Hypothesis testing Chapter 8 - PowerPoint PPT Presentation

1 / 17
About This Presentation
Title:

Hypothesis testing Chapter 8

Description:

The p-value is a measure of the statistical significance of a test. ... NOT: the probability of is small. 9/3/09. STAT 390 Spring 2002. 11. Hypothesis testing ... – PowerPoint PPT presentation

Number of Views:22
Avg rating:3.0/5.0
Slides: 18
Provided by: pipcou
Category:

less

Transcript and Presenter's Notes

Title: Hypothesis testing Chapter 8


1
Lecture 23
Outline
  • Hypothesis testing (Chapter 8)
  • Introduction setup
  • test statistics
  • p-values

2
Hypothesis testing introduction
  • Recall in the cloud seeding example, we found
    that a 95 confidence interval for
  • Based on this interval, do you believe

is
some differences are negative!
3
Introduction to hypothesis testing
  • Example paint drying time. A consumer
    protection agency wants to test a claim that the
    average drying time of a new fast-drying paint
    is 20 minutes. A member of its research staff
    takes 36 boards and paints each with paint from
    36 different cans of paint and measures the time
    it takes each board to dry.
  • How do we determine whether the paint drying time
    is 20 minutes or longer?

4
The hypothesis testing setup
  • The null-hypothesis is that the mean drying time
    is 20 minutes
  • this hypothesis is what we are trying to refute
  • to do so we begin by assuming that it is true!
  • to refute the null, we determine how likely is
    our data (36 drying times) under the assumption
    that the null hypothesis is true

5
Paint drying time.
paint drying time

normal probability plot
see lecture 22, slide 16
6
Test statistics
  • Hypothesis tests are based on test statistics,
    since and, underit seems reasonable to base
    a test on
  • how reasonable is 2.94 under

t-distribution introduced in lecture 20, on
slide 11
7
p-values
  • A p-value is the probability of observing a
    sample with a test statistic as extreme or more
    extreme than the one we observed, assuming
    is true.

one sided alternative
T35 distribution
two sided alternative
observed t
8
p-values
  • the p-value in the paint drying example is

very unlikely outcome if the average drying
time is in fact 20 minutes
9
Example paint drying test
  • Summary
  • There is convincing evidence against the claim
    that the mean paint drying time is 20 minutes
    (p-value 0.0031, one sample t-test). The
    sample average paint drying time in our
    experiment was 20.758 minutes a 95 lower
    confidence limit for the mean paint drying time
    is 20.319 minutes.

10
Notes about p-values
  • The p-value is a measure of the statistical
    significance of a test. Small p-values are
    evidence against
  • The words as extreme or more extreme are
    relative to the direction of
  • Interpretation A small p-value means it is
    unlikely that we get a sample that gives us more
    evidence against the null than the one we have
    seen.

11
Hypothesis testing procedure
  • State the null and the alternative hypotheses
  • Decide on a test statistic
  • known distribution under null hypothesis
  • Calculate the p-value (observed significance
    level)
  • Report the results, evidence against

12
Other hypothesis tests
  • The crux of the testing procedure is deciding on
    the test statistic (needs to have known
    distribution) here are some examples

13
Other hypothesis tests
14
Example
  • Recall the cloud seeding experiment from lecture
    21. we wish to testvswhere
  • use the test statistic

15
Example
  • recall
  • Summary There is convincing statistical evidence
    the average log rainfall is greater for seeded
    clouds than unseeded clouds (p-value 0.0072).
    A 95 lower confidence bound for this difference
    is 0.3903

interpretation?
16
Notes on hypothesis testing
  • Never misinterpret a p-value
  • The 0.05 level of significance
  • Statistical significance differs from practical
    significance
  • The results of a test do not give the full story
    and thus are usually accompanied by a confidence
    interval
  • Relationship between hypothesis tests and
    confidence intervals

17
Some code
the t-test
lSeed_log(CloudsSeeded) lUSeed_log(CloudsUnseede
d) t.test(lSeed,lUSeed,pairedF,var.equalF,alt"g
reater")
Write a Comment
User Comments (0)
About PowerShow.com