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![Page 1: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/1.jpg)
© 2014 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
HLTH 300 Biostatistics for Public Health Practice,
Raul Cruz-Cano, Ph.D.4/14/2014, Spring 2014
Fox/Levin/Forde, Elementary Statistics in Social Research, 12e
Chapter 8: Analysis of Variance
1
![Page 2: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/2.jpg)
© 2014 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Understand the logic of analysis of variance
Understand and calculate the sum of squares
Understand and calculate the mean square
Understand and calculate the F ratio
Conduct a multiple comparison of means to determine where a significant difference lies
CHAPTER OBJECTIVES
8.1
8.2
8.3
8.4
8.5
8.6 Understand the requirements for using the F ratio
![Page 3: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/3.jpg)
Understand the logic of analysis of variance
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
8.1
![Page 4: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/4.jpg)
Comparing More than Two Groups8.1
Multiple t Ratios
Analysis of Variance
vs.
Combing t ratios increases the chance of making a Type I error
A single overall decision as to whether a significant difference exists
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The Logic of Analysis of Variance 8.1
Total Variation
VariationbetweenGroups
Variationwithin Groups
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8.1
Figure 8.1
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8.1
Figure 8.2
![Page 8: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/8.jpg)
The Logic of Analysis of Variance 8.1
![Page 9: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/9.jpg)
Understand and calculate the sum of squares
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
8.2
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8.2
10
The sum of squared deviations from the mean• Total sum of squares• Between-group sum of squares• Within-group sum of squares
The Sum of Squares
2
total total
2
within group
2
between group group total
SS
SS
SS
X X
X X
N X X
Definitional Formulas Computational Formulas
2 2total total total total
2 2within total group group
2 2between group group total total
SS
SS
SS
X N X
X N X
N X N X
![Page 11: © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649c525503460f948fc488/html5/thumbnails/11.jpg)
Understand and calculate the mean square
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
8.3
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8.3
12
The value of the sum of squares grows as variation and sample size increase
• The mean square (or variance) controls for these influences
The Mean Square
betweenbetween
between
withinwithin
within
SSMS
df
SSMS
df
number of groupsk
between
within total
df 1
df
k
N k
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Understand and calculate the F ratio
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
8.4
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8.4
14
A comparison of the variation between groups and variation within groups
• It must be evaluated for significance– The larger the F ratio, the more likely it is to be statistically significant – Interpret the F ratio with Table D in Appendix C (pages 554-555)
The F ratio
between
within
MS
MSF
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8.4
Table 8.4
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Conduct a multiple comparison of means to determine where a significant difference lies
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
8.5
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8.5
17
A significant F ratio does not tell us where the difference lies
We can use Tukey’s Honesty Significant Difference (HSD) to determine this
• Allows for a comparison of any two means against HSD• Takes into account Type I error
A Multiple Comparison of Means
found in Table Eq
within
group
MSHSD q
N
A set of several t-test are also acceptable but take more time
Now just compare the values of the difference between each pair of means and HSD. A difference is significant if it is greater than the HSD
(Page 556)
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Understand the requirements for using the F ratio
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
8.6
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Requirements for Using the F Ratio8.6
A Comparison between Three or More Independent Means
Interval Data
Random Sampling
A Normal Distribution
Equal Variances
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Example
20
Problem 17-18Problem 37
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Homework
21
Chapter 8 Problems: 28 and 34-35Also Chapter 7 Problem 42
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Exam #2
22
Confidence IntervalsHypothesis Testing (two-sided only)ANOVA
I’ll give you some statistics
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© 2014 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved
Analysis of variance examines the variance between and within groups to determine if a significant
difference exists
The sum of squares examines the total deviation, the between-group deviation and the within-group
deviation
The mean square controls for the increase in the sum of squares that naturally occurs as variation and
sample size increase
The F ratio compares variation between groups and variation within groups
CHAPTER SUMMARY
8.1
8.2
8.3
8.4
Tukey’s HSD is used to determine where a significant difference lies once a significant F ratio has been found
There are several requirements that must be met in order to conduct an analysis of variance test
8.5
8.6