Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different:...
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Transcript of Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different:...
![Page 1: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/1.jpg)
Chapter 13 Two Groups Too Many?
Try Analysis of Variance (ANOVA)
Part IVSignificantly Different:
Using Inferential Statistics
![Page 2: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/2.jpg)
What you will learn in Chapter 13
What Analysis of Variance (ANOVA) is and when it is appropriate to use
How to compute the F statistic
How to interpret the F statistic
How to use SPSS to conduct an ANOVAsingle factor design
![Page 3: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/3.jpg)
Analysis of Variance (ANOVA)
Used when more than two group means are being tested simultaneouslyGroup means differ from one another on a
particular score / variableExample: DV = GRE Scores & IV = Ethnicity
Test statistic = F testR.A. Fisher, creator
![Page 4: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/4.jpg)
Path to Wisdom & KnowledgeHow do I know if ANOVA is the right test?
![Page 5: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/5.jpg)
Different Flavors of ANOVA
ANOVA examines the variance between groups and the variances within groupsThese variances are then compared against
each otherSimilar to the t Test…only in this case you
have more than two groupsOne-way ANOVA
Simple ANOVASingle factor (grouping variable)
![Page 6: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/6.jpg)
More Complicated ANOVAFactorial Design
More than one treatment/factor examinedMultiple Independent Variables
One Dependent VariableExample – 3x2 factorial design
Number of Hours in Preschool
Gender
Male5 hours per week
10 hours per week
20 hours per week
Female 5 hours per week
10 hours per week
20 hours per week
![Page 7: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/7.jpg)
Computing the F Statistic
Rationale…want the within group variance to be small and the between group variance to be large in order to find significance.
![Page 8: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/8.jpg)
Hypotheses
Null hypothesis
Research hypothesis
![Page 9: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/9.jpg)
Source Table
Source SS df MS F
Between 1,133.07 27 566.54 8.799
Within 1,738.40 29 64.39
Note: F value for two group is the same as t2
![Page 10: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/10.jpg)
Degrees of Freedom (df)
NumeratorNumber of groups minus onek-13 groups --- 3 – 1 = 2
DenominatorTotal number of observations minus the number
of groupsN-1100 participants --- 30 – 3 = 97
Represented: F (2, 27)
![Page 11: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/11.jpg)
How to Interpret
F (2,27) = 8.80, p < .05F = test statistic 2,27 = df between groups & df within groups
{Ah ha…3 groups and 30 total scores examined}8.80 = obtained value
Which we compared to the critical valuep < .05 = probability less than 5% that the
null hypothesis is trueMeaning the obtained value is GREATER than the
critical value
![Page 12: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/12.jpg)
Omnibus Test
The F test is an “omnibus test” and only tells you that a difference exists
Must conduct follow-up t tests to find out where the difference is…BUT…Type I error increases with every follow-
up test / possible comparison made1 – (1 – alpha)k
Where k = number of possible comparisons
![Page 13: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/13.jpg)
Using the ComputerSPSS and the One-Way ANOVA
![Page 14: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/14.jpg)
What does it all mean?
SPSS Output
![Page 15: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/15.jpg)
Post Hoc Comparison
![Page 16: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/16.jpg)
Glossary Terms to Know
Analysis of varianceSimple ANOVAOne-way ANOVAFactorial design
Omnibus testPost Hoc comparisonsSource table
![Page 17: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/17.jpg)
Chapter 17 What to Do When You’re Not Normal:
Chi-Square and Some Other Nonparametric Tests
Part IVSignificantly Different:
Using Inferential Statistics
![Page 18: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/18.jpg)
What you will learn in Chapter 17
A brief survey of nonparametric statisticsWhen they should be usedHow they should be used
![Page 19: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/19.jpg)
Introduction
Parametric statistics have certain assumptionsVariances of each group are similarSample is large enough to represent the
populationNonparametric statistics don’t require the
same assumptionsAllow data that comes in frequencies to be
analyzed…they are “distribution free”
![Page 20: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/20.jpg)
One-Sample Chi-Square
Chi-square allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance.One-sample chi-square (goodness of fit test)
only has one dimensionTwo-sample chi-square has two dimensions
![Page 21: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/21.jpg)
Computing Chi-Square
What do those symbols mean?
22 (O E)
Ex
![Page 22: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/22.jpg)
More Hypotheses
Null hypothesis
H0: P1 = P2 = P3
Research hypothesis
H1: P1 P2 P3
![Page 23: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/23.jpg)
Computing Chi Square
Category O E D (O-E)2 (O-E)2/2
For 23 30 7 49 1.63
Maybe 17 30 13 169 5.63
Against 50 30 20 400 13.33
Total 90 90 C2 = 20.6
![Page 24: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/24.jpg)
So How Do I Interpret…
x2(2) = 20.6, p < .05
x2 represents the test statistic2 is the number of degrees of freedom20.6 is the obtained valuep < .05 is the probability
![Page 25: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/25.jpg)
Using the ComputerOne-Sample Chi Square using SPSS
![Page 26: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/26.jpg)
SPSS Output
What does it all mean?
![Page 27: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/27.jpg)
Other Nonparametric Tests
![Page 28: Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e0d5503460f94af6ffc/html5/thumbnails/28.jpg)
Glossary Terms to Know
ParametricNonparametricOne-sample Chi Square