def calc_ttest_1(sample, x0, counts, alpha=0.05):
"""Calculates statistical power for a one-sample t test
Parameters
----------
sample : array
The sample to be compared
x0 : float
The mean value compared to the distribution
counts : array
The sample sizes used to calculate power
alpha : float, optional
The critical value for power. Default is 0.05.
Returns
-------
power : array
This describes the probability of seeing a signifigant difference
between the sample and mean for the specified number of observations
(count) and critical value based on the one sample t test.
"""
# Gets the distribution paramteres
[x, s] = _get_vitals(sample)
# Gets the degrees of freedom
df = counts - 1
# Gets the noncentrality paramter
noncentrality = np.absolute(x - x0) / s * np.sqrt(counts)
# Gets the t statistic
tsu = stats.t.ppf(1 - alpha / 2, df)
tsl = stats.t.ppf(alpha / 2, df)
# Calculates the power
power = 1 - (sp.nctdtr(df, noncentrality, tsu) +
sp.nctdtr(df, noncentrality, tsl))
return power
def calc_pearson(sample1, sample2, counts, alpha=0.05):
"""Calculates power for pearsons r"""
r = stats.pearsonr(sample1, sample2)[0]
noncentrality = r / np.sqrt(1 - np.square(r)) * np.sqrt(counts)
df = counts - 2
ts = stats.t.ppf(1 - alpha / 2, df)
power = (1 - sp.nctdtr(df, noncentrality, ts) +
sp.nctdtr(df, noncentrality, -ts))
return power
def calc_ttest_ind(sample1, sample2, counts, alpha=0.05):
"""Calculates statistical power for a two sample t test
This is based on [1]_.
Parameters
----------
sample1, sample2 : array
The samples being tested
counts : array
the number of observations per sample to be used to test the power
alpha : float
The critical value for power calculations
Returns
-------
ndrray
This describes the probability of seeing a signifigant difference
between the samples for the specified number of observations
(count) and critical value based on the independent two sample t test.
References
----------
.. [1] Lui, X.S. (2014) *Statistical power analysis for the social and
behavioral sciences: basic and advanced techniques.* New York: Routledge.
378 pg.
"""
# Gets the distribuation characterization
[x1, s1] = _get_vitals(sample1)
[x2, s2] = _get_vitals(sample2)
d = effect_ttest_ind(sample1, sample2)
# Calculates the degrees of freedom
df = (counts - 1) * np.square(s1 + s2) / (np.square(s1) + np.square(s2))
# Calculates the non centrality parameter
noncentrality = np.absolute(d) * np.sqrt(counts / 2)
tsu = stats.t.ppf(1 - alpha / 2, df)
tsl = stats.t.ppf(alpha / 2, df)
power = 1 - (sp.nctdtr(df, noncentrality, tsu) +
sp.nctdtr(df, noncentrality, tsl))
return power
def calc_ttest_1(sample, x0, counts, alpha=0.05):
"""Calculates statistical power for a one-sample t test
This is based on [1]_.
Parameters
----------
sample : array
The sample to be compared
x0 : float
The mean value compared to the distribution
counts : array
The sample sizes used to calculate power
alpha : float, optional
The critical value for power. Default is 0.05.
Returns
-------
ndarray
This describes the probability of seeing a signifigant difference
between the sample and mean for the specified number of observations
(count) and critical value based on the one sample t test.
References
----------
.. [1] Lui, X.S. (2014) *Statistical power analysis for the social and
behavioral sciences: basic and advanced techniques.* New York: Routledge.
378 pg.
"""
# Gets the effect size
d = effect_ttest_1(sample, x0)
# Gets the degrees of freedom
df = counts - 1
# Gets the noncentrality paramter
noncentrality = np.absolute(d) * np.sqrt(counts)
# Gets the t statistic
tsu = stats.t.ppf(1 - alpha / 2, df)
tsl = stats.t.ppf(alpha / 2, df)
# Calculates the power
power = 1 - (sp.nctdtr(df, noncentrality, tsu) +
sp.nctdtr(df, noncentrality, tsl))
return power
def calc_ttest_ind(sample1, sample2, counts, alpha=0.05):
"""Calculates statistical power for a two sample t test
This is based on
Lui, X.S. (2014) *Statistical power analysis for the social and
behavioral sciences: basic and advanced techniques.* New York:
Routledge. 378 pg.
Parameters
----------
sample1, sample2 : array
The samples being tested
counts : array
the number of observations per sample to be used to test the power
alpha : float
The critical value for power calculations
Returns
-------
ndrray
This describes the probability of seeing a signifigant difference
between the samples for the specified number of observations
(count) and critical value based on the independent two sample t test.
