1. Hypothesis testing
Week 10 Lecture 2

2. Functions of inferential statistics
To estimate a population parameter from a random sample
If you draw two random samples of the same size from a population, it is very likely that the two means you get will be different
Standard error of the mean is the standard deviation of all sample means:
To test hypotheses
data are from sample
The probability that our result is due to chance alone
If you get data from whole population, no hypothesis testing is required.
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

3. Two types of hypotheses
Research hypothesis (alternative hypothesis)
A prediction of the relation between variables
Null hypothesis (H0)
There will be no relation between the variables
Any relation observed are due to chance alone
Examples:
The higher the annual income, the greater the Internet usage
There is no relation between annual income and Internet usage
It is the null hypothesis that is tested
We look at the probability that our result is due to chance alone.
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

4. Result of hypothesis testing
Reject Null hypothesis
Indirectly accept the research hypothesis
Research hypothesis is supported
Fail to reject null hypothesis
Research hypothesis is not supported
How do we determine whether or not to reject the null hypothesis
Compute some statistics reflecting the difference
Find out the probability that any difference is due to chance
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

5. ISYS3015 Analytical Methods for IS professionals
Probability
The likelihood of something happening
Denote by p
Numerical value ranging from 1 to 0
Probability of discrete variables
Probability of continuous variables
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

6. Statistical significance
How far must an outcome be away from the expected?
At what level of probability we believe a result is more likely due to a real difference (caused by experiment) than to chance
Level of significance (significance level)
a =0.05, 0.01, 0.1, 0.001
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

7. Making errors in hypothesis testing
Type I error
Reject the null hypothesis when it is true
Type II error
Fail to reject the null hypothesis when it is false
Significance level --  (0.05)
The probability of rejecting null hypothesis when it is true
Power – 1- (0.80)
The ability to reject a false null hypothesis
Actual situation: null hypothesis is
Conclusion
True
False
Fail to reject H0
Correct decision
Type II error
Probability: 1- 
Probability: 
Reject H0
Type I error
Probability: 
Probability: 1-
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

8. One-tailed and two tailed hypotheses
One-tailed hypothesis
The direction of the relation is predicted in the alternative hypothesis
Example
People with high education are more interested in politics than people with low education
H1: m1 > m2
Two-tailed hypothesis
No prediction about the direction of the relationship is made
There is a difference in interest of politics between people with high education and people with low education
H1: m1 ≠ m2
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

9. Drawing conclusion from hypothesis test
p-value
The p-value indicates the probability that one would obtained a test statistic which is more extreme than the observed one when the null hypothesis is true.
The possibility that any observed difference is due to chance.
if p-value < a, reject null hypothesis
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

10. ISYS3015 Analytical Methods for IS professionals
One-tailed test
Upper tail test
Critical region (reject region) locates on the upper tail
The area indicates the maximum probability that you can reject a null hypothesis (a)
The corresponding value of its boundary is the critical value
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

11. ISYS3015 Analytical Methods for IS professionals
Two tailed test
Two critical regions locate on two tails
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

12. One and two-tailed tests
Easier to reject a null hypothesis in a one-tailed than in a two-tailed test if the test statistic falls in the expected direction
One tailed-test can not handle the situation when the test statistic falls in the “wrong” tail
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

13. p-value in one and two-tailed test
p-value from a two-tailed test is double the value from a one-tailed test
p = P (z >= zobservedH0 is true ) (upper-tailed test)
p = 2P (z >= | zobserved |H0 is rue) (two-tailed test)
Some test returns either one or two-tailed test results, some returns both
Find the p-value suitable for your hypothesis
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

14. Simplest hypothesis testing statistic
t-test
Assesses whether the means of two groups are statistically different from each other
Sample size is small
Dependent variable is interval or ratio scale
Independent variable has two levels
Approximately normal distribution of the measure in the two groups is assumed
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

15. ISYS3015 Analytical Methods for IS professionals
t-score
t-score
difference between means/standard error of the difference
Give both one- and two-tailed p-value
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney

16. ISYS3015 Analytical Methods for IS professionals
t-test case
Scenario
You want to measure the acquisition of mathematical skills by distance learning and traditional classroom learning. The study involves the comparison of 20 students, ten taught in classroom and ten taught by distance learning program. The final test scores were collected as dependent variable.
Write down your null hypothesis
Write a two-tailed hypothesis and a one-tailed hypothesis
Friday, May 21, 2004
ISYS3015 Analytical Methods for IS professionals
School of IT, University of Sydney