The following data is from M. Hakeem (1945). “Glueck Method of Parole Prediction

Question

The following data is from M. Hakeem (1945). “Glueck Method of Parole Prediction Applied to 1861 Cases of Burglars”, Journal of Criminal Law and Criminology, Vol. 36, #2, pp 87-97. The contingency table below summarizes psychiatric evaluations and the parole outcomes for 1728 burglars placed on parole. The psychiatric prognoses are Unfavorable, Doubtful and Favorable. The parole outcomes are Major violation, Minor violation and Success

.............................................Evaluation
Outcome... Unfavorable.........Doubtful....... Favorable..... Total
Major............ 84................... 195................ 65............... 344
Minor.............101 ................254 ..................100............ 455
Success........67 ..................410 .................452 .............929
Total............. 252................. 859.................. 617 ............1728

(a) State the null and alternative hypotheses of the 2 test for independence.
(b) What are the assumptions for this test?
(c) Compute the table of expected counts.
(d) Calculate the 2 test statistic and state your decision for this test at the = 0.05 significance
level. Show your work.
(e) What is the relationship between the p-value in (d) and the strength of the association between
the psychiatric evaluation and parole outcome?
(f) Compute the conditional probability of each parole outcome given the psychiatric prognosis.
(g) Describe any patterns in (f).

Explanation / Answer

a)H0: There is no association between the psychiatric evaluation and parole outcome

    H1: There is association between the psychiatric evaluation and parole outcome

b) The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions.

Simple random sample

The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability of selection. Variants of the test have been developed for complex samples, such as where the data is weighted. Other forms can be used such as purposive sampling.

Sample size (whole table)

A sample with a sufficiently large size is assumed. If a chi squared test is conducted on a sample with a smaller size, then the chi squared test will yield an inaccurate inference. The researcher, by using chi squared test on small samples, might end up committing a Type II error.

Expected cell count

Adequate expected cell counts. Some require 5 or more, and others require 10 or more. A common rule is 5 or more in all cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero expected count. When this assumption is not met,Yates's correction is applied.

Independence

The observations are always assumed to be independent of each other. This means chi-squared cannot be used to test correlated data (like matched pairs or panel data). In those cases you might want to turn to McNemar's test.

(c) The expected frequencies are calcuated as

d) Test statistic is calculated as follows

Chisqure value = 182.985

e)

Critical X^2:        9.48772
P-Value:             0.0000

Here P value (0.000) < alpha (0.05) we reject H0.

Thus we conclude that, there is association between the psychiatric evaluation and parole outcome

f) The conditional probability of each parole outcome given the psychiatric prognosis is

Outcome Unfavorable Doubtful Favorable Total Major 50.167 171.005 122.829 344.001 Minor 66.354 226.183 162.462 454.999 Success 135.479 461.812 331.709 929 Total 252 859 617 1728

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.