Data interpretation practicum

Correlation Introduction Correlation is used to investigate the extent of linear relationship between any two variables (Cohen, Cohen, West, & Leona 48). In this analysis, the association between injury rate and number of hours worked will be investigated. Under this test, it is assumed that the observations are independent. A correlation test is the most preferred as it will reveal whether there is a corresponding increase (or decrease) in the number of injuries as compared to the number of hour worked. Regression could also be used in place of correlation as it would show how the number on injuries (dependent variable) changes as a result of increased number of working hours (independent variable). A regression procedure would further help in predicting the injury rate based on working hours. However, discriminant analysis cannot be used.
Hypothesis
The correlation test will test the level of association between injury rate and number of hours worked will be investigated consequently, our hypotheses are as follows:
Null Hypothesis, H0: Injury rate and hours worked are correlated
Alternative Hypothesis, H1: Injury rate and hours worked are not correlated
A scatterplot of the data is shown below:
From this plot, it is seen that the injury rate is inversely proportional to hours worked, i. e. the two variables exhibit a negative correlation.
Descriptive statistics of the data is shown below:
Descriptives
Statistic
Std. Error
Hours Worked
Mean
49960. 78
2183. 070
95% Confidence Interval for Mean
Lower Bound
45575. 96
Upper Bound
54345. 61
Std. Deviation
15590. 236
Minimum
10400
Maximum
93600
InjuryRate
Mean
15. 175696
2. 4469443
95% Confidence Interval for Mean
Lower Bound
10. 260864
Upper Bound
20. 090528
Std. Deviation
17. 4746773
Minimum
. 0000
Maximum
76. 9231
The average working hours in the three states is 2183. 07 hour while the average injury rate in the three states is 2. 4446. The true population mean for average working hours in the three states is bound between 45575. 96 and 54345. 61 while true injury rate mean for average working hours in the three states is bound between 10. 26 and 20. 09.
Correlation Analysis
The output for the correlation test is shown 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).
From this output, the correlation coefficient between hours worked and injury rate is -0. 636. This implies that as work hours increases, injury rate reduces (p-value ~ 0. 000). The test is significant, hence we reject the null hypothesis and conclude that the two variables are correlated. This value is consistent with the observation from a scatterplot of the two variables shown above.
A possible explanation for the observation made is that only a few injuries are normally witnessed, hence, increasing the hours worked does not necessarily lead to an increase in the number of injuries. Since injury rate is obtained by dividing the number of hours worked by the number of injuries, the values reduces as hours worked increases. The value of the correlation coefficient does not imply that increasing the number of working hours results into less injuries.
Reference
Cohen, J., Cohen, P., West, S., & Leona, S. A. (2002). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). NY: Psychology Press.