scipy.stats.binomtest#

scipy.stats.binomtest(k, n, p=0.5, alternative='two-sided')[source]#

Perform a test that the probability of success is p.

The binomial test [1] is a test of the null hypothesis that the probability of success in a Bernoulli experiment is p.

Details of the test can be found in many texts on statistics, such as section 24.5 of [2].

Parameters:

kint: The number of successes.
nint: The number of trials.
pfloat, optional: The hypothesized probability of success, i.e. the expected proportion of successes. The value must be in the interval 0 <= p <= 1. The default value is p = 0.5.
alternative{‘two-sided’, ‘greater’, ‘less’}, optional: Indicates the alternative hypothesis. The default value is ‘two-sided’.

Returns:

resultBinomTestResult instance

The return value is an object with the following attributes:

kint: The number of successes (copied from binomtest input).
nint: The number of trials (copied from binomtest input).
alternativestr: Indicates the alternative hypothesis specified in the input to binomtest. It will be one of 'two-sided', 'greater', or 'less'.
statisticfloat: The estimate of the proportion of successes.
pvaluefloat: The p-value of the hypothesis test.

The object has the following methods:

proportion_ci(confidence_level=0.95, method=’exact’) :: Compute the confidence interval for statistic.

Notes

New in version 1.7.0.

References

[1]

Binomial test, https://en.wikipedia.org/wiki/Binomial_test

[2]

Jerrold H. Zar, Biostatistical Analysis (fifth edition), Prentice Hall, Upper Saddle River, New Jersey USA (2010)

Examples

>>> from scipy.stats import binomtest

A car manufacturer claims that no more than 10% of their cars are unsafe. 15 cars are inspected for safety, 3 were found to be unsafe. Test the manufacturer’s claim:

>>> result = binomtest(3, n=15, p=0.1, alternative='greater')
>>> result.pvalue
0.18406106910639114

The null hypothesis cannot be rejected at the 5% level of significance because the returned p-value is greater than the critical value of 5%.

The test statistic is equal to the estimated proportion, which is simply 3/15:

>>> result.statistic
0.2

We can use the proportion_ci() method of the result to compute the confidence interval of the estimate:

>>> result.proportion_ci(confidence_level=0.95)
ConfidenceInterval(low=0.05684686759024681, high=1.0)