2009 - andy field - discovering statistics using spss
TRANSCRIPT
7/24/2019 2009 - Andy FIELD - Discovering Statistics Using SPSS
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THIRD EDITION
DISCOVERING STATISTICS
USING SPSS
and sex and drugs and rock n roll)
N Y FIELD
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ONT NTS
Preface
How to use this book
Acknowledgements
Dedication
Symbols used in this book
Some maths revision
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xxxiii
1
Why is my evi ecturer forcing me to earn statistics
1 1 What will this chapter tell me? <D
1 2 What the hell am I doing here? I don t belong here <D
1 2 1 The research process <D
1 3 Initial observation: finding something that needs explaining <D
1 4 Generating theories and testing them <D
1 5 Data collection 1 : what to measure <D
1 5 1 Variables <D
1 5 2 Measurement error <D
1 5 3 Validity and reliability <D
1 6 Data collection 2: how to measure <D
1 6 1 Correlational research methods <D
1 6 2 Experimental research methods <D
1 6 3
Randomization
<D
1 7 Analysing data
<D
1 7 1 Frequency distributions <D
1 7 2 The centre of a distribution <D
1 7 3 The dispersion in a distribution
<D
1 7 4 Using a frequency distribution to go beyond the data <D
1 7 5 Fitting statistical modeis to the data <D
What have I discovered about statistics? <D
Key terms that I ve discovered
Smart Alex s stats quiz
Further reading
Interesting real research
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DISCOVERING STATISTICS USING SPSS
Everything you ever wanted to
know about
statistics
well, sort of
2 What will this chapter tell me? CD 31
2.2. Building statistical mod eis CD 32
2.3.
Populations and samples
CD
34
2.4. Simple statistical modeis CD 35
2.4.1. The mean a very simple statistical model CD 35
2.4.2. Assessing the fit of the mean: sums of squares variance and standard
deviations CD 35
2.4.3. Expressing the mean as amodel ® 38
2.5. Going beyond the data CD 40
2.5.1.
The standard error
CD 40
2.5.2.
Confidence intervals
®
43
2.6. Using statistical modeis to test research questions CD 48
2.6.1.
Test statistics
CD
52
2.6.2.
One- and two-tailed tests
CD
54
2.6.3. Type I and Type II errors CD 55
2.6.4. Effect sizes
®
56
2.6.5. Statistical power ® 58
What have I discovered about statistics? CD 59
Key terms that I ve discovered 59
Smart Alex s stats quiz 59
Further reading 60
Interesting real research 60
4
The SPSSenvironment
3.1. What will this chapter tell me? CD
3.2.
Versions of SPSS CD
3.3. Getting started
CD
3 4
The data editor CD
3.4.1. Entering data into the data editor CD
3.4.2. The Variable View CD
3.4.3. Missing values CD
3.5.
The SPSS viewer
CD
3.6.
The SPSS SmartViewer CD
3.7. The syntax window
@
3.8. Saving files CD
3.9. Retrieving a file CD
What have I discovered about statistics? CD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutoriais
Exploring data with graphs
4.1.
What will this chapter tell me?
CD
4.2. The art of presenting data CD
4.2.1.
What makes a good graph?
