hypothesis testing (hs yam - rev a).ppt

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.