Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 6 Statistical Inference 267

From the output in Figure 6-23, we note that the median revenue from

nonrural nursing homes is $17,538, whereas the median revenue of rural hos-

pitals is $10,921. The median difference is $4,463 (remember that the median

difference is not the difference between the two medians). This difference is

statistically signifi cant with a p value of 0.026. Note that by using a test that

reduces the infl uence of outliers, we achieve a more signifi cant p value.

Our fi nal decision: We reject the null hypothesis that revenue generated

by rural homes was equal to revenue generated by nonrural homes and ac-

cept the hypothesis that they were not equal. The 95% confi dence interval

gives a range of values for this difference. We conclude that the median dif-

ference is not less than $343 and not more than $9,196.

To complete your work:

1 Save your changes to the workbook and close the fi le.

Final Thoughts about Statistical Inference

The previous example displays some of the challenges and dangers in doing

statistical inference. It is tempting to see a p value or a confi dence interval

as the authoritative answer to your research. However, to use the tools of

statistical inference properly, you should always be aware of the limitations

of your statistical tests. Here are some general rules you should follow when

performing statistical inference.

1. State your hypotheses clearly and, if possible, before collecting and ana-
   lyzing your data.


2. Understand the nature and limitations of the statistical tests you use. Be
   aware of any assumptions that the test makes about the nature of your
   data. Try to verify that these assumptions are met (or at least that there is
   no evidence that they are being violated).


3. Graph your data; it will help you more easily detect any departures from
   the assumptions of your statistical test. Calculate descriptive statistics of
   your data for the same reason.


4. If appropriate, perform more than one kind of statistical test. A different
   test, such as a nonparametric one, may provide important insight into
   your data.


5. Your goal is not to reject the null hypothesis. A study that fails to reject
   the null hypothesis is not a failure, nor is a low p value a sign of success
   (especially if you’re rejecting the null hypothesis in error). Your goal
   should be to determine what, if any, conclusions you can reach about
   your data in a fair and impartial way and then to ascertain how reliable
   those conclusions are.