![]() A type I error occurs when the statistical test erroneously indicates a significant result. Alpha controls how often we'll get a type I error. In statistical tests, this is done by setting a significance threshold $\alpha$ (alpha). It depends on how you define statistical significance. In a statistical setting, you'd interpret these unusually large differences as evidence that the two samples are statistically different. There is, however, still a probability of seeing a very large difference between values, even though they're estimates of the same population parameters. You must sample with replacement in order to ensure the independence assumption between elements of the sample. You can see that if you took two samples from this population, the difference between the mean of samples 1 and 2 is very small (this can be tried repeatedly). choice ( pop, 100, replace = True ) print ( "Sample 2 Summary" ) stats. choice ( pop, 100, replace = True ) print ( "Sample 1 Summary" ) stats. How would you ensure the independence between the elements of these samples? k = 100 sample1 = np. Now take two samples from this population and comment on the difference between their means and standard deviations. # Create a population with mean=100 and sd=20 and size = 1000 pop = np. set ( color_codes = True )įirst, create a population of 1000 elements with a mean of 100 and a standard deviation of 20. ![]() ![]() import numpy as np import pandas as pd import scipy.stats as stats import matplotlib.pyplot as plt import math import random import seaborn as sns sns. Now you will attempt to create a simulation to visualize this phenomenon using Python. Most medical literature uses a beta cut-off of 20% (0.2), indicating a 20% chance that a significant difference is missed. not detecting a difference when one actually exists.īeta is directly related to study power (Power = $1 - \beta$) which you will investigate further in the next lesson. Most medical literature uses an alpha cut-off of 5% (0.05), indicating a 5% chance that a significant difference is actually due to chance and is not a true difference.īeta ($\beta$): is the probability of a Type II error i.e. ![]() finding a difference when a difference does not exist.
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