B3. In this exercise, we will be testing the null hypothesis that smoking status (smoker) is unrelated to having a health limitation. Because we want “cell a” to be the cell with the risk factor and the unfavorable outcome, we will recode smoker (which is coded 1 for smokers and 0 for nonsmokers) so that smokers are coded 2. Similarly, we recode hlthlimt so that those without a limitation are coded 2 rather than 0. Click Transform ➜ Recode ➜

Into Different Variables. Select smoker and move it into the Numeric Variables slot. Then type in a new variable name (newsmoke) in the slot for Output Variable, and click Change. Do the same process for hlthlimit, creating a new variable newlimit. Now click on the pushbutton for Old and New Values. In the next dialog box, in the Old Value field, enter 1, and also enter 1 for New Value (we are keeping code 1 the same), and then click Add. Next, enter 0 for Old Value and 2 for New Value, and click Add, Continue, and OK. The two new variables are at the end of the data file, and you can label them by clicking the Variable View tab at the bottom of the data editor.

Now, run Analyze ➜ Descriptive Statistics ➜ Crosstabs, placing newsmoke in the slot for Rows and newlimit in the slot for Columns. For Cell options, click Observed, Expected, and Row Percentages. For options in the Statistics dialog box, click Chi-square and Risk. Then click Continue and OK and answer the following questions:

(a) What was the absolute risk of having a health limitation among smokers? And among nonsmokers?

(b) What is the value of the chi-square statistic in this analysis?

(c) Is this statistically significant for a .05?

What is the probability level, and what does this mean?

(d) What is the odds ratio for this analysis? What does this mean?

(e) What is the 95% CI around the odds ratio?

(f) What is the relative risk of having a health limitation for smokers, relative to nonsmokers?