CD
4.2.2. Ues damned lies and ... erm graphs CD
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CONTENTS
4 3 The SPSS Chart Builder
CD
4 4 Histograms a good way to spot obvious problems CD
4 5 Boxplots box-whisker diagrams)
CD
4 6 Graphing means: bar charts and error bars CD
4.6.1. Simple bar charts for independent means CD
4.6.2. Clustered bar charts for independent means CD
4.6.3. Simple bar charts for related means
CD
4.6.4. Clustered bar charts for related means CD
4.6.5. Clustered bar charts for mixed designs CD
4 7 Line charts CD
4 8
Graphing relationships the scatterplot
CD
4.8.1. Simple scatterplot
CD
4.8.2. Grouped scatterplot CD
4.8.3. Simple and grouped 3-0 scatterplots CD
4.8.4. Matrix scatterplot CD
4.8.5. Simple dot plot or density plot
CD
4.8.6. orop-line graph CD
4 9 Editing graphs CD
What have I discovered about statistics? CD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
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5
ExpLoring assumptions
5 What will this chapter tell me? CD
5 2
What are assumptions? CD
5 3 Assumptions of parametric data
CD
5 4 The assumption of normality CD
5.4.1. Oh no, it s that pesky frequency distribution again checking
normality visually CD
5.4.2. Quantifying normality with numbers
CD
5.4.3. Exploring groups of data CD
5 5 Testing whether a distribution is normal CD
5.5.1. ooing the Kolmogorov-Smirnov test on SPSS
CD
5.5.2. Output from the explore procedure CD
5.5.3. Reporting the K-S test CD
5 6 Testing for homogeneity of variance CD
5.6.1. Levene s test CD
5.6.2. Reporting Levene s test
CD
5 7 Correcting problems in the data ®
5.7.1. oealing with outliers ®
5.7.2. oealing with non-normality and unequal variances ®
5.7.3. Transforming the data using SPSS
®
5.7.4. When it all goes horribly wrong @
What have I discovered about statistics?
CD
Key terms that I v e discovered
Smart Alex s tasks
Online tutorial
Further reading
3
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6
Correlation
DISCOVERING STATISTICS USING SPSS
7
6 What will this chapter tell me? CD
6 2
Looking at relationships
CD
6 3
How do we measure relationships?
CD
6.3.1. A detour into the murky world of covariance
CD
6.3.2. Standardization and the correlation coefficient CD
6.3.3. The significance of the correlation coefficient @
6.3.4. Confidence intervals for
r@
6.3.5. A word of warning about interpretation: causality
CD
6 4
Data entry for correlation analysis using SPSS
CD
6 5 Bivariate correlation CD
6.5.1. General procedure for running correlations on SPSSCD
6.5.2. Pearson s correlation coefficient
CD
6.5.3. Spearman s correlation coefficient
CD
6.5.4. Kendall s tau non-parametric)
CD
6.5.5. Biserial and point-biserial correlations @
6 6 Partial correlation ®
6.6.1. The theory behind part and partial correlation ®
6.6.2. Partial correlation using SPSS®
6.6.3. Semi-partial or part) correlations ®
6 7
Comparing correlations @
6.7.1. Comparing independent
@
6.7.2. Comparing dependent
@
6 8 Calculating the effect size CD
6 9
How to report correlation coefficents
CD
What have I discovered about statistics? CD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
Regression
7
What will this chapter tell me?
CD
7 2 An introduction to regression CD
7.2.1. Some important information about straight lines eD
7.2.2. The method of least squares CD
7.2.3. Assessing the goodness of fit: sums of squares,
and
CD
7.2.4. Assessing individual predictors
CD
7 3 Doing simple regression on SPSS CD
7 4
Interpreting a simple regression CD
7.4.1. Overall fit of the model
CD
7.4.2. Model parameters
CD
7.4.3. Using the model
CD
7 5 Multiple regression: the basics ®
7.5.1. An example of a multiple regression model®
7.5.2. SulTisof squares, and ®
7.5.3. Methods of regression
®
7 6
How accurate is my regression model? ®
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ONTENTS
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7 9
7 1
7 11
7.6.1. Assessing the regression modeil: diagnostics ®
7.6.2. Assessing the regression modelll: generalization ®
How to do multiple regression using SPSS ®
7.7.1. Some things to think about before the analysis
®
7.7.2. Main options ®
7.7.3. Statistics
®
7.7.4. Regression plots ®
7.7.5. Saving regression diagnostics ®
7.7.6. Further options ®
Interpreting multiple regression ®
7.8.1. Descriptives ®
7.8.2. Summary of model ®
7.8.3. Model parameters ®
7.8.4. Excluded variables ®
7.8.5. Assessing the assumption of no multicollinearity ®
7.8.6. Casewise diagnostics
®
7.8.7. Checking assumptions
®
What
if
I violate an assumption? ®
How to report multiple regression ®
Categorical predictors and multiple regression ®
7.11.1. Dummy coding ®
7.11.2. SPSS output for dummy variables ®
What have I discovered about statistics? eD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
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8
Logistic regression
64
8 1 What will this chapter tell me?
