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
def t_test_power(alpha, mu_1, mu_2, n_1, n_2, sigma_1, sigma_2):
nu = ((sigma_1**2 / n_1 + sigma_2**2 / n_2)**2) / ((
(sigma_1**2 / n_1)**2) / (n_1 - 1) + ((sigma_2**2 / n_2)**2) /
(n_2 - 1))
theta = (mu_1 - mu_2) / ((sigma_1**2 / n_1 + sigma_2**2 / n_2)**0.5)
t_cut = t.ppf(1 - alpha / 2, nu)
power = 1 - (nct.cdf(t_cut, nu, theta) - nct.cdf(-t_cut, nu, theta))
return power
def pt(q,df,ncp=0):
"""
Calculates the cumulative of the t-distribution
"""
from scipy.stats import t,nct
if ncp==0:
result=t.cdf(x=q,df=df,loc=0,scale=1)
else:
result=nct.cdf(x=q,df=df,nc=ncp,loc=0,scale=1)
return result
def g_(p, n, K): from scipy.stats import nct return 1 - nct.cdf(sqrt(n) * K, n-1, sqrt(n) * x_scipy(p))
# Display the probability density function (``pdf``): x = np.linspace(nct.ppf(0.01, df, nc), nct.ppf(0.99, df, nc), 100) ax.plot(x, nct.pdf(x, df, nc), 'r-', lw=5, alpha=0.6, label='nct 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 = nct(df, nc) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = nct.ppf([0.001, 0.5, 0.999], df, nc) np.allclose([0.001, 0.5, 0.999], nct.cdf(vals, df, nc)) # True # Generate random numbers: r = nct.rvs(df, nc, size=1000) # And compare the histogram: ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) ax.legend(loc='best', frameon=False) plt.show()
lam=(mean_h1-mean_h0)/stderr
dsr=mean_h1/sigma
#set up x axis for plotting
xmin=mean_h0-3*stderr
xmax=mean_h1+3*stderr
xs=np.linspace(xmin,xmax,200)
#define H0 distribution
h0pdf=t.pdf(xs,df=n-1,loc=mean_h0,scale=stderr)
alpha_xval=t.isf(alphas,df=n-1,loc=mean_h0,scale=stderr)
ymax=h0pdf.max()
#define H1 distribution
h1pdf=nct.pdf(xs,df=n-1,nc=lam,scale=stderr)
betah=nct.cdf(alpha_xval,df=n-1,nc=lam,scale=stderr)
if sided==1.2:
betal=nct.cdf(-alpha_xval,df=n-1,nc=lam)
betacalc=betah-betal
else:
betacalc=betah
#plot results
plt.plot(xs,h0pdf,label="H0")
plt.plot(xs,h1pdf,label="H1")
plt.axvline(alpha_xval,ls="--",color="blue")
if sided==2:
plt.fill_between(xs,0,h0pdf,where=(xs>alpha_xval)|(xs<-alpha_xval),color="blue",alpha=.2,
label="alpha")
plt.fill_between(xs,0,h1pdf,where=(xs<alpha_xval)&(xs>-alpha_xval),color="orange",alpha=.2,
label="beta")
def g_(p, n, K):
from scipy.stats import nct
return 1 - nct.cdf(sqrt(n) * K, n - 1, sqrt(n) * x_scipy(p))