powerfun.py

##------------------##
#   POWER FUNCTION   #
##------------------##

import plotly.plotly as py
from plotly.graph_objs import *
import numpy as np
from scipy.stats import norm


def f1(x, c, th0, sigma, n):
    return c + (th0 - x)/(sigma/np.sqrt(n))

trace1 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 30, th0 = 5.4)),
    name = "$1-\\Phi\\left[c'+\\frac{\\theta_0-\\theta}{\\sigma/\\sqrt{n}}\\right]$"
)
trace2 = Scatter(
    x = [5.2, 5.4],
    y = [1 - norm.cdf(f1(x = 5.4, c = 1.645, sigma = 1, n = 30, th0 = 5.4)), 0],
    name = "Critical Value",
    mode = "lines+text",
    text = ["$\\;\\alpha$", "$\\;\\theta_{0}$"],
    textposition = 'top right',
    textfont = Font(
      family = "sans serif",
    ),
    line = Line(
        shape = 'hv'
    )
)
layout = Layout(
    title = "Power Function",
    xaxis = XAxis(
        title = "$\\theta$"
    ),
    yaxis = YAxis(
        title = "$\\beta(\\theta)$"
    ),
    legend = Legend(
        x = 0.6,
        y = 0.3,
        traceorder = 'normal',
        font = Font(
            family = 'sans-serif',
            size = 12,
            color = '#000'
        )
    )
)

data = Data([trace1, trace2])
fig = Figure(data = data, layout = layout)
plot_url = py.plot(fig, filename = 'betatheta')


##-----------------##
#   TYPE II ERROR   #
##-----------------##

import plotly.plotly as py
from plotly.graph_objs import *
import numpy as np
from scipy.stats import norm


def f1(x, c, th0, sigma, n):
    return c + (th0 - x)/(sigma/np.sqrt(n))

trace1 = Scatter(
    x = np.linspace(5.4, 6.2, num = 100),
    y = norm.cdf(f1(x = np.linspace(5.4, 6.2, num = 100), c = 1.645, sigma = 1, n = 30, th0 = 5.4))
)
layout = Layout(
    title = "Type II Error",
    xaxis = XAxis(
        title = "$\\theta$"
    ),
    yaxis = YAxis(
        title = "$1 - \\beta(\\theta)$"
    ),
    legend=Legend(
        x = 0.6,
        y = 0.3,
        traceorder = 'normal',
        font = Font(
            family = 'sans-serif',
            size = 12,
            color = '#000'
        )
    )
)

data = Data([trace1])
fig = Figure(data = data, layout = layout)
plot_url = py.plot(fig, filename = 'type2')


##-----------------------------------------##
#   POWER FUNCTION WITH SAMPLE SIZE N = 35  #
##-----------------------------------------##

import plotly.plotly as py
from plotly.graph_objs import *
import numpy as np
from scipy.stats import norm


def f1(x, c, th0, sigma, n):
    return c + (th0 - x)/(sigma/np.sqrt(n))

trace1 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 34.25878, th0 = 5.4)),
    name = "$1-\\Phi\\left[1.645+\\frac{5.4-\\theta}{1/\\sqrt{34.25878}}\\right]$"
)
trace2 = Scatter(
    x = [5.2, 5.4],
    y = [1 - norm.cdf(f1(x = 5.4, c = 1.645, sigma = 1, n = 34.25878, th0 = 5.4)), 0],
    name = "Condition 1",
    mode = "lines+text",
    text = ["$\\;\\beta(\\theta_0)=0.05$", "$\\;\\theta_{0}$"],
    textposition = 'top right',
    textfont = Font(
      family = "sans serif",
    ),
    line = Line(
        shape = 'hv'
    )
)
trace3 = Scatter(
    x = [5.2, 5.9],
    y = [1 - norm.cdf(1.645 - np.sqrt(34.25878) / 2), 0],
    name = "Condition 2",
    mode = "lines+text",
    text = ["$\\;\\beta(\\theta_0+\\sigma/2)=0.9$", "$\\;\\theta_0+\\sigma/2$"],
    textposition = 'top right',
    textfont = Font(
      family = "sans serif",
    ),
    line = Line(
        shape = 'hv'
    )
)
layout = Layout(
    title = "Power Function with Sample Size, n ≈ 35",
    xaxis = XAxis(
        title = "$\\theta$"
    ),
    yaxis = YAxis(
        title = "$\\beta(\\theta)$"
    ),
    legend = Legend(
        x = 0.02,
        y = 0.85,
        traceorder = 'normal',
        font = Font(
            family = 'sans-serif',
            size = 12,
            color = '#000'
        )
    )
)

data = Data([trace1, trace2, trace3])
fig = Figure(data = data, layout = layout)
plot_url = py.plot(fig, filename = 'betatheta2')


##-----------------------------------------------##
#   EFFECT OF SAMPLE SIZE ON THE POWER FUNCTION   #
##-----------------------------------------------##

import plotly.plotly as py
from plotly.graph_objs import *
import numpy as np
from scipy.stats import norm


def f1(x, c, th0, sigma, n):
    return c + (th0 - x)/(sigma/np.sqrt(n))

trace1 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 10, th0 = 5.4)),
    name = "$n=10$"
)
trace2 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 30, th0 = 5.4)),
    name = "$n=30$"
)
trace3 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 50, th0 = 5.4)),
    name = "$n=50$"
)
trace4 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 70, th0 = 5.4)),
    name = "$n=70$"
)
trace5 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 100, th0 = 5.4)),
    name = "$n=100$"
)
trace6 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 200, th0 = 5.4)),
    name = "$n=200$"
)
trace7 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 500, th0 = 5.4)),
    name = "$n=500$"
)
trace8 = Scatter(
    x = np.linspace(5.2, 6.2, num = 100),
    y = 1 - norm.cdf(f1(x = np.linspace(5.2, 6.2, num = 100), c = 1.645, sigma = 1, n = 1000, th0 = 5.4)),
    name = "$n=1000$"
)
layout = Layout(
    title = "Effect of Sample Size on Power Function",
    xaxis = XAxis(
        title = "$\\theta$"
    ),
    yaxis = YAxis(
        title = "$\\beta(\\theta)$"
    ),
    legend = Legend(
        x = 0.85,
        y = 0.4,
        traceorder = 'normal',
        font = Font(
            family = 'sans-serif',
            size = 12,
            color = '#000'
        )
    )
)

data = Data([trace1, trace2, trace3, trace4, trace5, trace6, trace7, trace8])
fig = Figure(data = data, layout = layout)
plot_url = py.plot(fig, filename = 'effectofn')