Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
9th Edition
ISBN: 9781337098120
Author: Frederick J Gravetter, Larry B. Wallnau, Lori-Ann B. Forzano
Publisher: Cengage Learning
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Textbook Question
Chapter 12.1, Problem 1LC
How many levels are there in a single-factor independent-measures design comparing depression scores of participants with and without treatment?
a. 1
b. 2
c. 3
d. 4
Expert Solution & Answer
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+
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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…
Question 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…
A 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?
Chapter 12 Solutions
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Ch. 12.1 - How many levels are there in a single-factor...Ch. 12.1 - When is the distinction between the testwise alpha...Ch. 12.1 - Which of the following accurately describes the...Ch. 12.2 - For an analysis of variance, the differences...Ch. 12.2 - What is suggested by a large value for the F-ratio...Ch. 12.3 - An analysis of variances produces dfbetween...Ch. 12.3 - An analysis of variance is used to evaluate the...Ch. 12.3 - A research study compares three treatments with n...Ch. 12.4 - A researcher uses analysis of variance to test for...Ch. 12.4 - The following table shows the results of an...
Ch. 12.4 - A research report concludes that there are...Ch. 12.5 - Under what circumstances are post hoc tests...Ch. 12.5 - Prob. 2LCCh. 12.6 - Which combination of factors is most likely to...Ch. 12.6 - If an analysis of variance is used for the...Ch. 12.6 - A researcher uses an ANOVA to evaluate the mean...Ch. 12 - Why should you use ANOVA instead of several t...Ch. 12 - What value is expected for the F-ratio, on...Ch. 12 - Describe the similarities between an F-ratio and a...Ch. 12 - Calculate SSwith, SSbetween, SSwithin for the...Ch. 12 - A researcher uses an ANOVA to compare three...Ch. 12 - A researcher reports an F-ratio with dfbetween2...Ch. 12 - A researcher reports an F -ratio with df = 3.24...Ch. 12 - The following values are from an...Ch. 12 - A researcher conducts an experiment comparing four...Ch. 12 - The following summary table presents the results...Ch. 12 - A developmental psychologist is examining the...Ch. 12 - The following data were obtained from an...Ch. 12 - The following data were obtained from an...Ch. 12 - A research study comparing three treatment...Ch. 12 - The following values are from an...Ch. 12 - A research report from an independent-measures...Ch. 12 - Several factors influence the size of the F-ratio....Ch. 12 - A researcher used ANOVA and computed F = 4.25 for...Ch. 12 - The following Data were obtained from an...Ch. 12 - For the preceding problem you should find that...Ch. 12 - The following data summarize the results from an...Ch. 12 - To create the following data we started with the...Ch. 12 - An ANOVA produces an F-ratio with df 1.34. Could...Ch. 12 - The following scores are from an independent...
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