Data Interpretation Practicum Paper
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Week 7 Application: Data Interpretation Practicum
The Pearson product-moment correlation coefficient (Pearson’s correlation) is a measure of the strength and direction of association that exists between two variables measured on at least an interval or ratio scale (Ghauri, 2005). From the data set, several variables will be tested to determine if any relationship occurs among the variables under study. The tests will be conducted at a significance level to determine if the possible relationships occur due to chance or a possible relationship.
Assumptions of Pearson’s correlation
1: The two variables should be measured at the interval or ratio level (i.e., they are continuous)
2: There needs to be a linear relationship between the two variables. Whilst there are a number of ways to check whether a linear relationship exists between the two variables, create a scatter plot using SPSS, where one can plot the dependent variable against the independent variable, and then visually inspect the scatter plot to check for linearity. If the relationship displayed in the scatter plot is not linear, either run a non-parametric equivalent to Pearson’s correlation or transform your data, which can be done using SPSS.
3: There should be no significant outliers. Outliers are simply single data points within your data that do not follow the usual pattern (Ghauri, 2005).
Hypothesis Testing
In this study, the relationship between the number of hours worked and the injury rate will be investigated. The following hypothesis was formulated to study the relationship;
H0: The rate of injury is independent from the number of hours worked in the manufacturing locations.
H1: The rate of injury changes (increases or decreases) with the number of hours worked in the manufacturing locations
To test the above hypothesis, Pearson’s correlation test was conducted to establish if there existed any significant relationship between injury rate and the number of hours worked at a 95% confidence interval using SPSS.
Procedure
Load data into SPSS from the excel spreadsheet. From the data editor menu bar, select analyze and from the drop down menu which pops up, choose correlate and then proceed to bivariate correlation. A bivariate correlations window appears where you choose the variable to test from the left hand side box and move them to the right. Highlight on number of hours worked and move it to the right and repeat the same procedure for the injury rate. From the same window, proceed to the correlation coefficients section and select Pearson by checking in the box preceding it. Proceed to the test of significance section and check the two tailed radio button then select ok to conduct the test (Kumar, 2009).
A linear relationship exists between the variables under study is an important assumption in conducting a Pearson’s correlation. To investigate the presence of this relationship, a scatter plot is drawn using SPSS. The procedure involves; from the SPSS data editor menu bar, select graphs then from the drop down menu that appears, choose legacy dialogs then select scatter/dot plot. A dialog box pops up where you select simple scatter and click define. A simple scatter window appears with the variables on the left hand side from where you highlight on hours worked and move it to the x axis box and then choose injury rate and move it to the y axis box. Click ok to produce the scatter plot using SPSS.
The output obtained from the tests conducted is explained below.
| Correlations | |||
| Hours Worked | InjuryRate | ||
| Hours Worked | Pearson Correlation | 1 | -.636** |
| Sig. (2-tailed) | .000 | ||
| N | 51 | 51 | |
| InjuryRate | Pearson Correlation | -.636** | 1 |
| Sig. (2-tailed) | .000 | ||
| N | 51 | 51 | |
| **. Correlation is significant at the 0.01 level (2-tailed). | |||
Table 1
Decision Rule
Reject H0 if (Creswell, 2003). From table 1 above, p value = 0.000 which is less than 0.05 hence we reject the null hypothesis.
Conclusion
We can conclude that the injury changes (increases or decreases) with the number of hours worked in the manufacturing locations at a 95% level of precision. The Pearson Correlation coefficient posted a result of -0.636 which indicates a strong negative relationship between the injury rate and the number of hours worked. The p value reading of 0.000 confirms that no single outcome occurs due to chance and the test significant. The scatter plot confirms the negative relationship of the 2 variables as indicated by the coefficient (Gay et al, 2009). The scatter plot does not post a perfect relationship of -1 due to the presence of outliers but the strong relationship was confirmed by the scatter dots as shown in figure 1 in the appendix section.
Regression Analysis
Linear regression is the next step up after correlation. It is used when we want to predict the value of a variable based on the value of another variable. The variable we want to predict is called the dependent variable (or sometimes, the outcome variable). The variable we are using to predict the other variable’s value is called the independent variable or sometimes, the predictor variable (Ghauri, 2005).
Assumptions of Regression Analysis
1: The two variables to be studied should be measured at the continuous level (i.e., they are either interval or ratio variables)
2: There needs to be a linear relationship between the two variables. Whilst there are a number of ways to check whether a linear relationship exists between the two variables, one can create a scatter plot using SPSS Statistics where one can plot the dependent variable against the independent variable and then visually inspect the scatter plot to check for linearity.
