1. A researcher ran a series of analyses looking at the associations among the b
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Question
1. A researcher ran a series of analyses looking at the associations among the burglary rate, robbery rate and assault rate in her home state. She wanted to see if there were any statistically significant correlations among these variables. Below is a chart showing the results of her SPSS analyses of the data:
a. Identify the obtained values of the correlation coefficient r. Please describe the two variables being compared for each coefficient.
b. For each of the r values, state whether you would reject the null hypothesis at an alpha of .05 and how you reached that decision. (Note: you do not have to perform all 5 steps. Just use the information in the output to make your decision.
c. State the substantive conclusion for each test.
d. As appropriate, interpret the sign, magnitude, and coefficient of determination for each test.
Correlations Burglary Rate Robbery RateAssault Rate 422* 298* Pearson Correlation Burglary Rate Sig. (2-tailed) 220 330* 220 220 422* Pearson Correlation Robbery Rate Sig. (2-tailed) 220 220 330* 220 Pearson Correlation 298* Assault Rate Sig. (2-tailed) 220 220 220Explanation / Answer
a. Identified values of correlation coefficient:
Burglary Rate and Robbery Rate = 0.422
Burglary Rate and Assault Rate = 0.298
Robbery Rate and Assault Rate = 0.330
b. In each of the experiments:
Null Hypothesis H0 = Variables are not correlated to each other, there is no relationship, r =0
Alternate Hypothesis Ha = r != 0, variables are correlated
At 5 % level of confidence, we would reject the null hypothesis if probability against alternate hypothesis, p value of significance test is less than .05.
In all the significance tests it can be seen that p values are equal to 0.000, since p value less than 0.05, we would reject the null hypothesis.
c. The substantive conclusion is that all the variables burglary rate, robbery rate and robbery rate are correlated to each other with statistical significance, that there is relationship between them at 5% level of confidence.
d. Interpretation:
Between Burglary Rate and Robbery Rate = 0.422, hence burglary rate is positively correlated to robbery rate, a positive change or increase in burglary would result in an increase in robbery rate and vice versa. The magnitude of correlation is relatively strong, at 0.422 and this is the strongest among all three variables.
Between Burglary Rate and Assault Rate = 0.298, hence burglary rate is positively correlated to burglary rate, a positive change or increase in burglary would result in an increase in assault rate but only partially strong and vice versa. The magnitude of correlation is relatively weak, at 0.0.298 and this is the weakest among all three variables.
Between Robbery Rate and Assault Rate = 0.330, hence robbery rate is positively correlated to robbery rate, a positive change or increase in robbery would result in an increase in assault rate but only partially strong and vice versa. The magnitude of correlation is mediumly strong, at 0.33.
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