (think plateau), which, as shown at the right in the red curve, represents a relatively greater number of scores in the tails of the curves. A leptokurtic curve is tall and thin (think leapt for the sky), which, as shown in the orange curve, represents a data distribution of relatively fewer number of scores in the tails (Field, 2005). Platykurtic and leptokurtic cu rves can challenge the assumption of normal ity, even when the curve is bell -shaped. The data may also be asymmetrical with the data more heavily distributed to one side of the curve or the other. When the data distribution curve is asymmetrical, it is ref erred to as skewness. Below are examples of negative skewness and positive skewness. Like p latykurtic and leptokurtic curves, those exhibiting skewness also threaten the assumption of normality. The assumption of normality can be evaluated visually by describing the frequency of responses in a data set. The frequency table below shows the results of a 120 -point safety test administered to 500 employees. For example, two employees scored in the tes t range of 50 –54, 90 employees scored in the range of 85 –89, and three employees scored in the range of 110 –114. Left -skewed and right -skewed graphs (Sundberg, 201 4) Distribution curves MBA 5652, Research Methods 5 UNIT x STUDY GUIDE Title When the frequency data is plotted in a histogram, the curve of the data can be observed. To create a histogram, the data values (test score ranges) from the data set are plotted on the x-axis , and the frequency of the values are plotted on the y-axis. So , using the same example from the discussion of the frequency table, it can be seen in the histogram that two employees scored in the test ran ge of 50 –54, 90 employees scored in t he range of 85 –89, and three employees scored in the range of 110 –114. By observing the histogram below, it appears the data are approximately normally distributed , and there are no visible outliers. While there is no skewness observed, the kurtosis favors a leptokurtic curve. Skewness and kurtosis can be confirmed by generating descriptive statistics, which is a routine function in statistical packages, including Excel Data Analysis Toolpak. There is a lot of debate re garding acceptable level s of skewness and kurtosis among researchers. George and Mallery (2010) suggest skewness and Kurtosis scores between -2 and +2 as satisfactory results to accept normal distribution. All researchers agree that t he closer skewness and kurtosis are to 0, the better. The more kurtosis and skewness deviate from 0, the greater the chances that the data is not normally distributed (Field, 2005). As shown in the descriptive statistics table, both skewness and kurtosis ar e both relatively clo se to 0. It should also be noted that the mean, median, and mode are similar in the descriptive data table below. As noted above, the mean, median, and mode are identical in a perfect distribution. The data presented here would suggest that it is approx imately a normal distribution of data. MBA 5652, Research Methods 6 UNIT x STUDY GUIDE Title Descriptive Statistics Mean 80.546 Standard Error 0.446621439 Median 81 Mode 75 Standard Deviation 9.986758969 Sample Variance 99.73535471 Kurtosis 0.095314585 Skewness 0.065078019 Range 64 Minimum 53 Maximum 117 Sum 40273 Count 500 Largest(1) 117 Smallest(1) 53 The frequency distribution should also be observed for outliers. Outliers are extreme scores far away from the mean in the left or right tails of the curve. Outliers can bias the mean due to their extreme scores. There are different recommendations for how to treat outliers, such as removing the outlier from the data set, but the ramifications should be understood before taking any such action. This is an example where consulting the literature is strongly recommended. Finally, normality can be tested statistically. Several tests can be used to objectively test for normality including Kolmogorov -Smirnov, Shapiro -W ilk, chi -square, Jarque -Bera, Anderson -Darling, and others. Each test has advantages and disadvantages. Once again, this is where the researcher is well -serve d to consult the literature to determine the most appropriate test for his or her project. The Kolmogorov -Smirnov (KS) test is often used to test for normality. KS compares the frequency distribution of the sample data set to a model of normally distribut ed data with the same mean and distribution as the sample d ata. The KS test is performed to test a null and alternative hypothesis, like any other statistical test. The following are the hypotheses . Ho1: There is no statistically significant difference in normality between the sample data and model data. Ha1: There is a statistically significant difference in normality between the sample data and model data. If the results are statistically significant at a p level < .05, the null hypothesis is rejected , and the alternative hypothesis is accepted that there is a statistically significant difference in normality between the sample data and model data. Therefore, we would conclude that the assumption of normality is not met , and a non – parametric test would be required to test our data. If the results are not statistically significant at a p level > .05, the null hypothesis is accepted (and the alternative rejected) that there is no statistically significant difference in normality between the sample data an d model data. Therefore, we would conclude that the assumption of normality is met , and a parametric test would be acceptable to test our data. It is important to note that the above steps for evaluating the assumption of normality require a holistic view . No single description of the data is sufficient to make a decision about normality. For example, the KS test is sensitive to small changes in normality for large sample sizes. The result is that it can be prone to Type I errors. Therefore, the researcher should consider all the available inform ation, both visual inspection and statistical analysis, before making a decision about normality (Field, 2005). If, after following the steps above, MBA 5652, Research Methods 7 UNIT x STUDY GUIDE Title the assumption of normality does not appear to be met, non -paramet ric statistical procedures should be considered in lieu of parametric tests. Assumptions Other Than Normality There are two additional assumptions that should be met for any statistical test. They are measurement scales and measures of central tendency. Measurement scales : Statistical procedures used to test hypotheses have unique assumptions about the scales on which the data are measured . Data are measure d on nominal, ordinal, interval, or ratio scales. It is important to determine the assumption of measurement scales for any statistical procedure being considered to test the data. For