eD
264
8
Background to logistic regression
eD
265
8 3 What are the principles behind logistic regression? ® 265
8.3.1. Assessing the model the log likelihood statistic® 267
8.3.2. Assessing the model
and
®
268
8.3.3. Assessing the contribution of predictors the Wald statistic® 269
8.3.4. The odds ratio Exp B ® 270
8.3.5. Methods of logistic regression
®
271
8 4
Assumptions and things that can go wrong 273
8.4.1. Assumptions ® 273
8.4.2. Incomplete information from the predictors 273
8.4.3. Complete separation 274
8.4.4. Overdispersion 276
8 5
Binary logistic regression an example that will make you feel eel ® 277
8.5.1. The main analysis ® 278
8.5.2. Method of regression ® 279
8.5.3. Categorical predictors ® 279
8.5.4. Obtaining residuals ® 280
8.5.5. Further options ® 281
8 6
Interpreting logistic regression ® 282
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x DISCOVERING STATISTICS USING SPSS
8 7
8 8
8 9
8.6.1. The initial model ®
8.6.2. Step l intervention @
8.6.3. Listing predicted probabilities ®
8.6.4. Interpreting residuals ®
8.6.5. Calculating the effect size ®
How to report logistic regression
®
Testing assumptions another example ®
8.8.1. Testing for linearity of the logit @
8.8.2. Testing for multicollinearity @
Predicting several categories multinomiallogistic regression @
8.9.1. Running multinomiallogistic regression in SPSS@
8.9.2. Statistics @
8.9.3. Other options @
8.9.4. Interpreting the multinomiallogistic regression output @
8.9.5. Reporting the results
What have I discovered about statistics? eD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
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Comparing two means
9 What will this chapter tell me? eD
9
Looking at differences
eD
9.2.1. A problem with error bar graphs of repeated measures designs eD
9.2.2. Step 1 calculate the mean for each participant ®
9.2.3. Step 2 calculate the grand mean®
9.2.4. Step 3 calculate the adjustment factor ®
9.2.5. Step 4 create adjusted values for each variable ®
9 3 The t t st
eD
9.3.1. Rationale for the t t st eD
9.3.2. Assumptions of the t t st eD
9 4 The dependent t t st
eD
9.4.1. Sampling distributions and the standard error
eD
9.4.2. The dependent t t st equation explained eD
9.4.3. The dependent t t st and the assumption of normality
eD
9.4.4. Dependent t tests using SPSS eD
9.4.5. Output from the dependent t t st eD
9.4.6. Calculating the effect size®
9.4.7. Reporting the dependent t t st
eD
9 5 The independent t t st eD
9.5.1. The independent
t t st
equation explained eD
9.5.2. The independent t t st using SPSS
eD
9.5.3. Output from the independent
t t st eD
9.5.4. Calculating the effect size®
9.5.5. Reporting the independent t t st eD
9 6
Between groups or repeated measures? eD
9 7 The t t st as a generallinear model ®
9 8
What if my data are not normally distributed? ®
3 6
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CONTENTS
What have I discovered about statistics?
