Final Exam for MSC 3370
Refer to: http://onlinestatbook.com/case_studies_rvls/physical_strength/index.html
The link above will take you to a case study on the relationship between physical strength and job performance done using 147 workers as a sample. You are free to explore the links on this page. Note that the following links exist on the left-hand margin of the webpage:
- Background
- Method and Procedure
- Univariate Statistics
- Scatterplots
- Correlations
- Regression
- Raw Data
You will see that the webpage is set up for understanding the process of applying statistics in the real world. Here is what you are expected to do as a part of your Final Exam for this class. First, get familiar with the raw data and copy it over to an Excel sheet. Alternatively, use the Excel Sheet that is included with this assignment. Then, write out the case study in your own words using the following sections. You are expected to run the tables, plots, correlations, and regressions using Excel and provide the tables as a part of your write up. You are also required to submit your Excel file along with your Word document that includes these sections. Include citations where relevant.
- Introduction: Give a short background of the case and describe the potential for a relationship that could exist between the variables being considered. Clearly identify which specific relationship you are interested in (the webpage talks about two relationships, and you can choose which one you would like to pursue for your study).
- Hypothesis: This section should only be about 1 or 2 sentences long with clear null and alternate hypotheses identified separately.
- Data Characteristics: Include the following in this section:
- Summary Statistics – basic statistical table(s) for all variables of interest
- Scatterplots and Correlations – identify which variables need to be plotted and create a correlation table for variables of interest
- Regression Analysis and Results: This is where you would present the results of the regression analysis that tests the relationship, you’re interested in. Discuss the meaning of these results in one or two sentences.
- Conclusion: Identify what is the result of your study and whether you rejected or failed to reject your null hypothesis in one or two sentences.
Introduction:
The report shows the logic behind using statistical principles and methods for solving an applied problem. The exploration of this case shows that several statistical measures were used to carry out the analysis of the problem prescribed. The methods used include correlation, scatter plots, linear regression, descriptive statistics, and multiple regressions.
Background:
For all the physically demanding jobs, the job interview needs to include a measure which can ensure that the interviewers can judge the physical competencies of the interviewees by using it. There are various jobs like mechanics, electrician, etc., which are judged by their requirement to have physical strength. The companies searching for the perfect worker for this type of job cannot take the rehearsals from the interview participants as it would be impractical. The research is based on the measures of Arm strength, and Grip strength of a group of 147 individuals who are working in demanding jobs requiring physical strength. Other than that the performance of the employees is measured through the ratings given by their employers and the results and standardization of the simulations. The following report analyzes the relationship between these variables to find out if any process can be established through which the potential performance of an applicant from its isometric tests can be deduced (RVLS, 2018).
Relationship between Variables
The relationship between the variables is expected to be strongly positive in this research. The strong positive relationship between the variables shows that an increase or decrease in one variable would cause similar behavior in the other variable. The amount of similarity between the behaviors of these variables may vary (Black, 2009).
Hypothesis:
Null Hypothesis | H0:
Negative Correlation exists between the Dependent variables (GRIP and ARM) and independent variables (RATINGS and SIMULATIONS).
Alternate Hypothesis | H1:
Strong Correlation exists between the Dependent variables (GRIP and ARM) and independent variables (RATINGS and SIMULATIONS).
Data Characteristics:
Summary Statistics:
The summary statistics of the variables are shown below.
ARMS:
| ARM | |
| Mean | 78.7517 |
| Standard Error | 1.741069 |
| Median | 81.5 |
| Mode | 69.5 |
| Standard Deviation | 21.10933 |
| Sample Variance | 445.604 |
| Kurtosis | 0.077278 |
| Skewness | -0.30143 |
| Range | 113 |
| Minimum | 19 |
| Maximum | 132 |
| Sum | 11576.5 |
| Count | 147 |
The mean of this variable is 78, and the median is 81. The standard deviation of the variable is 21. The minimum value is 19, and the maximum value is 132 which are the lowest and the highest arm strength which an individual has shown. The Skewness value is negative showing that the distribution of the data is skewed left. The bar chart shows the same skewness with more data on the left side of the axis. In fact, it shows that much data is gathered in the center zone.
GRIP
| GRIP | |
| Mean | 110.2313 |
| Standard Error | 1.948959 |
| Median | 111 |
| Mode | 124.5 |
| Standard Deviation | 23.62987 |
| Sample Variance | 558.3708 |
| Kurtosis | 1.251379 |
| Skewness | 0.023725 |
| Range | 160 |
| Minimum | 29 |
| Maximum | 189 |
| Sum | 16204 |
| Count | 147 |
The mean of this variable is 110, and the median is 111. The standard deviation of the variable is 23. The minimum value is 29, and the maximum value is 189 which are the lowest and the highest arm strength which an individual has shown. The Skewness value is positive showing that the distribution of the data is skewed right. The data of GRIP seems to be more towards the right side of the axis.
