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Concept explainers
1.
Identify the
1.
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Answer to Problem 12CAP
Phi-
Explanation of Solution
The given information is that, correlation coefficient between Activity (active, inactive) and depression (depressed, not depressed) is to be studied.
Phi-correlation coefficient:
When the two factors are measured on nominal scale, then the strength and direction of the linear relationship between the two dichotomous factors can be measured by Phi-correlation coefficient. This is denoted by
The table denoting the notation of Phi-correlation coefficient is,
Variable X | ||||
Variable Y | a | b | A | |
c | d | B | ||
C | D |
Table 1
Justification: The factors in the study are Activity (active, inactive) and depression (depressed, not depressed). The factor ‘Activity’ is dichotomous which has two levels ‘active, inactive’ and factor ‘depression’ is dichotomous which has two levels ‘depressed, not depressed’. The phi-correlation coefficient is used to measure the relationship when two factors are dichotomous.
Hence, Phi-correlation coefficient should be used when studying relation between when studying relation between Activity (active, inactive) and depression (depressed, not depressed).
2.
Identify the correlation coefficient that should be used when studying relation between time spent at school and time spent studying in hours per week.
2.
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Answer to Problem 12CAP
Pearson correlation coefficient should be used when studying relation between times spent at school and time spent studying in hours per week.
Explanation of Solution
The given information is that, correlation coefficient between Time spent at school and time spent studying in hours per week is to be studied.
Pearson correlation coefficient:
When the two factors are measured on either interval scale or ratio scale, then the strength and direction of the linear relationship between the two factors can be measured by Pearson correlation coefficient. This is also termed as product-moment correlation coefficient. The formula is,
In the formula,
Justification: The factors in the study are ‘times spent at school’ and ‘time spent studying in hours per week’. These two factors involve times which are measured on ratio scale. The Pearson correlation coefficient is used to measure the relationship when two factors are measured on ratio scale.
Hence, Pearson correlation coefficient that should be used when studying relation between times spent at school and time spent studying in hours per week.
3.
Identify the correlation coefficient that should be used when studying relation between Veteran (yes, no) and level of patriotism indicated on a rating scale.
3.
![Check Mark](/static/check-mark.png)
Answer to Problem 12CAP
Point-biserial correlation coefficient should be used when studying relation between Veteran (yes, no) and level of patriotism indicated on a rating scale.
Explanation of Solution
The given information is that, correlation coefficient between Veteran (yes, no) and level of patriotism indicated on a rating scale is to be studied.
Point-biserial correlation coefficient:
When the one factor is continuous that is measured on either interval scale or ratio scale and other is dichotomous that is measured on nominal scale, then the strength and direction of the linear relationship between the two factors can be measured by Point-biserial correlation coefficient. It is denoted by
In the formula, p and q are the proportion of scores for the dichotomous factor at each level,
Justification: The factors in the study are ‘Veteran (yes, no)’ and ‘level of patriotism indicated on a rating scale’. The factor ‘Veteran’ is dichotomous which has two levels ‘yes, no’ and factor ‘level of patriotism indicated on a rating scale’ is measured on nominal scale. The Point-biserial correlation coefficient is used to measure the relationship when one factor is dichotomous and other is measured on nominal scale.
Hence, Point-biserial correlation coefficient that should be used when studying relation between Veteran (yes, no) and level of patriotism indicated on a rating scale.
4.
Identify the correlation coefficient that should be used when studying relation between hierarchical ranking of a litter of mice for play and social behaviour.
4.
![Check Mark](/static/check-mark.png)
Answer to Problem 12CAP
Spearman correlation coefficient should be used when studying relation between hierarchical ranking of a litter of mice for play and social behaviour.
Explanation of Solution
The given information is that, correlation coefficient between the hierarchical ranking of a litter of mice for play and social behaviour is to be studied.
Spearman correlation coefficient:
When the two factors are measured on either ranked scale or ordinal scale, then the strength and direction of the linear relationship between the two factors can be measured by Spearman correlation coefficient. This is also termed as Spearman
In the formula, D denotes the difference of ranks for factor X and factor Y, n denotes the
Justification: The factors in the study are ‘ranking of a litter of mice for play’ and ‘ranking of a litter of mice for social behaviour’. Both the factors are ranked on a ranking scale. The Spearman correlation coefficient is used to measure the relationship when two factors are ranked.
Hence, Spearman correlation coefficient should be used when studying relation between hierarchical ranking of a litter of mice for play and social behaviour.
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Chapter 15 Solutions
Statistics for the Behavioral Sciences
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- - + ++ Table 2: Crack Experiment for Exercise 2 A B C D Treatment Combination (1) Replicate I II 7.037 6.376 14.707 15.219 |++++ 1 བྱ॰༤༠སྦྱོ སྦྱོཋཏྟཱུ a b ab 11.635 12.089 17.273 17.815 с ас 10.403 10.151 4.368 4.098 bc abc 9.360 9.253 13.440 12.923 d 8.561 8.951 ad 16.867 17.052 bd 13.876 13.658 abd 19.824 19.639 cd 11.846 12.337 acd 6.125 5.904 bcd 11.190 10.935 abcd 15.653 15.053 Question 3 Continuation of Exercise 2. One of the variables in the experiment described in Exercise 2, heat treatment method (C), is a categorical variable. Assume that the remaining factors are continuous. (a) Write two regression models for predicting crack length, one for each level of the heat treatment method variable. What differences, if any, do you notice in these two equations? (b) Generate appropriate response surface contour plots for the two regression models in part (a). (c) What set of conditions would you recommend for the factors A, B, and D if you use heat treatment method C = +? (d) Repeat…arrow_forwardQuestion 2 A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are: pouring temperature (A), titanium content (B), heat treatment method (C), amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm x10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown in Table 2. 1 (a) Estimate the factor effects. Which factor effects appear to be large? (b) Conduct an analysis of variance. Do any of the factors affect cracking? Use a = 0.05. (c) Write down a regression model that can be used to predict crack length as a function of the significant main effects and interactions you have identified in part (b). (d) Analyze the residuals from this experiment. (e) Is there an…arrow_forwardA 24-1 design has been used to investigate the effect of four factors on the resistivity of a silicon wafer. The data from this experiment are shown in Table 4. Table 4: Resistivity Experiment for Exercise 5 Run A B с D Resistivity 1 23 2 3 4 5 6 7 8 9 10 11 12 I+I+I+I+Oooo 0 0 ||++TI++o000 33.2 4.6 31.2 9.6 40.6 162.4 39.4 158.6 63.4 62.6 58.7 0 0 60.9 3 (a) Estimate the factor effects. Plot the effect estimates on a normal probability scale. (b) Identify a tentative model for this process. Fit the model and test for curvature. (c) Plot the residuals from the model in part (b) versus the predicted resistivity. Is there any indication on this plot of model inadequacy? (d) Construct a normal probability plot of the residuals. Is there any reason to doubt the validity of the normality assumption?arrow_forward
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