1 Hypothesis testing Week 10 Lecture 2. Friday, May 21, 2004 ISYS3015 Analytical Methods for IS professionals School of IT, University of Sydney 2 Functions

1

Hypothesis testing

Week 10 Lecture 2

Friday, May 21, 2004

ISYS3015 Analytical Methods for IS professionals

School of IT, University of Sydney 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.

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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.




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




Probability

The likelihood of something happening Denote by p Numerical value ranging

from 1 to 0 Probability of discrete

variables Probability of continuous

variables




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) 0.05, 0.01, 0.1, 0.001




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 errorType II error

Probability: 1- Probability:

Reject H0 Type I errorType I error Correct decision

Probability: Probability: 1-




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:

Two-tailed hypothesis No prediction about the direction of the relationship is made Example

There is a difference in interest of politics between people with high education and people with low education

H1: ≠




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 < reject null hypothesis




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

The corresponding value of its boundary is the critical value




Two tailed test

Two critical regions locate on two tails




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




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 >= zobservedH0 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




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 twotwo levels Approximately normal distribution of the measure

in the two groups is assumed




t-score

t-score difference between

means/standard error of the difference

Give both one- and two-tailed p-value

2

22

1

21

21

nn

t




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

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1 Hypothesis testing Week 10 Lecture 2. Friday, May 21, 2004 ISYS3015 Analytical Methods for IS professionals School of IT, University of Sydney 2 Functions