3: There should be no significant outliers. An outlier is an observed data point that has a dependent variable value that is very different to the value predicted by the regression equation. As such, an outlier will be a point on a scatter plot that is (vertically) far away from the regression line indicating that it has a large residual.
4: There should be independence of observations, which can easily be checked using the Durbin-Watson statistic, which is a simple test to run using SPSS Statistics..
5: Your data needs to show homoscedasticity, which is where the variances along the line of best fit remain similar as you move along the line.
6: Finally, check that the residuals (errors) of the regression line are approximately normally distributed. Two common methods to check this assumption include using either a histogram (with a superimposed normal curve) or a Normal P-P Plot (Ghauri, 2005).
Hypothesis Testing
In this study, the relationship between the number of hours worked and the injury rate will be investigated. The following hypothesis was formulated to study the relationship;
H0: The rate of injury is independent from the number of hours worked in the manufacturing locations.
H1: The rate of injury changes (increases or decreases) with the number of hours worked in the manufacturing locations
To test the above hypothesis, a linear regression or goodness of fit test was conducted to investigate the presence of linear relationship between the 2 variables as stated at 95% level of precision.
Procedure
After loading the data into SPSS, select analyze from the SPSS data editor menu bar. From the drop down menu which appears, choose regression then linear. A dialog box with the variables on the left hand side where injury rate is selected and moved to the dependant variable box while the number of hours worked is moved to the independent variable box. On the right hand side of the same dialog box select plots then move the predictor variable to the x axis and the residuals to the y axis and choose histogram and normal probability plot then click ok to conduct the test (Kumar, 2009). The output obtained is explained below;
| Model Summary | ||||
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
| 1 | .636a | .405 | .393 | 1.361737129585175E1 |
| a. Predictors: (Constant), Hours Worked | ||||
Table 2
| ANOVAb | ||||||
| Model | Sum of Squares | df | Mean Square | F | Sig. | |
| 1 | Regression | 6182.010 | 1 | 6182.010 | 33.338 | .000a |
| Residual | 9086.207 | 49 | 185.433 | |||
| Total | 15268.217 | 50 | ||||
| a. Predictors: (Constant), Hours Worked | ||||||
| b. Dependent Variable: Injury Rate | ||||||
Table 3
| Coefficientsa | ||||||
| Model | Un-standardized Coefficients | Standardized Coefficients | t | Sig. | ||
| B | Std. Error | Beta | ||||
| 1 | (Constant) | 50.809 | 6.459 | 7.866 | .000 | |
| Hours Worked | .000 | .000 | -.636 | -5.774 | .000 | |
| a. Dependent Variable: Injury Rate | ||||||
Table 4
Decision Rule
Reject H0 if (Creswell, 2003). From table 1 above, p value = 0.000 which is less than 0.05 hence we reject the null hypothesis.
Conclusion
We can conclude that the injury changes (increases or decreases) with the number of hours worked in the manufacturing locations at a 95% level of precision. The linear regression model posted an R value of 0.636 which indicates a strong relationship between the injury rate and the number of hours worked as shown in table 2. The R squared reading of .405 indicated that 40% of the variation in the injury rate can be explained by the number of hours worked. Table 3 gives F statistic (F 50= 33.338) which is a measure of the absolute fit of the model to the data. Here, the F-test outcome is highly significant (less than .001, as you can see in the last column), so the model does fit the data. A straight line, depicting a linear relationship, described the relationship between these two variables. Table 4 gives the coefficients of the model as follows; Injury Rate = 50.809+ 0 hours worked (Kumar, 2009). The histogram with a superimposed normal curve and the normal p- p plot confirm the assumption that the residuals (errors) of the regression line are approximately normally distributed shown in figure 2 & 3 in the appendix section
Discriminant analysis which highly related to regression analysis was not the best test to conduct since it is very robust to violations of assumptions and in turn, it can yield less powerful statistics when assumptions are violated (Gay et al, 2009).
References
Creswell, J. W. (2003). Qualitative, quantitative, and mixed methods approaches(2nd ed.). Thousand Oaks, CA: Sage.
Gay, L,R., Mills, E. G., & Airasian, P.,(2009). Educational Research: Competencies for Analysis and Applications (10th ed.)
Ghauri, P. (2005). Research Methods in Business Studies: a Practical Guide.
Kumar, R. (2009). Research Methodology: A step-by-step Guide for Beginners. Greater Kalash: Sage Publications.
Appendix
Figure 1
Figure 2
Figure 3
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