scipy.stats.binomtest

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

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'.

pvaluefloat

The p-value of the hypothesis test.

proportion_estimatefloat

The estimate of the proportion of successes.

The object has the following methods:

proportion_ci(confidence_level=0.95, method=’exact’) :

Compute the confidence interval for proportion_estimate.

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 estimated proportion is simply 3/15:

>>> result.proportion_estimate
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)