13.86 BMD and Depression. In the paper Depression and Bone Mineral Density: Is T

Question

13.86 BMD and Depression. In the paper Depression and Bone Mineral Density: Is There a Relationship in Elderly Asian Men Osteoporosis International, Vol. 16, pp. 610-615), S. Wong et al. published results of their study on bone mineral density (BMD) and depression for 1999 Hong Kong men aged 65 to 92 years. Here are the cross-classified data Depression Depressed Not depressed Total 35 533 1262 1830 38 602 1359 1999 Osteoporitic BMD Low BMD Normal Total 69 97 169 At the 1% significance level, do the data provide sufficient evidence to conclude that BMD and depression are statistically dependent for elderly Asin men?

Explanation / Answer

Given table data is as below

------------------------------------------------------------------

calculation formula for E table matrix

------------------------------------------------------------------

expected frequecies calculated by applying E - table matrix formulae

------------------------------------------------------------------

calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

------------------------------------------------------------------

set up null vs alternative as

null, Ho: BMD and depression are independent

alternative, H1: BMD and depression are dependent to each other

level of significance, ? = 0.01

from standard normal table, chi square value at right tailed, ?^2 ?/2 =9.21

since our test is right tailed,reject Ho when ?^2 o > 9.21

we use test statistic ?^2 o = ?(Oi-Ei)^2/Ei

from the table , ?^2 o = 10.095

critical value

the value of |?^2 ?| at los 0.01 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 9.21

we got | ?^2| =10.095 & | ?^2 ? | =9.21

make decision

hence value of | ?^2 o | > | ?^2 ?| and here we reject Ho

?^2 p_value =0.006

ANSWERS

---------------

null, Ho: BMD and depression are independent

alternative, H1: BMD and depression are dependent to each other

test statistic: 10.095

critical value: 9.21

p-value:0.006

decision: reject Ho

have evidence that BMD and depression are statistically dependent for elderly asian men

MATRIX col1 col2 TOTALS row 1 3 35 38 row 2 69 533 602 row 3 97 1262 1359 TOTALS 169 1830 N = 1999

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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