def test_mean_diff_with_pop_variance(n1: int, mean1: float,
pop_variance1: float, n2: int,
mean2: float, pop_variance2: float,
significance: float) -> (bool, float):
"""
母分散既知において平均値の差に関するz検定を行う．
## Parameters
`n1`: 1つめの標本の大きさ
`mean1`: 1つめの標本の標本平均
`pop_variance1`: 1つめの標本の既知の母分散
`n2`: 2つめの標本の大きさ
`mean2`: 2つめの標本の標本平均
`pop_variance2`: 2つめの標本の既知の母分散
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`z`: 実現値
"""
z = (mean1 - mean2) / math.sqrt(pop_variance1 / n1 + pop_variance2 / n2)
bottom = stats.norm.ppf(significance / 2)
top = stats.norm.ppf(1 - significance / 2)
side = "double"
is_reject = stats_test.is_reject(z, stats_test.side_from_str(side), bottom,
top, None, None)
return (is_reject, z)
def test_var_ratio(n1: int, sample_variance1: float, n2: int,
sample_variance2: float,
significance: float) -> (bool, float):
"""
分散比に関するF検定を行う．
## Parameters
`n1`: 1つめの標本の大きさ
`sample_variance1`: 1つめの標本の既知の母分散
`n2`: 2つめの標本の大きさ
`sample_variance2`: 2つめの標本の既知の母分散
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`z`: 実現値
"""
f = n1 * (n2 - 1) * sample_variance1 / (n2 * (n1 - 1) * sample_variance2)
df1 = n1 - 1
df2 = n2 - 1
bottom = stats.f.ppf(significance / 2, df1, df2)
top = stats.f.ppf(1 - significance / 2, df1, df2)
side = "double"
is_reject = stats_test.is_reject(f, stats_test.side_from_str(side), bottom,
top, None, None)
return (is_reject, f)
def test_mean_diff_without_pop_variance(n1: int, mean1: float,
variance1: float, n2: int,
mean2: float, variance2: float,
significance: float) -> (bool, float):
"""
平均値の差に関するt検定を行う．
## Parameters
`n1`: 1つめの標本の大きさ
`mean1`: 1つめの標本の標本平均
`variance1`: 1つめの標本の標本分散
`n2`: 2つめの標本の大きさ
`mean2`: 2つめの標本の標本平均
`variance2`: 2つめの標本の標本分散
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`t`: 実現値
"""
df = n1 + n2 - 2
u = (n1 * variance1 + n2 * variance2) / df
t = (mean1 - mean2) / math.sqrt(u * (1 / n1 + 1 / n2))
bottom = stats.t.ppf(significance / 2, df)
top = stats.t.ppf(1 - significance / 2, df)
side = "double"
is_reject = stats_test.is_reject(t, stats_test.side_from_str(side), bottom,
top, None, None)
return (is_reject, t)
def cmd(z_test: bool, n: int, hypothesis: float, mean: float, variance: float, stdev: float, level: float, side: str):
if level <= 0 or level >= 1:
import sys
print("信頼係数は(0, 1)の範囲で指定してください．", file=sys.stderr)
exit()
if stdev <= 0:
stdev = math.sqrt(variance)
if z_test:
(is_reject, test_stat) = test_mean_with_pop_variance(
n, hypothesis, mean, stdev, level, stats_test.side_from_str(side))
else:
(is_reject, test_stat) = test_mean_without_pop_variance(
n, hypothesis, mean, stdev, level, stats_test.side_from_str(side))
print(stats_test.show_result(is_reject, test_stat, "μ", hypothesis))
def test_stats_test_mean_with_pop_var1(self):
n = 30
hypothesis = 60
mean = 56.75
pop_stdev = 15
level = 0.05
side = "double"
(is_reject, test_stat) = stats_test_mean.test_mean_with_pop_variance(
n, hypothesis, mean, pop_stdev, level,
stats_test.side_from_str(side))
self.assertFalse(is_reject)
