Comparing Two Treatments

1
Chapter 11

• Comparing Two Treatments

2
Chapter 11

• Comparing two means or comparing two proportions
• Read Chapter 11 but dont worry about comparing
  the sample standard deviations.

3
When Comparing Means

• Always start off with side-by-side boxplots!

4
How to determine if Dependent or Independent
samples

• If the data is matched, as in before/after data,
  then the data are dependent on each other. An
  example would be weight of a subject prior to
  starting a new training program versus weight
  after 6 weeks of the program.
• If the data come from two distinct populations,
  say men in new program, compared to woman in new
  program, the data are independent.

5
Lets Do It

• Page 625 LDI 11.2

6
Notation for Two Dependent Samples

• µD mean value of the differences d for the
  population of paired data

7
Notation for Two Dependent Samples
d mean value of the differences d for the
paired sample data (equal to the mean
of the x y values)
8
Notation for Two Dependent Samples

• sD standard deviation of the difference d for
  the paired sample data
• n number of pairs of data.

9
Hypothesis Tests

• Test Statistic for Two Dependent Samples

Note that usually
10
Claims for Paired Samples

• There is no difference . . .
• Symbolic form
• There is a difference . . . is interpreted as
  it is expected that the mean of the d values to
  be different from 0.
• Symbolic form

11
Confidence Intervals
where

• degrees of freedom n 1

12
Examples

• Page 638 11.9.
• Text book problem. Note that the paired data uses
  our old pal the t-test.

13
Test of Independent Means
14
Different Than the Text

• There really are only one options for beginning
  statistics practitioners, the unpooled t-test
  statistic. Pooling the standard deviation is not
  generally used unless there is strong evidence to
  do so.
• We will rely on the TI-83 for our calculations.

15
Method Well Use

• Use your calculator and do not pool the standard
  deviation.
• By pooling the standard deviation we are
  inferring the populations have equal standard
  deviations. This is tough to test and does not
  significantly improve the results of the test.

16
LDI

• Page 653 11.5 Assume that the population
  variances are not equal.

17
Homework 21

• LDI 11.2, 11.5
• Problems 7-9, 11, 14-16

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Inferences about Two Proportions

• Assumptions
• 1. We have two independent sets of randomly
  selected sample data.
• 2. For both samples, the conditions are
  satisfied.

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Two Proportions Hypothesis Tests
20
Two Proportions Confidence Intervals
21
I Love My Calculator )

• Page 673 11.30
• Page 671 11.7
• Page 674 11.31

22
Homework 22

• LDI 11.7
• Problems 29, 30, 33-35, 38, 39, 45, 47, 48