Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 10 Comparing Two Groups Section 10.3 Other Ways of Comparing Means and Comparing Proportions

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 3 An alternative t-method can be used when, under the null hypothesis, it is reasonable to expect the variability as well as the mean to be the same. This method requires the assumption that the population standard deviations be equal. Alternative Method for Comparing Means Figure 10.7 Two Groups With Equal Population Standard Deviations. Question: What would a graph of the sample data look like to make you doubt this assumption?

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 4 This alternative method estimates the common value of and by: The Pooled Standard Deviation

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 5 Using the pooled standard deviation estimate, a 95% CI for is: This method has SUMMARY: Comparing Population Means, Assuming Equal Population Standard Deviations

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 6 The test statistic for is: This method has SUMMARY: Comparing Population Means, Assuming Equal Population Standard Deviations

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 7 These methods assume:  Independent random samples from the two groups.  An approximately normal population distribution for each group. (This is mainly important for small sample sizes, and even then, the CI and the two-sided test are usually robust to violations of this assumption).  (In practice, this type of inference is not usually relied on if one sample standard deviation is more than double the other one). SUMMARY: Comparing Population Means, Assuming Equal Population Standard Deviations

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 8 Calculate the P-Value and determine if there is a statistical difference between Arthroscopic surgery and Placebo at 5% level of significance. Example: Arthroscopic Surgery With a P-value of 0.63, we should not reject the null that there is no difference between placebo and Arthroscopic surgery. Table 10.7 Summary of Knee Pain Scores The descriptive statistics compare lavage and debridement arthroscopic surgery to a placebo (fake surgery) treatment.

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 9 Calculate a 95% Confidence Interval. We are 95% Confident that the difference between the placebo and surgery is in this range to 6.4. Notice that 0 is within this range. Thus, we should not reject the null hypothesis at the 5% significance level that there is no difference between the two treatment groups. Table 10.8 MINITAB Output for Comparing the Mean Knee Pain for Placebo and Arthroscopic Surgery Groups. Example: Arthroscopic Surgery

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 10 The ratio of proportions for two groups is: In medical applications for which the proportion refers to a category that is an undesirable outcome, such as death or having a heart attack, this ratio is called the relative risk. The ratio describes the sizes of the proportions relative to each other. The Ratio of Proportions: The Relative Risk

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 11 Recall Physician’s Health Study: This means that the proportion of the placebo group who had a cancer death was 1.30 times the proportion of the aspirin group who had a cancer death. The Ratio of Proportions: The Relative Risk