self.assertAlmostEqual(test_stat, -1.187, places=3)
def test_stats_test_mean_without_pop_var1(self):
n = 10
hypothesis = 12
mean = 12.36
stdev = math.sqrt(0.910)
level = 0.05
side = "double"
(is_reject,
test_stat) = stats_test_mean.test_mean_without_pop_variance(
n, hypothesis, mean, stdev, level, stats_test.side_from_str(side))
self.assertFalse(is_reject)
self.assertAlmostEqual(test_stat, 1.132, places=3)
def test_stats_test_mean_with_pop_var2(self):
n = 50
hypothesis = 30
mean = 28.1
pop_stdev = math.sqrt(60)
level = 0.05
side = "left"
(is_reject, test_stat) = stats_test_mean.test_mean_with_pop_variance(
n, hypothesis, mean, pop_stdev, level,
stats_test.side_from_str(side))
self.assertTrue(is_reject)
self.assertAlmostEqual(test_stat, -1.734, places=3)
def test_no_correl(n: int, r: float, significance: float) -> (bool, float):
"""
無相関かどうかのt検定を行う．
## Parameters
`n`: 標本の大きさ
`r`: 標本相関係数
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`t`: 実現値
"""
df = n - 2
t = r * math.sqrt(df) / math.sqrt(1 - math.pow(r, 2))
bottom = stats.t.ppf(significance / 2, df)
top = stats.t.ppf(1 - significance / 2, df)
side = stats_test.side_from_str("double")
is_reject = stats_test.is_reject(t, side, bottom, top, None, None)
return (is_reject, t)
def test_variance(n: int, target_variance: float, sample_variance: float,
significance: float) -> (bool, float):
"""
分散に関するカイ2乗検定を行う．
## Parameters
`n`: 標本の大きさ
`target_variance`: 帰無仮説において等しいと仮定する分散
`sample_variance`: 標本分散
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`x`: 実現値
"""
x = n * sample_variance / target_variance
df = n - 1
bottom = stats.chi2.ppf(significance / 2, df)
top = stats.chi2.ppf(1 - significance / 2, df)
side = "double"
is_reject = stats_test.is_reject(x, stats_test.side_from_str(side), bottom,
top, None, None)
return (is_reject, x)
def test_correl_diff(n1: int, n2: int, r1: float, r2: float,
significance: float) -> (bool, float):
"""
相関係数に関するz検定を行う．
## Parameters
`n`: 標本の大きさ
`target_r`: 帰無仮説で等しいと仮定する相関係数
`r`: 標本相関係数
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`z`: 実現値
"""
x1 = math.log((1 + r1) / (1 - r1)) / 2.0
x2 = math.log((1 + r2) / (1 - r2)) / 2.0
z = (x1 - x2) / math.sqrt(1 / (n1 - 3) + 1 / (n2 - 3))
bottom = stats.norm.ppf(significance / 2)
top = stats.norm.ppf(1 - significance / 2)
side = stats_test.side_from_str("double")
is_reject = stats_test.is_reject(z, side, bottom, top, None, None)
return (is_reject, z)
def test_correl(n: int, target_r: float, r: float,
significance: float) -> (bool, float):
"""
相関係数に関するz検定を行う．
## Parameters
`n`: 標本の大きさ
`target_r`: 帰無仮説で等しいと仮定する相関係数
`r`: 標本相関係数
`significance`: 有意水準
## Returns
`is_reject`: 帰無仮説が棄却されるかどうか
`z`: 実現値
"""
x = math.log((1 + r) / (1 - r)) / 2.0
xi = math.log((1 + target_r) / (1 - target_r)) / 2.0
z = (x - xi) * math.sqrt(n - 3)
bottom = stats.norm.ppf(significance / 2)
top = stats.norm.ppf(1 - significance / 2)
side = stats_test.side_from_str("double")
is_reject = stats_test.is_reject(z, side, bottom, top, None, None)
return (is_reject, z)