CHAPTER 21 Comparing Two Means Basic Practice of
CHAPTER 21: Comparing Two Means Basic Practice of Statistics 7 th Edition Lecture Power. Point Slides
In Chapter 21, We Cover … �Two-sample problems �Comparing two population means �Two-sample t procedures �Robustness again �Avoid the pooled two-sample t procedures* �Avoid inference about standard deviations*
Two-Sample Problems Suppose we want to compare the mean of some quantitative variable for the individuals in two populations―Population 1 and Population 2. Our parameters of interest are the population means µ 1 and µ 2. The best approach is to take separate random samples from each population and to compare the sample means. We use the mean response in the two groups to make the comparison. Here’s a table that summarizes these two situations: 3
Comparing Two Population Means � Population 1 2 Variable Mean Standard deviation
Comparing Two Population Means � Population 1 2 Sample size Sample mean Sample standard deviation
Two-Sample t Procedures �
Two-Sample t Procedures �
Two-Sample t Procedures: Confidence Interval for µ 1 - µ 2 �
Example �
Example � Group Std. Dev. , s 1 (lean) 10 525. 751 107. 121 2 (obese) 10 373. 269 67. 498
Two-Sample t Procedures: Two-Sample t Test �
Two-Sample t Test for the Difference Between Two Means 12
Example � Group Condition s 1 Service 57 105. 32 14. 68 2 No service 17 96. 82 14. 26
Example �
Robustness Again �
Avoid the Pooled Two-Sample t Procedures* �Many calculators and software packages offer a choice of two-sample t statistics. One is often labeled for “unequal” variances; the other for “equal” variances. �The “unequal” variance procedure is our two-sample t. �Never use the pooled t procedures if you have software or technology that will implement the “unequal” variance procedure.
Avoid Inference About Standard Deviations* �There are methods for inference about the standard deviations of Normal populations. The most common such method is the “F test” for comparing the standard deviations of two Normal populations. �Unlike the t procedures for means, the F test for standard deviations is extremely sensitive to non. Normal distributions. �We do not recommend trying to do inference about population standard deviations in basic statistical practice.
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