flopscope.numpy.random.f
fnp.random.f(dfnum, dfden, size=None)[flopscope source]
Draw samples from an F distribution.
Adapted from NumPy docs np.random.f
Sampling; cost = numel(output).
Samples are drawn from an F distribution with specified parameters,
dfnum (degrees of freedom in numerator) and dfden (degrees of
freedom in denominator), where both parameters must be greater than
zero.
The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates.
New code should use the f method of a Generator instance instead; please see the random-quick-start.
Parameters
- dfnum:float or array_like of floats
Degrees of freedom in numerator, must be > 0.
- dfden:float or array_like of float
Degrees of freedom in denominator, must be > 0.
- size:int or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k), thenm * n * ksamples are drawn. If size isNone(default), a single value is returned ifdfnumanddfdenare both scalars. Otherwise,flops.broadcast(dfnum, dfden).sizesamples are drawn.
Returns
- out:ndarray or scalar
Drawn samples from the parameterized Fisher distribution.
See also
- scipy.stats.f probability density function, distribution or cumulative density function, etc.
- we.flops.random.Generator.f which should be used for new code.
Notes
The F statistic is used to compare in-group variances to between-group
variances. Calculating the distribution depends on the sampling, and
so it is a function of the respective degrees of freedom in the
problem. The variable dfnum is the number of samples minus one, the
between-groups degrees of freedom, while dfden is the within-groups
degrees of freedom, the sum of the number of samples in each group
minus the number of groups.
References
1
Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
Fifth Edition, 2002.2
Wikipedia, "F-distribution",
https://en.wikipedia.org/wiki/F-distributionExamples
An example from Glantz[1], pp 47-40:
Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children's blood glucose levels? Calculating the F statistic from the data gives a value of 36.01.
Draw samples from the distribution:
>>> dfnum = 1. # between group degrees of freedom
>>> dfden = 48. # within groups degrees of freedom
>>> s = flops.random.f(dfnum, dfden, 1000)The lower bound for the top 1% of the samples is :
>>> flops.sort(s)[-10]
7.61988120985 # randomSo there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level.