1 / 20

Chapter 10

Chapter 10. Two-Sample Tests. 10-1: Comparing Two Independent Samples. Hypothesis Test 1: z Test for the difference in means. Hypothesis Test 2: Pooled-variance t Test for the difference in two means. Hypothesis Test 3: Separate-Variance t Test for Differences in two means.

darryl
Télécharger la présentation

Chapter 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10 Two-Sample Tests

  2. 10-1: Comparing Two Independent Samples • Hypothesis Test 1: z Test for the difference in means. • Hypothesis Test 2: Pooled-variance t Test for the difference in two means. • Hypothesis Test 3: Separate-Variance t Test for Differences in two means. • Confidence Interval Estimate for the difference between the means of two independent groups.

  3. 10-1: Comparing the Means of Two Independent Populations • Two means—other tests are coming. • Two Independent samples. • Describe Hypothesis testing procedure. • Chapter 10 Summary chart, page 382.

  4. Configuring Hypotheses (!) • What’s the variable of interest? Hypothesizing about a difference. • 1-tail or 2-tail? • Key words • Status quo • What do you want to conclude? • Which test to use? • Do you know the variance? • Do you suspect that the variances of the 2 populations are the same?

  5. Rejection Region • Reject Null Hypothesis for calculated value of test statistic more extreme than critical value of test statistic. • 2-tailed tests have 2 rejection regions! • Reject Null Hypothesis for observed significance (p-value) less than alpha.

  6. Test Statistic • Test statistic = (point estimate – hypothesized value) / appropriate standard deviation • The appropriate standard deviation is more often called the “standard error.” Its formula will usually change depending on the test that you are using: • Z • Pooled-variance t • Different variance t

  7. Notes • Random sampling. • However you define populations 1 and 2, you must get the same result. • Text considers upper tail only. • Z-test, pooled-variance t test, and separate variance t test might give conflicting answers. • Separate-Variance t test has a simpler standard error but a more complicated degrees of freedom in critical value.

  8. More Notes • Populations are assumed to be normally distributed. • The pooled-variance t test is robust to departures from normality, provided the sample sizes are large. • Normality Comment, page 351. • Equation 10.3, page 352.

  9. 10.2 Comparing the Means of Two Related Populations • Paired or matched samples. Sometimes described as “dependent” test or sampling or as “repeated measurements.” • Table 10.3, page 359: “Difference” is the variable of interest.

  10. Hypotheses • Can be 1-tail or 2-tail. • H0: μD = 0 or 1-tail.

  11. Rejection Region or Decision Rule; Test Statistic • Reject H0 for value of test statistic more extreme than critical value. • Critical value is either a “z” or “t” value from the appropriate table, obtained in the usual way. • Degrees of freedom for “t” is = n –1 (# of pairs!). • Test statistic is either “z” or “t”. It is calculated in the usual way:

  12. Notes • Random samples. • Normally distributed population (tests are robust to this assumption). • The confidence interval exists. • See note on page 365. • We will return to this concept when we discuss “blocking.”

  13. 10.3 Comparing Two Population Proportions • Consider only the z test on page 368. • Proportions are calculated for ___ data. • The confidence interval exists (page 372).

  14. 10.4: F Test for the difference between two variances • Recall that we had 2 “t” tests for differences in means (in 10.1). • The difference between those 2 “t” tests is whether or not you can assume that the variance for population 1 is the same as the variance for population 2. • You can test for differences between the 2 variances.

  15. Hypothesis Test • Can be 1 tail or 2 tail. • Can be written for variance or standard deviation.

  16. Rejection Region Reject null hypothesis for calculated test statistic more extreme than a critical value. • Reject null hypothesis for p-value less than alpha. • The critical value is “F.” It has two d.f. calculations.

  17. More on Rejection Region • Critical values of F come from a table. • A 2-tail test requires 2 critical values: an upper and a lower (Figure 10.18, p 377) • The table will not give lower critical values directly. Use formula 10.12, page 377. • A 1-tail test should be written so that it is an upper-tail test.

  18. Examine Sample, Calculate Test Statistic • The test statistic is “F” • F = S12 / S22

  19. Decide and Conclude • At alpha = 0.05, there is sufficient information to say that the population variances are not equal. • At alpha = 0.05, there is insufficient information to say that the population variances are not equal. • At alpha = 0.05, there is sufficient information to say that the first population variance is larger than the second population variance.

  20. Notes • Test is most often used to decide which “t” test to use on the means. Use the 2-tail test. • When concerned about comparing variability across processes, you will most often use a 1-tail test. • This test is sensitive to departures from normality.

More Related