def pf(q,df1,df2,ncp=0):
"""
Calculates the cumulative of the F-distribution
"""
from scipy.stats import f,ncf
if ncp==0:
result=f.cdf(x=q,dfn=df1,dfd=df2,loc=0,scale=1)
else:
result=ncf.cdf(x=q,dfn=df1,dfd=df2,nc=ncp,loc=0,scale=1)
return result
def anova2_test_power(arms, alpha, mus, n, sigma):
n_cell = 0
ndf = 0
ddf = 0
n_cell = arms * 2
ndf = n_cell - 1
ddf = n * n_cell - ndf - 1
nu = n * np.sum((mus - np.mean(mus))**2) / sigma / sigma
f_cut = f.ppf(1 - alpha, ndf, ddf)
power = 1 - ncf.cdf(f_cut, ndf, ddf, nu)
return power
def anovaf_test_power(arms, alpha, mus, n, sigma):
ndf = arms - 1
ddf = (arms - 1) * (n)
nu = n * sum((mus - np.mean(mus))**2) / sigma / sigma
f_cut = f.ppf(1 - alpha, ndf, ddf)
power = 1 - ncf.cdf(f_cut, ndf, ddf, nu)
return power
def f_power(model, design, effect_size, alpha):
"""Calculates the power of an F test.
This calculates the probability that the F-statistic is above its critical
value (alpha) given an effect of some size.
:param model: A patsy formula for which to calculate power.
:type model: patsy.formula
:param design: A pandas.DataFrame representing a design.
:type design: pandas.DataFrame
:param effect_size: The size of the effect that the test should be able to detect (also called a signal to noise
ratio).
:type effect_size: float
:param alpha: The critical value that we want the test to be above.
:type alpha: float between 0 and 1
:returns: A list of percentage probabilities that an F-test could detect an effect of the given size at the given
alpha value for a particular column.
Usage:
>>> design = dexpy.factorial.build_factorial(4, 8)
>>> print(dexpy.power.f_power("1 + A + B + C + D", design, 2.0, 0.05))
[ 95.016, 49.003, 49.003, 49.003, 49.003 ]
"""
X = dmatrix(model, design)
residual_df = X.shape[0] - X.shape[1]
XtXi = np.linalg.inv(np.dot(np.transpose(X), X))
non_centrality = 1 / np.diag(XtXi)
# pre-calculate crit value for 1 df, most common case
crit_value = f.ppf(1 - alpha, 1, residual_df)
power = []
for t in range(0, X.shape[1]):
nc = adjust_non_centrality(non_centrality[t], X[:,t])
nc *= effect_size * effect_size / 4.0
p = (1 - ncf.cdf(crit_value, 1, residual_df, nc))
power.append(p)
return power
def _compute_ppvals_33(self, pcurvetype="full"):
family = self._df_results["family"].values
df1, df2, stat, pvals, ncp33 = self._df_results[[
"df1", "df2", "stat", "p", "ncp33"
]].to_numpy().T
if pcurvetype == "full":
pthresh = .05 # Only keep p-values smaller than .05
propsig = 1 / 3 # Under 33% power, 1/3 of p-values should be lower than .05
else:
pthresh = .025 # Only keep p-values smaller than .025
# We don't know which prop of p-values should be smaller than .025 under 33% power, so compute it
propsig = 3 * self._compute_prop_lower_33(.025, family, df1, df2,
pvals, ncp33)
# We then stretch the ppval on the [0, 1] interval.
pp_33_f = (1 / propsig) * (ncf.cdf(stat, df1, df2, ncp33) -
(1 - propsig))
pp_33_chi = (1 / propsig) * (ncx2.cdf(stat, df1, ncp33) -
(1 - propsig))
pp_33 = np.where(family == "F", pp_33_f, pp_33_chi)
return np.array([
self._bound_pvals(pp) if p < pthresh else np.nan
for (p, pp) in zip(pvals, pp_33)
])
plt.annotate("beta= "+str(np.round(betacalc,3)),(mean_h0-stderr,.1*ymax))
plt.annotate("n= "+str(n),(alpha_xval+stderr/2,.2*ymax))
plt.legend(loc=1)
plt.xlabel("Effect Size")
plt.ylabel("Probability")
plt.title("Sample Size and Power Calculation")
plt.show()
#optimize beta to desired value
print("Power of test as entered (n={})= {:.2f}%".format(n,100*(1-betacalc)))
print("[nct power= {:.2f}%]".format((1-betacalc)*100))
#compute F dist power :
fcrit=f.ppf(1-alpha*sided,1,n-1)
dsr=mean_h1/sigma
betacalc_f=ncf.cdf(fcrit,1,n-1,n*dsr**2)
print("[fct power= {:.2f}%]".format((1-betacalc_f)*100))
def opt_n(n):
stderr_n=sigma/n**.5
lam_n=(mean_h1-mean_h0)/stderr_n
alpha_xval_n=t.isf(alphas,df=n-1,scale=stderr_n)
betah_n=nct.cdf(alpha_xval_n,df=n-1,nc=lam_n,scale=stderr_n)
if sided==2:
betal_n=nct.cdf(-alpha_xval_n,df=n-1,nc=lam_n)
betacalc_n=betah_n-betal_n
else:
betacalc_n=betah_n
return betacalc_n
# Display the probability density function (``pdf``): x = np.linspace(ncf.ppf(0.01, dfn, dfd, nc), ncf.ppf(0.99, dfn, dfd, nc), 100) ax.plot(x, ncf.pdf(x, dfn, dfd, nc), 'r-', lw=5, alpha=0.6, label='ncf pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = ncf(dfn, dfd, nc) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = ncf.ppf([0.001, 0.5, 0.999], dfn, dfd, nc) np.allclose([0.001, 0.5, 0.999], ncf.cdf(vals, dfn, dfd, nc)) # True # Generate random numbers: r = ncf.rvs(dfn, dfd, nc, size=1000) # And compare the histogram: ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2) ax.legend(loc='best', frameon=False) plt.show()