example, an assumption of Pearson’s r is that data be measured at the in terval or ratio level. Pearson’s r could not be used to analyze ordinal data. The non -parametric test, Spearman’s rho, would be required to analyze ordinal data for correlation. Rules for Measurement Scales Nominal: Nominal data can be classified but not ordered and have no meaningful distance between variables or unique origin (true zero). This is also referred to as categorical data. Examples include names or categories, like gender and marital status. Examples of statistical procedures that use nominal data include chi -square (Cooper & Schindler, 2014). Ordinal: Ordinal data can be classified and ordered but have no meaningful distance between data values or unique origin (true zero). Examples include survey s with responses ranked on a five -point Liker t scale, such as strongly agree to strongly disagree. Examples of statistical procedures that use ordinal data include Spearman’s rho, Mann -W hitney test, Wilcoxon test, Kruskal -Wallis test, and Friedman test (Cooper & Schindler, 2014). Interval: Interval data can be classified and ordered and have meaningful distance between data values but no unique origin (true zero). A classic example of an interval level of measurement is temperature measured in degrees. The data is ordered, there are differe nces between measures, but there is no true zero. Since there is no true zero, it would be improper to say 40 degrees is twice as cold as 20 degrees. Examples of statistical procedures that use interval data include Pearson’s r, regression analysis, t test , and ANOVA (Cooper & Schindler, 2014). Ratio: Ratio data can be classified and ordered, have meaningful distance between data values, and have unique origin (true zero). Examples include age in years and income in dollars. Examples of statistical procedures that use ratio data include Pearson’s r, regression analysis, t test, and ANOVA (Cooper & Schindler, 2014). It should be noted that parametri c tests are used to analyze data measure at the interval and ratio levels but cannot be used to analyze data measured at the nominal and ordinal levels. Measures of central tendency : It may have become evident by now, from the use of the histogram and the discussion of normality, that there is interest in how the data points are dispersed around the mid -point of the curve. This is called central tendency and is the foundation for stati stical analysis using linear models. In short, our statistical procedures evaluate how much our data vary from that midpoint when a straight line is fit to the data (Field, 2005). The important takeaway is that the central tendency of that midpoint can be measured in three different ways : a) mean, b) median, and c) mode. As was seen in the descriptive statistics output above, mean, median, and mode are usually included in descriptive statistics generated by software. As was the case with normality and level s of measurement, i t is important to determine the assumption of central tendency for any statistical procedure being considered to test the data. Mean: The arithmetic mean is the most commonly used measure of central tendency. It is calculated by adding the data scores and dividing by the number of cases. The mean is the measure of central tendency used with interval and ratio data and is used for statistical procedures like correlation, regression analysis, t test, and ANOVA (Salkind, 2009). Median : The median is the score among the distribution of data, when ordered from highest to lowest, where half of the data points occur above the median and half of the data points occur below the median. In the data MBA 5652, Research Methods 8 UNIT x STUDY GUIDE Title set 1, 3, 5, 7, and 9, the median would be 5 sinc e half of the values occur above and half below. The median is the measure of central tendency used with ordinal data (Salkind, 2009). Mode: The mode is the data value that occurs most frequently in the data set, regardless of order. In a data set of 5, 5, 5, 3, 3, 9, 9, 9, 9, 1, 1, 1, 7, 7, 7, 7, 7, the mode would be 7 because it is the value that occurs most frequently in the data set. The mode is the measure of central tendency used with nominal levels of measurement (Salkind, 2009). In Closing — A Word About Validity and Reliability Although some of the most important and common assumptions of statistical testing have been discussed in this lesson , there are still more. This may seem like a very taxing and laborious process to partake in before even get ting to the point of testing the research hypotheses. It is absolutely critical that researchers ensure assumptions are met to have certainty that their results reflect the integrity of validity and reliability. To be able to make confident decisions usin g research, the statistical results must be both valid and reliable. Validity means that the statistical procedure measures what was intended to be measured. As was discussed about normality, if a parametric statistical procedure is used for a data set tha t lacks a normal distribution of data, the results will be invalid. Reliability refers to repeatability. If a second research study was conducted by replicating the conditions of the original research study (e.g. , sampling, data collection, levels of meas urement, statistical test, etc.), the results should be similar if the original research results were reliable. It should also be noted that research results can be reliable but not valid. It is conceivable that a research study could be replicated multip le times and reliably generate the same invalid results each time. A classic example is the broken bathroom scale. Assume a person’s actual weight is 150 pounds. Each morning , for a week they step on the bathroom scale and the reading is 145 pounds. The me asurement is invalid because, due to calibration problems, the measurement is incorrect. The test, however, is reliable because the same result was replicated each day. For research results to have integrity, they must be both valid and reliable. Referen ces Cooper, D. R., & Schindler, P. S. (2014 ). Business research methods (12th ed.). New York , NY : McGraw – Hill /Irwin. Field, A. (2005). Discovering stats using SPSS (2nd ed.). London, England: Sage. George, D., & Mallery, P. (2010). SPSS for Windows step by step: A simple guide and r eference , 17.0 update (10 th ed.) . Boston , MA : Pearson. Norusis, M. J. (2008). SPSS 16.0 guide to data analysis (2nd ed .). Upper Saddle River, NJ: Prentice Hall. Salkind, N. J. (2009). Exploring research (7th ed.). Upper Saddle River, NJ: Pearson. Sundbe rg, S. (2014). Skewed distribution: Definition, examples [Image]. Retrieved from http://www.statisticshowto.com/probability -and -statistics/skewed -distribution/

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