"""
# Gets the distribuation characterization
[x1, s1] = _get_vitals(sample1)
[x2, s2] = _get_vitals(sample2)
# Calculates the degrees of freedom
df = (counts - 1) * np.square(s1 + s2)/(np.square(s1) + np.square(s2))
# Calculates the non centrality parameter
noncentrality = (np.absolute(x1 - x2) /
(np.sqrt(np.square(s1) / counts + np.square(s2) / counts))
)
tsu = stats.t.ppf(1 - alpha / 2, df)
tsl = stats.t.ppf(alpha / 2, df)
power = 1 - (sp.nctdtr(df, noncentrality, tsu) +
sp.nctdtr(df, noncentrality, tsl))
return power
def calc_ttest_1(sample, x0, counts, alpha=0.05):
"""Calculates statistical power for a one-sample t test
This is based on
Lui, X.S. (2014) *Statistical power analysis for the social and
behavioral sciences: basic and advanced techniques.* New York:
Routledge. 378 pg.
Parameters
----------
sample : array
The sample to be compared
x0 : float
The mean value compared to the distribution
counts : array
The sample sizes used to calculate power
alpha : float, optional
The critical value for power. Default is 0.05.
Returns
-------
ndarray
This describes the probability of seeing a signifigant difference
between the sample and mean for the specified number of observations
(count) and critical value based on the one sample t test.
"""
# Gets the distribution paramteres
[x, s] = _get_vitals(sample)
# Gets the degrees of freedom
df = counts - 1
# Gets the noncentrality paramter
noncentrality = np.absolute(x - x0) / s * np.sqrt(counts)
# Gets the t statistic
tsu = stats.t.ppf(1 - alpha / 2, df)
tsl = stats.t.ppf(alpha / 2, df)
# Calculates the power
power = 1 - (sp.nctdtr(df, noncentrality, tsu) +
sp.nctdtr(df, noncentrality, tsl))
return power
def calc_pearson(sample1, sample2, counts, alpha=0.05):
"""Calculates power for pearsons R
This is based on [1]_.
Parameters
----------
sample1, sample2 : ndarrays
Arrays of observations to be tested. The samples must be of the same
length, and sample positions should match samples.
counts : array
the number of observations per sample to be used to test the power
alpha : float
The critical value for power calculations
Returns
-------
ndarray
This describes the probability of seeing a signifigant difference
between the samples for the specified number of observations
(count) and critical value based on the pearson method.
References
----------
.. [1] Lui, X.S. (2014) *Statistical power analysis for the social and
behavioral sciences: basic and advanced techniques.* New York: Routledge.
378 pg.
"""
r = stats.pearsonr(sample1, sample2)[0]
noncentrality = r / np.sqrt(1 - np.square(r)) * np.sqrt(counts)
df = counts - 2
ts = stats.t.ppf(1 - alpha / 2, df)
power = (1 - sp.nctdtr(df, noncentrality, ts) +
sp.nctdtr(df, noncentrality, -ts))
return power
def calc_ttest_ind(sample1, sample2, counts, alpha=0.05):
"""Calculates statistical power for a two sample t test
Parameters
----------
sample1, sample2 : array
The samples being tested
counts : array
the number of observations per sample to be used to test the power
alpha : float
The critical value for power calculations
Returns
-------
power : array
This describes the probability of seeing a signifigant difference
between the samples for the specified number of observations
(count) and critical value based on the independent two sample t test.
"""
# Gets the distribuation characterization
[x1, s1] = _get_vitals(sample1)
[x2, s2] = _get_vitals(sample2)
# Calculates the degrees of freedom
df = (counts - 1) * np.square(s1 + s2) / (np.square(s1) + np.square(s2))
# Calculates the non centrality parameter
noncentrality = (
np.absolute(x1 - x2) /
(np.sqrt(np.square(s1) / counts + np.square(s2) / counts)))
tsu = stats.t.ppf(1 - alpha / 2, df)
tsl = stats.t.ppf(alpha / 2, df)
power = 1 - (sp.nctdtr(df, noncentrality, tsu) +
sp.nctdtr(df, noncentrality, tsl))
return power
def calc_pearson(sample1, sample2, counts, alpha=0.05):
"""Calculates power for pearsons R
This is based on
Lui, X.S. (2014) *Statistical power analysis for the social and
behavioral sciences: basic and advanced techniques.* New York:
Routledge. 378 pg.
Parameters
----------
sample1, sample2 : ndarrays
Arrays of observations to be tested. The samples must be of the same
length, and sample positions should match samples.
counts : array
the number of observations per sample to be used to test the power
alpha : float
The critical value for power calculations
Returns
-------
ndarray
This describes the probability of seeing a signifigant difference
between the samples for the specified number of observations
(count) and critical value based on the pearson method.
"""
r = stats.pearsonr(sample1, sample2)[0]
noncentrality = r / np.sqrt(1 - np.square(r)) * np.sqrt(counts)
df = counts - 2
ts = stats.t.ppf(1 - alpha / 2, df)
power = (1 - sp.nctdtr(df, noncentrality, ts) +
sp.nctdtr(df, noncentrality, -ts))
return power
def _cdf(self, x, df, nc):
return special.nctdtr(df, nc, x)
def _cdf(self, x, df, nc):
return special.nctdtr(df, nc, x)