CD
Key terms that I ve discovered
Smart Alex s task
Further reading
Online tutorial
Interesting real research
10 Comparing several means: ANOVA GLM 1
1 1
What will this chapter tell me? CD
1 2
The theory behind ANOVA
®
1 2 1
Inflated error rates
®
1 2 2
Interpreting F
®
1 2 3
ANOVA as regression
®
1 2 4
Logic of the F-ratio ®
1 2 5
Total sum of squares SST)
®
1 2 5
Model sum of squares SSM)
®
1 2 7
Residual sum of squares SSR)®
1 2 8
Mean squares ®
1 2 9
The F-ratio ®
1 2 1
Assumptions of ANOVA @
1 2 11
Planned contrasts
®
1 2 12 Post hoc
procedures
®
1 3 Running one-way ANOVA on SPSS ®
1 3 1
Planned comparisons using SPSS ®
1 3 2 Post hoc
tests in SPSS
®
1 3 3
Options ®
1 4
Output from one-way ANOVA ®
1 4 1
Output for the main analysis ®
1 4 2
Output for planned comparisons
®
1 4 3
Output for post hoc tests ®
1 5
Calculating the effect size
®
1 6
Reporting results from one-way independent ANOVA
®
10.7. Violations of assumptions in one-way independent ANOVA ®
What have I discovered about statistics? CD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutoriais
Interesting real research
11 Analysis of covariance, ANCOVA GLM 2
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11 1
11 2
11 3
11 4
What will this chapter tell me? ®
What is ANCOVA?
®
Assumptions and issues in ANCOVA @
11 3 1
Independence of the covariate and treatment effect @
11 3 2
Homogeneity of regression slopes @
Conducting ANCOVA on SPSS
®
11 4 1
Inputting data
CD
11 4 2
Initial considerations: testing the independence of the independent
variable and covariate ®
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DISCDVERING STATISTICS USING SPSS
11 5
11 6
11 7
11 8
11 9
11 10
4 3 The main analysis ®
4 4 Contrasts and other options ®
Interpreting the output from ANCOVA ®
5 What happens when the covariate is exciuded7
®
5 2 The main analysis ®
5 3
Contrasts
®
5 4 Interpreting the covariate ®
ANCOVA run as a multiple regression ®
Testing the assumption of homogeneity of regression slopes
®
Calculating the effect size ®
Reporting results ®
What to do when assumptions are violated in ANCOVA ®
What have I discovered about statistics? ®
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutoriais
Interesting real research
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2 FactoriaL ANOVA GLM 3
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12 2
12 3
12 4
12 5
12 6
12 7
12 8
12 9
What will this chapter tell me?
®
Theory of factorial ANOVA between-groups) ®
2 2 Factorial designs ®
2 2 2 An example with two independent variables ®
2 2 3 Total sums of squares SST)®
2 2 4 The model sum of squares SSM)®
2 2 5
The residual sum of squares SSR)
®
2 2 6 The F-ratios ®
Factorial ANOVA using SPSS ®
2 3 Entering the data and accessing the main dialog box
®
2 3 2 Graphing interactions
®
2 3 3 Contrasts ®
2 3 4 Post hoc
tests ®
2 3 5
Options
®
Output from factorial ANOVA
®
2 4
Output for the preliminary analysis
®
2 4 2 Levene s test ®
2 4 3 The main ANOVA table ®
2 4 4 Contrasts ®
2 4 5 Simple effects analysis ®
2 4 6 Post hoc
analysis ®
Interpreting interaction graphs ®
Calculating effect sizes ®
Reporting the results of two-way ANOVA
®
Factorial ANOVA as regression ®
What to do when assumptions are violated in factorial ANOVA
®
What have I discovered about statistics?
®
Key terms that I ve discovered
Smart Alex s tasks
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ONTENTS
Further reading
Online tutoriais
Interesting real research
13 Repeated-measures designs GLM 4
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13 1
13 2
13 3
13.4.
