Statistical Analysis for Education and Psychology Researchers

observed frequency, twenty-one less seventeen). The probabilities associated with
obtaining counts of 4, 3, 2, 1, and 0 are:
p 4 = 2.85−3; p 3 = 6.34−4; p 2 = 1.00−4; p 1 =1.00−5; p 0 = 4.77−7.^

Note, 2.85−3 is equal to 0.00285. The probability of obtaining 4 or fewer is the sum of
these five probabilities which is 0.0036.

Interpretation

Gardiner (1989) did not state in his paper whether a one- or a two-tailed test was used or
the alpha level selected (see earlier comment about brevity of statistical test details when
results are presented in periodicals). A cautious approach would be to use a two-tailed
test with alpha set to 5 per cent. When a two-tailed test is used the probability associated
with the smallest observed frequency is doubled. The p-value for the two-tailed sign test
is thus 0.0072. The null hypothesis is therefore rejected, and we conclude that there is a
statistically significant priming effect.

Computer Analysis

Calculation of binomial probabilities using the binomial equation is tedious and either
tables of binomial probabilities for p=0.5 can be consulted or the probabilities can be
determined using the SAS binomial function PROBBNML. Appropriate lines of SAS
code are:

data a;

p4=probbnml (0.5, 21, 4) ;

put p4=;

run;

The PROBBNML function is used as part of a SAS data step, here the first line of code
specifies the data set a (this is just a convenient name). The PUT statement tells SAS to
write the variable p4, evaluation of the binomial function, to the LOG File. See earlier
section 6.2 for details of the PROBBNML function. The following value is returned in
the SAS LOG file, p4=0.00359869

Worked Example

The numerical example of the sign test given by Sachdeva (1975) for twelve randomly
selected pairs of students is used to illustrate an extraordinary simple computational
procedure for evaluating the sign test which is based on the sample size only. For the
twelve matched pairs of students the signs of the differences are:
Sign for difference−−++ − −+−−++−

A simple formulae for making tests of significance at the 5 per cent level for a two-tailed
alternative hypothesis is,
(s+−f)^2 ≥ 4 n

Inferences involving binomial and nominal count data 191