RATINGS
| RATINGS | |
| Mean | 41.00988 |
| Standard Error | 0.702872 |
| Median | 41.3 |
| Mode | 32.4 |
| Standard Deviation | 8.521865 |
| Sample Variance | 72.62218 |
| Kurtosis | -0.81351 |
| Skewness | -0.10914 |
| Range | 35.6 |
| Minimum | 21.6 |
| Maximum | 57.2 |
| Sum | 6028.452 |
| Count | 147 |
The mean of this variable is 41, and the median is 41 as well. The standard deviation of the variable is eight lower than GRIP and ARM. The minimum value is 21, and the maximum value is 57 which are the lowest and the highest arm strength which an individual has shown. The Skewness value is negative showing that the distribution of the data is skewed left. The bar chart shows the same skewness with more data on the left side of the axis. In fact, it shows that much data is gathered in the center zone.
SIMULATION
| SIMS | |
| Mean | 0.201769 |
| Standard Error | 0.138479 |
| Median | 0.16 |
| Mode | 0.94 |
| Standard Deviation | 1.678974 |
| Sample Variance | 2.818954 |
| Kurtosis | 0.766815 |
| Skewness | 0.451297 |
| Range | 9.34 |
| Minimum | -4.17 |
| Maximum | 5.17 |
| Sum | 29.66 |
| Count | 147 |
The mean of this variable is 0.2, and the median is 0.16. The standard deviation of the variable is 1.67. The minimum value is -4.17 and the maximum value is 5.17 which are the lowest and the highest arm strength which an individual has shown. The Skewness value is positive showing that the distribution of the data is skewed right. The bar chart shows the same skewness with more data on the right side of the axis. In fact, it shows that much data is gathered in the center zone.
Scatter plots and Correlations
Scatter Plots
The scatter plots show the general trend of the two variables relationship. The scatter plots for each of the pair of variables are shown below.
GRIP & ARM:
The relationship of the GRIP and ARM variable as shown in the scatter plot shows that the data are more scattered irregularly, and thus no linear relationship seems to be existent.
GRIP & RATINGS:
The data for GRIP and Ratings shows that there seems to be some relationship between the variables as most data points exist in the same linear and horizontal zone.
GRIP & SIMS:
The data for GRIP and SIMS shows a similar linear and horizontal relationship as well. The data is mostly scattered in the same zone.
ARM & RATINGS:
As like the ARMS and SIMS, the relationship between these variables is also linearly present and is more gathered in line form.
ARM & SIMS:
It is more of a scattered plot as compared to the last ones showing the weaker the relationship between the two variables ARM and SIMS.
RATINGS & SIMS
Correlation:
| GRIP | ARM | RATING | SIMS | |
| GRIP | 1.00 | 0.63 | 0.18 | 0.64 |
| ARM | 0.63 | 1.00 | 0.22 | 0.69 |
| RATING | 0.18 | 0.22 | 1.00 | 0.17 |
| SIMS | 0.64 | 0.69 | 0.17 | 1.00 |
(Sharma, 2005)
The correlation of all the variables shows that the least correlated variables are the simulations and ratings with a correlation of 0.168 and the highest correlated variables are the arm strength and the work simulations with a correlation of 0.686. Other than these, a stronger correlation is also found in variables; ARM and GRIP (0.63), GRIP and SIMS (0.64). A slightly weaker correlation is found in ARM and Ratings.
