Applied Statistics Using SPSS, STATISTICA, MATLAB and R

178 5 Non-Parametric Tests of Hypotheses
data in a compact way, with a specific column containing the number of
occurrences of each case.
Commands 5.3. SPSS, STATISTICA, MATLAB and R commands used to
perform the binomial test.
SPSS Analyze; Nonparametric Tests; Binomial
STATISTICA
Statistics; Basic Statistics and Tables;
t-test, single sample
MATLAB [h,sig,ci]=ttest(x,m,alpha,tail)
R binom.test(x,n,p,conf.level=0.95)
When performing the binomial test with STATISTICA or MATLAB using the
single sample t test, a somewhat different value is obtained because no continuity
correction is used and the standard deviation is estimated from pˆ . This difference
is frequently of no importance. With MATLAB the test is performed as follows:
» x = [ones(176,1); zeros(48,1)];
» [h, sig, ci]=ttest(x,0.75,0.05,0)
h =
0
sig =
0.195
ci =
0.7316 0.8399
Note that x is defined as a column vector filled in with 176 ones followed by 48
zeros. The commands ones(m,n) and zeros(m,n) define matrices with m
rows and n columns filled with ones and zeros, respectively. The notation [A; B]
defines a matrix by juxtaposition of the matrices A and B side by side along the
columns (along the rows when omitting the semicolon).
The results of the test indicate that the null hypothesis cannot be rejected (h=0).
The two-tailed significance is 0.195, somewhat lower than previously found
(0.248), for the above mentioned reasons.
The arguments x, n and p of the R binom.test function represent the
number of successes, the number of trials and the tested value of p, respectively.
Other details can be found with help(binom.test). For the Example 5.3 we
run binom.test(176,176+48,0.75), obtaining a two-tailed significance of
0.247, nearly the double of the value published in Table 5.3 as it should. A 95%
confidence interval of [0.726, 0.838] is also published, containing the observed
proportion of 0.786.