Question

1. Chapter 17: Exercise 38, Page 575 (12 marks)

Depression: A study published in the archives of general Psychiatry examined the impact of depression on a patient’s ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated the for depression and followed the group for 4 years. Of the 361 patients with no depression 67 died. Of the 361 patients with no depression 67 died. Of the 89 patients with minor or major depression 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die then non-depressed ones.?

1. What kind of design was used to collect this data?

2. Write appropriate hypotheses

3. Are the assumptions and conditions necessary for interreference satisfied?

3. Test the hypothesis and state your conclusion

5. Explain in this context what your P value means

Answer 1

a) Prospective Observational Study

b) H₀= The proportion of cardiac patients without depression who died is the same as that of cardiac patients with depression who died. ( P_{No-depression} - P_Depression = 0)

H_A=The proportion of cardiac patients without depression who died is less than that of cardiac patients with depression who died. (P_{No-depression} - P_Depression < 0)

c) The samples are not associated ( Independent sample check)

All the sub-values are greater than 10 i.e ( for no-depression 67 and 294 >10 and for depression 26(dead) and 63 >10)

89 and 361 are less than 10% of the population ( i.e people with cardiac disease)

Hence all conditions are satisfied.

d)

Standard deviation Se pooled ( Prome - Peepression) I Ppooled Upooled pooled. a pooled None in Depressim - 89 V 361 Standard SE = 0.0479 Prone - Pdep - 2 - 26 7- -0.1065-0 - - 2 2234 0.0479 = 361 89 = 0.1856 -0.2921 = 120.1065 P-value - Plz<-2.2234) 20.013

e)

p-value is the value ( when significantly less) we reject the null hypothesis and in this case the hypothesis that proportion of cardiac patients without depression who died is the same as that of cardiac patients with depression who died.

Since the value of p is small we can reject the null hypothesis and establish that portion of deaths of cardiac patients without depression is less than the death of cardiac patients with depression

The summary of deaths of depression and no depression

np (no depression) = 6T nå (no depression) = 294 no (depression ) = 26 & nå (depression ) = 63