Regression Analysis & Results:
Results:
Rating & Arm
| Arm & Rating | |
| Regression Statistics | |
| Multiple R | 0.221280026 |
| R Square | 0.04896485 |
| Adjusted R Square | 0.042405987 |
| Standard Error | 8.339218709 |
| Observations | 147 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 519.1664155 | 519.1664155 | 7.465447789 | 0.007071712 |
| Residual | 145 | 10083.67246 | 69.54256868 | ||
| Total | 146 | 10602.83887 |
(Weisberg, 2013)
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 33.97490742 | 2.665031646 | 12.74840675 | 1.92558E-25 | 28.70758022 | 39.24223461 | 28.70758022 | 39.24223461 |
| ARM | 0.089331025 | 0.032694476 | 2.732297163 | 0.007071712 | 0.024711716 | 0.153950334 | 0.024711716 | 0.153950334 |
The linear Equation:
Rating=0.089(ARM)+ 33.9
ARM & SIMS
| ARM & SIMS | |
| Regression Statistics | |
| Multiple R | 0.686007289 |
| R Square | 0.470606 |
| Adjusted R Square | 0.466955007 |
| Standard Error | 1.225817898 |
| Observations | 147 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 193.6860598 | 193.6860598 | 128.8980799 | 9.01351E-22 |
| Residual | 145 | 217.8812803 | 1.502629519 | ||
| Total | 146 | 411.5673401 |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -4.09515997 | 0.391744551 | -10.4536488 | 2.06184E-19 | -4.869427221 | -3.32089272 | -4.869427221 | -3.320892717 |
| ARM | 0.054562995 | 0.004805903 | 11.35332902 | 9.01351E-22 | 0.045064323 | 0.064061668 | 0.045064323 | 0.064061668 |
(Bobko, 2001)
The linear Equation:
SIMS=0.054(ARM)+ 4.09
GRIP and RATINGS
| GRIP & Rating | |
| Regression Statistics | |
| Multiple R | 0.183257 |
| R Square | 0.033583 |
| Adjusted R Square | 0.026918 |
| Standard Error | 8.406386 |
| Observations | 147 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 356.0773 | 356.0773 | 5.038784 | 0.0263 |
| Residual | 145 | 10246.76 | 70.66732 | ||
| Total | 146 | 10602.84 |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 33.72471 | 3.318697 | 10.16203 | 1.19E-18 | 27.16544 | 40.28398 | 27.16544 | 40.28398 |
| GRIP | 0.06609 | 0.029442 | 2.244724 | 0.0263 | 0.007898 | 0.124281 | 0.007898 | 0.124281 |
(Winkler, 2009)
The linear Equation:
Rating=0.06(GRIP)+ 33.7
GRIP and SIMS
| GRIP & SIMS | |
| Regression Statistics | |
| Multiple R | 0.639845759 |
| R Square | 0.409402595 |
| Adjusted R Square | 0.40532951 |
| Standard Error | 1.294738965 |
| Observations | 147 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 168.4967 | 168.4967 | 100.5141 | 2.68E-18 |
| Residual | 145 | 243.0706 | 1.676349 | ||
| Total | 146 | 411.5673 |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -4.809675182 | 0.511141 | -9.40969 | 1.04E-16 | -5.81992 | -3.79943 | -5.81992 | -3.79943 |
| GRIP | 0.045462988 | 0.004535 | 10.02567 | 2.68E-18 | 0.0365 | 0.054426 | 0.0365 | 0.054426 |
The linear Equation:
SIMS=0.045(GRIP)+ 4.8
Interpretation
Looking at the Linear Equations for all the four regressions conducted will show us the best measure for anticipating physical strength and work performance relationship.
ARM and Rating:
Rating=0.089(ARM)+ 33.9
This linear equation shows that the relationship between the ARM strength and Ratings of the employer is positive and will yield a result which would show the performance of the individual better. The relationship is shown by slope 0.089 which is the highest among the four relationships.
Rating and GRIP:
This linear equation shows that the relationship between the GRIP strength and Ratings of the employer is positive and will yield a result which would show the performance of the individual but not better than the ARM measure. The relationship is shown by the slope 0.06 which is lower than the ARM/Rating measure.
Rating=0.06(GRIP)+ 33.7
ARM and SIMS:
This linear equation shows that the relationship between ARM strength and work simulation results is also positive and will yield a result which would show the performance of the individual but not better than the ARM measure. The relationship is shown by the slope 0.054 which is lower than the ARM/Rating as well as GRIP/Rating measure.
SIMS=0.054(ARM)+ 4.09
GRIP and SIMS:
This linear equation shows that the relationship between the GRIP strength and work simulation results is also positive and will yield a result which would show the performance of the individual but not better than the ARM measure. The relationship is shown by slope 0.045 which is the lowest among all four measures.
SIMS=0.045(GRIP)+ 4.8
Conclusion:
The results show that the null hypothesis is rejected, and the alternative hypothesis is accepted by proving that a positive correlation exists between the dependent and independent variables. The measure, which should be used for the performance evaluation of the physical strength of the individuals, should be Arm strength and Ratings.
References:
Black, K. (2009). Business Statistics: Contemporary Decision Making. Wiley & Sons.
Bobko, P. (2001). Correlation and Regression: Applications for Industrial Organizational Psychology and Management. SAGE.
RVLS. (2018). Physical Strength and Job Performance. Retrieved June 8, 2018, from RVLS: http://onlinestatbook.com/case_studies_rvls/physical_strength/index.html
Sharma, A. (2005). Textbook Of Correlations and Regression. Discovery Publishing House.
Weisberg, S. (2013). Applied Linear Regression. John Wiley & Sons.
Winkler, O. W. (2009). Interpreting Economic and Social Data: A Foundation of Descriptive Statistics. Springer Science & Business.
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