Function Reference: binotest

statistics: [h, pval, ci] = binotest (pos, N, p0)
statistics: [h, pval, ci] = binotest (pos, N, p0, Name, Value)

Test for probability p of a binomial sample

Perform a test of the null hypothesis p == p0 for a sample of size N with pos positive results.

Name-Value pair arguments can be used to set various options. "alpha" can be used to specify the significance level of the test (the default value is 0.05). The option "tail", can be used to select the desired alternative hypotheses. If the value is "both" (default) the null is tested against the two-sided alternative p != p0. The value of pval is determined by adding the probabilities of all event less or equally likely than the observed number pos of positive events. If the value of "tail" is "right" the one-sided alternative p > p0 is considered. Similarly for "left", the one-sided alternative p < p0 is considered.

If h is 0 the null hypothesis is accepted, if it is 1 the null hypothesis is rejected. The p-value of the test is returned in pval. A 100(1-alpha)% confidence interval is returned in ci.

Source Code: binotest

Example: 1

  

 % flip a coin 1000 times, showing 475 heads
 % Hypothesis: coin is fair, i.e. p=1/2
 [h,p_val,ci] = binotest(475,1000,0.5)
 % Result: h = 0 : null hypothesis not rejected, coin could be fair
 %         P value 0.12, i.e. hypothesis not rejected for alpha up to 12%
 %         0.444 <= p <= 0.506 with 95% confidence

h = 0
p_val = 0.1212
ci =

   0.4437   0.5065

Example: 2

  

 % flip a coin 100 times, showing 65 heads
 % Hypothesis: coin shows less than 50% heads, i.e. p<=1/2
 [h,p_val,ci] = binotest(65,100,0.5,'tail','left','alpha',0.01)
 % Result: h = 1 : null hypothesis is rejected, i.e. coin shows more heads than tails
 %         P value 0.0018, i.e. hypothesis not rejected for alpha up to 0.18%
 %         0 <= p <= 0.76 with 99% confidence

h = 1
p_val = 1.7588e-03
ci =

        0   0.7580