Goodness of Fit Practice Problems
1. University of New Mexico professor Jane hood investigated the fieldwork methods used by
qualitative sociologists (Teaching Sociology, July 2006). Searching for all published journal
articles, dissertations, and conference proceedings over the previous seven years in the
Sociological Abstracts database, she discovered fieldwork could be categorized as the following:
Interview, Observation + Participation, Observation Only, and Grounded Theory. Furthermore,
it has been hypothesized that 70% of fieldwork conducted is done by interview, 15% using
Observation + Participation, 10% using Observation Only, and 5% using Grounded Theory. The
table below summarizes the number of paper published in the last seven years that fall into
each of the above categories.
Fieldwork Method
Interview
Observation + Participation
Observation Only
Grounded Theory
Total
Number of Papers
5,079
1,042
848
537
7,506
a. Set up the null and alternative hypotheses that would be used to determine if the
observed data are consistent with the hypothesized values.
H0: pinterview = 0.70 pobservation+ partic = 0.15
Ha: Two or more differ
pobservation = 0.10
pgrounded = 0.05
b. Calculate the expected counts that would be used in the computation of the Chi-square
test statistic.
Fieldwork Method
Interview
Observation + Participation
Observation Only
Grounded Theory
Total
Expected Count
7506(0.70) = 5254.2
7506(0.15) = 1125.9
7506(0.10) = 750.6
7506(0.05) = 375.3
7,506
c. Using JMP, find the Chi-square test statistic and p-value for this study.
Test statistic = 94.4023
p-value = 0.0001
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d. Using the p-value from part c, is there evidence that the observed data are consistent
with the hypothesized values? Explain.
Evidence that the observed data are NOT consistent with the hypothesized
values.
2. In a study reported in the November 2007 issue of Nature, researchers investigated whether
infants take into account an individual’s actions towards others in evaluating that individual as
appealing or aversive, perhaps laying the foundation for social interaction. (Hamlin, Wynn, and
Bloom, 2007). In one component of the study, sixteen 10-month old infants were shown a
“climber” character (a piece of wood with “google” eyes glued onto it) that could not make it up
a hill in two tries. Then they were shown two scenarios for the climber’s next try, one where the
climber was pushed to the top of the hill by another character (“helper”) and one where the
climber was pushed back down the hill by another character (“hinderer”). The infant was
alternately shown these two scenarios several times. Then the child was presented with both
pieces of wood (the helper and the hinderer) and was asked to pick one to play with. The color
and shape and order (left/right) of the toys was varied and balanced among the 16 infants. A
video of the experiment can be found at the following link:
http://www.yale.edu/infantlab/socialevaluation/Helper-Hinderer.html.
Researchers found that 14 of the 16 infants chose the helper toy.
Sources:
 Introducing Concepts of Statistical Inference. Rossman, Chance, Cobb, and Holcomb. NSF/DUE/CCLI #
0633349
 Hamlin, J. Kiley, Karen Wynn, and Paul Bloom. “Social evaluation by preverbal infants.” November 22,
2007. Nature, Volume 150.
Research Question – Do we have statistical evidence that infants show a preference for
one toy over the other?
a. Determine the appropriate null and alternative hypotheses that would be used to test the
research question of interest.
H0: p = 0.50
Ha: p ≠ 0.50
b. Calculate the expected counts that would be used in the computation of the Chi-square test
statistic.
Helper = 16(0.50) = 8
Hinderer = 16(0.50) = 8
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c. Using JMP, find the Chi-square test statistic and p-value.
Test Statistic = 9
p-value = 0.0027
d. What conclusion can you make regarding the research question?
Evidence that infants show a preference for one toy over the other.
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