Trephination is one of the oldest known surgical techniques, originating in the
ID: 3170316 • Letter: T
Question
Trephination is one of the oldest known surgical techniques, originating in the Stone Age. It was a primitive form of surgery where part of the skull was chipped away. Some evidence suggests that this method was used to treat behavioral disorders, by providing an opening in the skull through which evil spirits could escape. A competing theory suggests that it was used to remove blood splinters and blood clots, most likely caused from blows to the head during combat.
A study was conducted on 69 specimens that had evidence of trephination. The specimens were divided into male and female, and further divided into trephination due to injury (Injury column) and trephination with no injury present (No Injury). Under theory 1, males and females would exhibit roughly equal rates of mental/behavioral illness, and we would expect the rates of trephination to be equal between injured and uninjured specimens. Under theory 2, males who had trephination were more likely to have had it due to injury from combat. In other words, no relationship between gender and injury rate would support theory 1, while a skewed distribution (more males with injuries) would support theory 2. The data is presented in the contigency table below: (Please explain with step-by step solutions to further my understanding. Thank you.)
No Injury
Injury
Total
Male
8
29
37
Female
16
16
32
Total
24
45
69
1a (10pts). A chi-square test on this table produces a statistically significant result. State the null and alternative hypotheses used in this test, and your interpretation of the result. You do not have to rerun the chi-square test.
b (10pts). Calculate the odds-ratio for the presented table, and interpret the result.
c (20pts). Is there anyway to make the odds-ratio easier to interpret? If so, show how you would do this with calculations and a written interpretation.
No Injury
Injury
Total
Male
8
29
37
Female
16
16
32
Total
24
45
69
Explanation / Answer
Solution:
while a skewed distribution (more males with injuries) would support theory 2. The data is presented in the contigency table below:
Here we have to test the hypothesis that,
H0 : The variales injury and gender are independent.
H1 : The variables injury and gender are not independent.
If we get significant results that is we reject H0 at alpha % level of significance.
b). Calculate the odds-ratio for this table, and interpret the result.
For odds ratio we need expected frequencies.
Expecte frequency we can find by using formula :
E = (row total) * (column total) / sample size
Expected frequencies are :
E11 = 12.87
E12 = 24.13
E21 = 11.13
E22 = 20.87
Odds ratio :
Odds[1] = injury[1] / no injury[1] = 29 / 8 = 3.625
Odds[2] = injury[2] / no injury[2] = 16/ 16= 1
Odds Ratio = Odds[1]/Odds[2]
Odds ratio = 3.625 / 1 = 3.625
Rate = proportion in group with condition present
Risk Ratio = Rate[1]/Rate[2]
Log Odds = natural logarithm of Odds Ratio
log odds = ln(3.625) = 1.2879
rate risk ratio odds odds ratio log odds group1 0.7838 1.5676 3.625 3.625 1.2879 group2 0.5 1Related Questions
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