def test_f_high(self):
"""F high should match values from R for integer successes"""
expected = {
(1, 1, 0): 1,
(1, 1, 1): 0.5,
(1, 1, 20): 0.1400487,
(1, 1, 1000000): 0.0006366196,
(1, 10, 0): 1,
(1,10, 5): 0.0493322,
(1, 10, 20): 0.001193467,
(10, 1, 0):1,
(10, 10, 14.7): 0.0001062585,
(13.7, 11.9, 3.8): 0.01340347, #test non-integer degrees of freedom
#used following series to track down a bug after a failed test case
(28, 29, 2): 0.03424088,
(28, 29, 10): 1.053019e-08,
(28, 29, 20): 1.628245e-12,
(28, 29, 300): 5.038791e-29,
(28, 35, 1): 0.4946777,
(28, 37, 1): 0.4934486,
(28, 38, 1): 0.4928721,
(28, 38.001, 1): 0.4928716,
(28, 38.5, 1): 0.4925927,
(28, 39, 1): 0.492319,
(28, 39, 10): 1.431901e-10,
(28, 39, 20): 1.432014e-15,
(28, 39, 30): 1.059964e-18,
(28, 39, 50): 8.846678e-23,
(28, 39, 10): 1.431901e-10,
(28, 39, 300): 1.226935e-37,
(28, 39, 50): 8.846678e-23,
(28,39,304.7): 9.08154e-38,
(28.4, 39.2, 304.7): 5.573927e-38,
(1032, 2050, 0): 1,
(1032, 2050, 4.15): 1.23535e-165,
(1032, 2050, 0.5): 1,
(1032, 2050, 0.1): 1,
}
e = expected.items()
e.sort()
for (key, value) in e:
self.assertFloatEqualRel(f_high(*key), value)
def f_two_sample(a, b, tails=None):
"""Returns the dfn, dfd, F-value and probability for two samples a, and b.
a and b: should be independent samples of scores. Should be lists of
observations (numbers).
tails should be None(default, two-sided test), 'high' or 'low'.
This implementation returns the same results as the F test in R.
"""
dfn, dfd, F = f_value(a, b)
if tails == 'low':
return dfn, dfd, F, f_low(dfn, dfd, F)
elif tails == 'high':
return dfn, dfd, F, f_high(dfn, dfd, F)
else:
if var(a) >= var(b):
side='right'
else:
side='left'
return dfn, dfd, F, fprob(dfn, dfd, F, side=side)
def ANOVA_one_way(a):
"""Performs a one way analysis of variance
a is a list of lists of observed values. Each list is the values
within a category. The analysis must include 2 or more categories(lists).
the lists must have a Mean and variance attribute. Recommende to make
the Numbers objects
An F value is first calculated as the variance of the group means
divided by the mean of the within-group variances.
"""
group_means = []
group_variances = []
num_cases = 0
all_vals = []
for i in a:
num_cases += len(i)
group_means.append(i.Mean)
group_variances.append(i.Variance * (len(i)-1))
all_vals.extend(i)
group_means = Numbers(group_means)
#get within group variances (denominator)
group_variances = Numbers(group_variances)
dfd = num_cases - len(group_means)
within_MS = sum(group_variances)/dfd
#get between group variances (numerator)
grand_mean = Numbers(all_vals).Mean
between_MS = 0
for i in a:
diff = i.Mean - grand_mean
diff_sq = diff * diff
x = diff_sq * len(i)
between_MS += x
dfn = len(group_means) - 1
between_MS = between_MS/dfn
F = between_MS/within_MS
return dfn, dfd, F, between_MS, within_MS, group_means, f_high(dfn, dfd, F)
