Hypothesis Testing

1
Hypothesis Testing

• Ginger Holmes Rowell, Ph. D.
• April 24, 2002

2
Hypothesis Testing (HT)

• Uses
• Types
• General Procedures
• Example
• Review of Error Types
• Type I Type II

3
Hypothesis Testing - Uses

• Medical Clinical Trials
• Show that Drug A lowers cholesterol more than the
  placebo (2-Sample for difference in means)
• Show that the percent of people who have side
  effects from from Drug A is NOT different from
  the group taking the placebo (2-Sample for
  difference in proportions)

4
Hypothesis Testing - Uses

• Agriculture
• Show that fertilizer A works better than
  fertilizer B
• Psychology Experiments
• Show that Intervention A keeps kids off of drugs
  better than what has been done traditionally
• Education
• Show that teaching method A is more effective
  than teaching method B

5
Two Broad Categories of HT

• Parametric Methods frequently used, more common
• Nonparametric Methods used if sample size is
  small and populations are not normal(We will not
  talk about this type of HT.)

6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
HT General Procedure - Steps

• Conduct a literature review or pilot study
• Form your hypothesis
• Set your threshold of error (determine desired
  significance level)
• Design your experiment
• Determine which HT to use
• Determine Needed Sample Size

10
HT Procedure Steps Contin.

• Collect your data
• Enter data into appropriate tool (calculator,
  statistical software)
• Examine data graphically
• Find descriptive statistics
• Use these methods to check for typos, errors,

11
HT Procedure Steps Contin.

• Find your test statistic and use it determine
  whether your data supports the null or
  alternative hypothesis.

12
HT Example

• Research Hypothesis
• Using CI Applets will help students learn more
  about CIs
• Set Error Limit 5 for Type I Error
• Design Experiment
• Give a pre-test, students use CI applet, give a
  post-test

13
Statistical Analysis

• Hypothesis
• Using the java applets will improve content
  knowledge for math teachers
• Ho mimprovement 0
• Ha mimprovement gt 0
• Improvement Posttest score Pretest Score
• Statistical Test
• Paired difference t-test (small sample)
• Average improvement was approximately normal

14
HT Example

• Decide which HT to use ???
• Decide the needed sample size
• Collect Data
• You helped with that part
• Examine Data
• Graphically, descriptive statistics
• Check for typos, errors, ...

15
HT Example - DATA
Points Improved post test score pre test
score (Each test is scored out of 5 possible
points)
16
HT Example - DATA
Variable N Mean StDev SE Mean Points
Improved 12 1.3 1.6 0.463
17

18
HT Example

• What does our data say?
• Is that enough evidence to reject the null in
  favor of the alternative?
• What do you think?
• How much evidence do you need?
• Especially with this small sample size.

19
HT Example - The WORK

• Test statistic
• Interpretation The test statistic tells you the
  number of standard deviations that the sample
  mean (or proportion or variance) falls from the
  hypothesized value.

20
Using Your TI-83 for HT

• Press STATgtTESTSgtt-test
• Input DATA
• m0 0
• LIST LI
• Freq 1
• m gt
• select Calculate

21
HT Example

• Test Statistic t 2.70
• What does this tell us? (Remember the Empirical
  Rule)
• If the null is true, the chance of getting a data
  set like ours or one that supports the
  alternative even more is small (1 chance).
• We got our data set did not make any errors.
• Do you believe the null hypothesis is true?

22
HT Example

• Conclusion
• Reject the null in favor of the alternative
  hypothesis
• What does that mean in the context of our
  problem?
• We can expect an average improvement in content
  knowledge for math teacher who use the Regression
  applet

23
HT Example

• Next Question How much improvement
• Answer Find a 95 confidence interval
• Review use your calculator to do this and
  interpret the result.

24
Conclusion Regression Applet

• A statistically significant improvement in their
  average content knowledge can be expected for
  math teachers using the Regression applet (Rice
  Probability Webs). (t2.7, n12, p0.01)
• We expect (with 95 confidence) that the average
  improvement in content knowledge of regression
  will be between 0.2 and 2.3 points on a 5 point
  scale.

25
Review

• Null Hypothesis
• Alternative

26
Type I and II Errors

• Type I Error
• Type II Error
• Power of Test

27
Sample Size

• What is the effect of sample size on statistical
  power?

28
Comments

• I hope you
• Understand how to think about forming a
  hypothesis
• Understand that actually testing the hypothesis
  is more than looking at the two sample averages
  and saying whether you think they are different.

29
Questions

• ????????