# Free Analyzing SPSS (Pasw) Software: Part 1 Essay Sample

## Introduction

According to Dembe et al., (2005), established working in jobs which had an overtime plan was associated with an increased chance of injury rate when compared to jobs that had no overtime plan. Specifically, working for 12hours per week was associated with a 37% increase in the injury rate. Although long working hours are associated with an increase in the exposure of the employee to the risk of work-related injuries, it has been established that long working hours significantly affects the wellbeing of employees.

In an analysis that consisted of 110,236 job records, the article proved that long working hours affect the health of a worker. Furthermore, studies have indicated that employees on overtime work plans have an increased chance of hypertension, cardiovascular disease, fatigue and musculoskeletal ailments. All these conditions increase the probability of an individual experiencing injury at the workplace (Dembe et al., 2005).

## Thesis Statement

The objective of this study is to establish if there is a relationship between injury rate and the umber of hours worked by the employee. The study considers employees and supervisors from three sites that make up a manufacturing firm. The outcomes of the study will be used in structuring a safety policy that will be used to reduce injury rates at the work place.

## Research Question

There is a probably a relationship between the number of actual hours worked by all employees in the team for the 12-month period and the average rate of injury per a hundred employees for the 12-month period. The injury rate is expected to increase with an increase in the number of actual hours worked by all the employees in the area for the 12 month period. The research question that the analysis is trying to answer is; Do the injury rate increase with an increase in hours worked?

## Hypotheses

We are testing the null and the alternative hypothesis to determine which is true according to the analysis done on the data presented. The null (H0) and alternative hypothesis (H1) will be;

H0: The number of hours worked by an employee in the 12 month period does not have any effect on the injury rate on any of the three manufacturing sites of the company.

H1: The number of hours worked by the employee in the 12 month period has an effect on the injury rate on any of the three manufacturing sites of the company.

## Results

The number of supervisors that participated in the study was 51. Hours worked represents the number of actual hours that were worked by all the employees in the team for the 12 month period. Injury rate represents the average rate of injuries 100 employees over the 12 month period. The mean number of hours worked by the employees for the 12 month period ending 12/31/2009 was 49960.78 and its standard deviation is 15590.24. the minimum hours worked was 10400 and the maximum hours worked was 93600 therefore the range is (93600-10400)= 83200. the standard error of the mean is 2183.07 and this gives the limits within which the mean lies to be 47777.71 and 52143.85. the variance of the variable hours worked is 243055455.37.

The mean injury rate was 15.176 and the standard deviation was 17.475. the range is 76.923 which is obtained by subtracting the minimum value 0 from the maximum value 76.923. the standard deviation and the range are a measure of how far the values of a data set are dispersed. The high standard deviation of the variable injury rate compared to the mean indicate that the values of the variable are highly dispersed. The standard error is an estimate of the standard deviation of the sample mean through the use of the population mean. The standard error of the mean can be used to estimate the limits within which the mean of a variable. Thus the standard error of 2.447 imply that the range within which the mean can be found is between 12.729 and 17.623. the variance of the variable injury rate is 305.36.

The minimum value for safe act representation is 0.423 and the maximum value is 1, the range is calculated to be 0.577. the mean value of the safe act representation is 0.866 and its standard deviation is 0.139. the standard error of the mean is 0.019 which gives a limit of 0.847 and 0.885. the variance of the variable safe act is 0.000361.

A linear regression is conducted to establish if there is a relationship between the variables injury rate and hours worked. Table 1 contains the descriptive statistics for the variables hours worked, and injury rate. A scatterplot is used to observe if the association is distinct and then a parametric test is used to establish if the relationship is significant. Figure 1 below is the scatterplot of the variable hours worked against injury rate. Figure 2 is a boxplot to determine if the outliers have an effect on the relationship between the variables injury rate and hours worked. There appears to be a high negative correlation between the variables injury rate and hours worked. However, this will have to be confirmed in the linear regression analysis through observation of the significance p-value.

The test is significant and as such we reject the null hypothesis that there is no association between the hours worked and injury rate. The F statistic F (1, 49) = 33.338, p = 0.00 < 0.05.

Therefore, we accept the alternative hypothesis that there is a significant relationship between the variables injury rate and hours worked. The 95% confidence interval of the gradient is (-0.001, 0.00). The standardized regression equation is predicted injury rate = -0.001 (Hours worked) + 50.809.

Figure 1: Scatterplot of Injury Rate against Hours Worked.

## Discussion

The scatterplot does not indicate a clear relationship between the injury rate and the hours worked because of the dispersed values. The upper bound of the 95% confidence interval of the slope is 0.00, and the lower limit is -0.001. The appendix contains a table with the 95% confidence interval of the coefficients. The value of the slope is somewhere within the range of these values. The values for the 95% confidence interval of the slope indicate that the change in injury rate is minuscule and in some instance it can be taken to be zero. Therefore, the 95% confidence interval of the slope indicate that there could be no relationship between the injury rate and the hours worked. The value of R2 is, however, large 0.405, which is interpreted to mean that the one variable can explain 40.5% of the variance of another variable. The significance level is also high because even if we were to set our rejection criterion at 0.01 significance level, the test would still be significant. Note that a significance level of 0.01 is too strict a standard as it increases the probability of rejecting a true null hypothesis. Therefore, since both the p-value and the coefficient of determination value (R2) support the alternative hypothesis, then the hours worked and injury rate have a significant relationship. The slope of the graph is minuscule, and as such it tends to reduce the value obtained when it is multiplied by hours worked. As such the values obtained for injury rate from the standardized regression equation are within the required limits (Groove, 2007).

## Conclusion

Figure 2: Boxplot of the variable injury rate.

When we exclude outliers from the data set, he test is still significant at 0.05 significance level although the values for F=10.104, R2=0.183, the gradient, and the p-value = 0.03 are altered. The analysis was successful in determining the relationship between the variables injury rate and hours worked.

## References:

Dembe, A, E, Erickson, J, B, Delbos, R G & Banks, S, M,. (2005).The impact of overtime and long work hours on occupational injuries and illnesses: new evidence from the United States. Occup Environ Med. 62 (9) Retrieved from http://oem.bmj.com/content/62/9/588.full

Grove, S. K. (2007). Statistics for health care research: A practical workbook. Edinburgh: Elsevier Saunders.

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