Chapter 6 Statistical Inference 253
percentage points (4 cities were unchanged). This information strengthens
our earlier conclusion that there was a signifi cant increase in women in the
workforce during those four years.
EXCEL TIPS
Excel doesn’t include a command to perform the signed rank
test, but you can approximate the p values and confi dence inter-
vals of the signed rank test by calculating the sign ranks of your
data and then performing a one-sample t test on those values.
To calculate the ranks of your data, use Excel’s RANK function.
If your data contain ties, you should use the RANKTIED func-
tion. StatPlus required.
To calculate the signed ranks of your data, use the SIGNRANK
function. StatPlus required.
The Sign Test
Another nonparametric test that makes even fewer assumptions than the
Wilcoxon Signed Rank test is the Sign test. In the Sign test, we ignore
the values entirely and simply count the number of positive values and the
number of negative values. We then test whether there are more positive (or
negative) values than there should be. The test is similar to what we might
use to test whether a two-sided coin is fair.
The Sign test is usually less effi cient (requiring a larger sample size) than
either the t test or the signed rank test, except in cases where the data come
from a heavy tailed distribution. In those cases, the Sign test may be more
effective than either the t test or the signed rank test.
Let’s apply the Sign test to our data set. Our hypotheses are
H 0 : Probability of a negative value 5 probability of a positive value
Ha: Probability of a negative value 2 probability of a positive value
To analyze the difference data using the Sign test:
1 Click One Sample Tests from the StatPlus menu and then click 1
Sample Sign test.
2 Verify that the 1-sample s test option button is selected.
3 Click the Input button, select Diff from the list of range names, and
click the OK button.
4 Click the Output button and select the New Worksheet option button.
Enter s test for the new worksheet name and click the OK button.
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