Question

Researchers were interested in examining the impact poverty may have on self-perceptions of health. Participants were asked to rate their health as in good or poor. Their income level was categorized as above or below the poverty line. Use the two tables below to answer the following questions.

Identify the null and alternate hypothesis.

Interpret test statistic and state conclusion based on original hypothesis. Assume alpha = .05

Interpret the odds ratio based on original research hypothesis.

Interpret the relative risk for those participants whose income was below the poverty line.

Chi-Square Tests

Value df Asymptotic Significance (2-sided) Exact sig (2-sided) Exact sig (1-sided)   

Pearson Chi Square 4.894 1 .027

Continuity Correction 4.208 1 .040

Likelihood Ration 5.595 1 .018

Fisher's Exact test .025 .016

Linear-by-linear assoc 4.888   1 .027

N of valid Cases 860

Risk Estimate

Value 95% confidence interval

lower upper

Odds Ratio for Poor health self-rating (not in poor health/ in poor health) .412 .183 .926

For cohort Poverty status = below poverty .844 .755 .943

For cohort Poverty status = above poverty 2.048 1.017 4.127

N of valid cases 860

Answer 1

Solution:

1)

Null hypothesis-

H0: There is no impact if poverty on self-rated health

Alternate hypothesis-

H1: Poverty may have a negative impact on health

2)  

Pearson Chi-Square= 4.894(1)

which is calculated from the Pearson Chi-Square test and p-value is given as

P-VALUE =.027 < 0.05 (level of significance )

therefore at 5% we reject the null hypothesis.

3)

In the term of the original research hypothesis, the odds ratio can be interpreted as

the odd of poor self-rated health is higher among poor than that of the non-poor

4)  

Odds Ratio for Poor health self-rating (Not in poor health / In poor health)= .412

which means that-

percentage = (1- 0.412) *100%= 58.8%

Now it can be interpreted easily as

The odds of poor self-rated health is 58% lower among the non-poor than to the poor.