Results of Study Comparing Radiation Therapy with Surgery in Treating Cancer of the Larynx

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CATEGORICAL DATA ANALYSIS
STA 731

INDIVIDUAL ASSIGNMENT

LECTURER’S NAME: PM DR ZAMALIA MAHMUD
STUDENT’S NAME: NAWWAR AQILAH BINTI OMAR
STUDENT’S ID: 2009528427

The table contains results of a study comparing radiation therapy with surgery in treating cancer of the larynx.

| |Cancer Controlled |Cancer Not Controlled | | |Surgery |3 |5 |8 | |Radiation Therapy |6 |4 |10 | | |9 |9 |18 |

a. Referring to the SPSS output below, test the association between treatment and cancer based on this hypothesis ( Ho: (= 1 against Ha: (< 1. What can you conclude from the test?
Suggest ways to investigate the significant effects and association in small samples.

b. Find the odds ratio.
Compute the probabilities for tables where [pic] is less than the odds ratio from the observed table as assumed under the alternative hypothesis, Ha. At what probability value do you find the claim to be reasonable?

ANSWER:

a. The resulting p-value = 0.343 from the Pearson Chi-Square test (0.900) indicates there is no statistically significant difference in the controlling cancer between surgery and radiation therapy treatment. We fail to reject the null hypothesis. The distributions are not well approximated, so the p-values are not good. This is because the number of observations for analysis is small that the chi-square test produced misleading results. A more appropriate way to investigate the significant effects and association in small samples is to use Fisher’s Exact Test.

b. For Ha : ( < 1 or a Left Tail test, we have...
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