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# STAT 477/577 – Homework Assignment 7

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STAT 477/577 – Homework Assignment 7

General homework guidelines: All homework assignments should be submitted using Canvas.
Please submit your answers separately, for each of the problems, as set-up in the Canvas submission portal.
You are allowed to either type in your answers, as well as submit graphs directly, within each submission
item. You are also allowed to submit a scanned copy of your answer, as long as the answers are submitted
a scanner or do not know how to use your phone to do so), or just submit a picture of your answer. Please
note that if we can’t read your answer, we won’t be able to award any (partial) credit.
has closed for some reason, please email Prof. Caragea explaining the situation and requesting permission
For full credit, please make sure you submit your HW by the deadline of March 29. A late submission is
possible, with a 20% penalty, as long as it is turned in before the end of the day on Thursday following the
due day (for this HW, it is March 31-st). No submissions will be accepted past this date.
Homework problems.
1. In lecture, we discussed results from one of the surveys in the baby pictures study that looked at the
effect of Dr. Nettleton’s son wearing a hat in the picture. In the problem below, we will analyze data
from another survey in this study. In this survey, judges (students) were asked to identify which baby
was Dr. Froelich’s twice, once when she was pictured as an adult and and then when she was pictured
as a baby. Similar to the survey we studied in class, judges were not allowed to revisit their response
to the previous question. The pictures used in the study are located in the file babypictures.pdf.
The babies selected by the 123 judges on the two questions is given in the table below. You will recall
that Baby C is the correct baby in the analysis.
Baby Selected With
Baby Parent Picture
Baby Selected With
Adult Parent Picture A B C D Total
A 7 1 4 0 12
B 18 12 8 5 43
C 17 7 22 8 54
D 3 2 2 7 14
Total 45 22 36 20 123
(a) Using McNemar’s test, determine whether there is a difference in the proportion of correct responses between the two questions. Do the judges perform differently based on which picture is
given? Hint: Collapse the table above to a 2 x 2 table in order to answer the question.
(b) Obtain a 95% confidence interval for the difference in the proportion of correct responses between
the two questions. Interpret this confidence interval in the context of the problem.
(c) Using the extension of McNemar’s test, conduct a test of marginal homogeneity for the baby
selected. Clearly write down the null and alternative hypotheses, the value of the test statistic
and the p-value (which you should obtain using R), and a conclusion within the context of the
problem.
(d) Describe the differences you find in the marginal distributions between the baby selected when
the parent was pictured as an adult versus when the parent was pictured as a baby.
1
2. In educational assessment, open-ended questions (called free-response questions) tend to provide more
information about learning than multiple choice questions. However, these open-ended questions are
more difficult and time consuming to grade than multiple choice questions. In an on-going project,
researchers at a large university are studying the accuracy of computer-scored open-ended responses
by comparing them to person-scored responses. In this example, the computer and a person scored
the same 1,011 student responses to the same open-ended question. Each question was scored as
either a 1 = minimal understanding of concept, 2 = moderate understanding of concept, or 3 = full
understanding of concept. The table below gives the cross-classification table of scores and the full
data set with all 1,011 rows can be found in the file Scores.csv.
Computer-scored
Person-scored 1 2 3
1 439 26 20
2 48 113 33
3 38 29 265
(a) Calculate Cohen’s kappa for these data.
(b) Calculate weighted Cohen’s kappa using the squared weight function for these data.
(c) Based on your answers to part (a) and (b), does there seem to be agreement between the computer