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?

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 92 1053 No Death 2953 1477 562 255 5247 Total 3429 1797 727 347 6300

Explanation / Answer

a) chi-square test of independence

b) expected cell count E=row total*column total/grand total =347*1053/6300=58.00

c) contribution to the test statistic =(0-E)2/E =(92-58)2/58=19.93

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