文档介绍：Hypothesis Testing
(Analyze Phase)
Scope of Module
Hypothesis
Sampling Risks
One-Tailed and Two-Tailed Tests
P-Value
Applications of Hypothesis Testing
Statistics — An Overview
Hypothesis
A hypothesis is a statement or claim about a property of a population.
The hypotheses to be tested consists of plementary statements:
1) The null hypothesis (denoted by H0) is a statement about the value of a population parameter; it must contain the condition of equality.
2) The alternative hypothesis (denoted by H1) is the statement that must be true if the null hypothesis is false.
. H0: = some value vs H1: some value
H0: some value vs H1: > some value
H0: some value vs H1: < some value
Egon S Pearson Jerzy Neyman
On the Problem of the Most Efficient Tests of Statistical Hypothesis
Philosophical Transactions of the Royal Society (1933)
Sampling Risks or Errors
Sampling Risks
is the risk of concluding that H0 is false, when it is true.
Also called Type I Error or Producer’s Risk.
1- is the Confidence Level for H0.
observed value
H0
Sampling Risks
is the risk of accepting H0, when it is false.
Also called Type II Error or Consumer’s Risk.
Power of a test (1-) is the chance of rejecting H0, when it is false.
observed value
H0
H1
Sampling Risks
H0 : = some value
H1 : some value
Null Hypothesis
True
False
Decision
Accept H
0
Reject H
0
Correct Decision
1 –
Correct Decision
1 –
Type I Error
Type II Error
Controlling Sampling Risks
1. For any fixed , an increase in the sample size will cause a decrease in .
2. For any fixed sample size, a decrease in will cause an increase in . Conversely, an increase in will cause a decrease in .
3. To decrease both and , increase the sample size.