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,
# test non-integer degrees of freedom
(13.7, 11.9, 3.8): 0.01340347,
# 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 = sorted(expected.items())
for (key, value) in e:
np.testing.assert_allclose(f_high(*key), value, atol=10e-7)
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).
Each category of the list, and overall list, is converted to a numpy array.
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 # total observations in all groups
all_vals = []
for i in a:
num_cases += len(i)
group_means.append(np.mean(i))
group_variances.append(i.var(ddof=1) * (len(i) - 1))
all_vals.extend(i)
# Get within Group variances (denominator)
dfd = num_cases - len(group_means)
# need to add a check -- if the sum of the group variances is zero it will
# error, but only if the between_Groups value is not zero
within_Groups = np.sum(group_variances) / dfd
if within_Groups == 0.:
return nan, nan
# Get between Group variances (numerator)
all_vals = np.array(all_vals)
grand_mean = all_vals.mean()
between_Groups = 0
for i in a:
diff = i.mean() - grand_mean
diff_sq = diff * diff
x = diff_sq * len(i)
between_Groups += x
dfn = len(group_means) - 1
between_Groups = between_Groups / dfn
F = between_Groups / within_Groups
return F, f_high(dfn, dfd, F)
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,
# test non-integer degrees of freedom
(13.7, 11.9, 3.8):
0.01340347,
# 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 = sorted(expected.items())
for (key, value) in e:
np.testing.assert_allclose(f_high(*key), value, atol=10e-7)
