The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

150 CHAPTER 9 Nonparametric Methods

If we want to do a one - sided test with the alternative that p > 1/2,
then we compute a 95% confi dence interval of the form (a, 1] and reject
the null hypothesis if a > 1/2, or for the opposite side and confi dence
interval of the form [0, b) with b < 1/2. Table 9.3 shows how the sign
test is applied comparing average temperatures in New York and
Washington paired by date.
We note that the number of plus signs is 12, which is the highest
possible, favoring Washington as being warmer than New York. So
since it is the most extreme; the probability of 12 pluses is the one - sided
p - value. So p = (1/2)^12 = 0.000244. Since the binomial distribution is
symmetric about 1/2 under the null hypothesis ( p = 1/2), the two - sided
p - value is just double the one - sided p - value which is 0.000488.

9.4 SPEARMAN ’ S RANK - ORDER

CORRELATION COEFFICIENT

Thus far, we know about Pearson ’ s correlation coeffi cient, which is
suitable for bivariate normal data, and its estimate is related to the slope

Table 9.3

Daily Temperatures for Two Cities: Paired Nonparametric

Sign Test

Day Washington mean

temperature ( ° F)

New York mean

temperature ( ° F)

Paired

difference

Sign

1. January 15 31 28 3 +
   2. February 15 35 33 2 +
   3. March 15 40 37 3 +
   4. April 15 52 45 7 +
   5. May 15 70 68 2 +
   6. June 15 76 74 2 +
   7. July 15 93 89 4 +
   8. August 15 90 85 5 +
   9. September 15 74 69 5 +
   10. October 15 55 51 4 +
   11. November 15 32 27 5 +
   12. December 15 26 24 2 +