A study prospectively examined whether sleep-disordered breathing was associated

Question

A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 6294 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the two-way table below.

Do the study findings give evidence of a significant relationship between the extent of sleep-disordered breathing and death?

(a) What is the appropriate test to address this question?

2-proportion z testone-way ANOVA F test    t-test for linear regressionchi-square test of independence

Under the null hypothesis of no relationship,
(b) the expected cell count that from the severe sleep-discorered breathing and death cell is  (round to 2 decimal places)

(c) the contribution to the test statistic that comes from the severe sleep-disordered breathing and death cell is  (round to 2 decimal places)

none mild moderate severe Total Death 476 320 165 91 1052 No Death 2953 1477 562 255 5247 Total 3429 1797 727 346 6299

Explanation / Answer

a) chi-square test of independence

b)

b) expected cell count that from the severe sleep-discorered breathing and death cell is=57.79

c) contribution to the test statistic that comes from the severe sleep-disordered breathing and death cell is =19.09

Observed O none mild moderate severe Total death 476 320 165 91 1052 No death 2953 1477 562 255 5247 Total 3429 1797 727 346 6299 Expected E=rowtotal*column total/grand total none mild moderate severe Total death 572.679 300.118 121.417 57.786 1052 No death 2856.321 1496.882 605.583 288.214 5247 Total 3429 1797 727 346 6299 chi square =(O-E)^2/E none mild moderate severe Total death 16.321 1.3171 15.6445 19.0911 52.374 No death 3.272 0.264 3.137 3.828 10.501 Total 19.594 1.581 18.781 22.919 62.8748

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