13 5
13 6
13 7
13 8
13 9
13 1
13 11
13 12
What will this chapter tell me? ®
Introduction to repeated-measures designs ®
13.2.1. The assumption of sphericity
®
13.2.2. How is sphericity measured? ®
13.2.3. Assessing the severity of departures from sphericity ®
13.2.4. What is the effect of violating the assumption of sphericity?
®
13.2.5. What do you do if you violate sphericity? ®
Theory of one-way repeated-measures ANOVA ®
13.3.1. The total sum of squares SST)®
13.3.2. The within-participant SSw)
®
13.3.3. The model sum of squares SSM)®
13.3.4. The residual sum of squares SSR)®
13.3.5. The mean squares
®
13.3.6. The F-ratio ®
13.3.7. The between-participant sum of squares®
One-way repeated-measures ANOVA using SPSS ®
13.4.1. The main analysis ®
13.4.2. Defining contrasts for repeated-measures ®
3 4 3 Post hoc tests and additional options ®
Output fo\ one-way repeated-measures ANOVA
®
13.5.1. Descriptives and other diagnostics
13.5.2. Assessing and correcting for sphericity: Mauchly s test ®
13.5.3. The main ANOVA®
13.5.4. Contrasts ®
3 5 5 Post hoc tests ®
Effect sizes for repeated-measures ANOVA ®
Reporting one-way repeated-measures ANOVA ®
Repeated-measures with several independent variables ®
13.8.1. The main analysis ®
13.8.2. Contrasts
®
13.8.3. Simple effects analysis®
13.8.4. Graphing interactions ®
13.8.5. Other options ®
Output for factorial repeated-measures ANOVA ®
13.9.1. Descriptives and main analysis ®
13.9.2. The effect of drink ®
13.9.3. The effect of imagery
®
13.9.4. The interaction effect drink x imagery) ®
13.9.5. Contrasts for repeated-measures variables ®
Effect sizes for factorial repeated-measures ANOVA ®
Reporting the results from factorial repeated-measures ANOVA
®
What to do when assumptions are violated in repeated-measures ANOVA ®
What have I discovered about statistics? ®
Key terms that I ve discovered
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Smart Alex s tasks
Further reading
Online tutoriais
Interesting real research
14 Mixed design ANOVA GLM 5
OISCOVERING STATISTICS USING SPSS
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14 2
14.3.
14 4
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14.7.
14 8
What will this chapter tell me? e
Mixed designs
®
What do men and women look for in a partner?
®
Mixed ANOVA on SPSS
®
14.4.1. The main analysis
®
14.4.2. Other options
®
Output for mixed factorial ANOVA: main analysis
14.5.1. The main effect of gender ®
14.5.2. The main effect of looks
®
14.5.3. The main effect of charisma ®
14.5.4. The interaction between gender and looks ®
14.5.5. The interaction between gender and charisma
®
14.5.6. The interaction between attractiveness and charisma ®
14.5.7. The interaction between looks charisma and gender
14.5.8. Conclusions
Calculating effect sizes
Reporting the results of mixed ANOVA ®
What to do when assumptions are violated in mixed ANOVA
What have I discovered about statistics?
®
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutoriais
Interesting real research
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15 Non-parametric tests
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What will this chapter tell me?
e
When to use non-parametric tests
e
Comparing two independent conditions: the Wilcoxon rank-sum test and
Mann-Whitney test
e
15.3.1. Theory
®
15.3.2. Inputting data and provisional analysis
e
15.3.3. Running the analysis e
15.3.4. Output from the Mann-Whitney test
e
15.3.5. Calculating an etfect size ®
15.3.6. Writing the results
e
Comparing two related conditions: the Wilcoxon signed-rank test
e
15.4.1. Theory of the Wilcoxon signed-rank test
®
15.4.2. Running the analysis
e
15.4.3. Output for the ecstasy group
e
15.4.4. Output for the alcohol group
e
15.4.5. Calculating an effect size
®
15.4.6. Writing the results
e
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CONTENTS
5 5
Differences between several independent groups the Kruskal Wallis test <D 559
15.5.1. Theory of the Kruskal Wallis test
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15.5.2. Inputting data and provisional analysis
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15.5.3. Doing the Kruskal Wallis test on SPSS <D 562
15.5.4. Output from the Kruskal Wallis test
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5 5 5 Post hoc
tests for the Kruskal Wallis test
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15.5.6. Testing for trends the Jonckheere Terpstra test
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15.5.7. Calculating an effect size
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15.5.8. Writing and interpreting the results <D 571
5 6 Differences between several related groups: Friedman s ANOVA
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15.6.1. Theory of Friedman s ANOVA
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15.6.2. Inputting data and provisional analysis
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15.6.3. Doing Friedman s ANOVA on SPSS
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15.6.4. Output from Friedman s ANOVA <D 576
5 6 5 Post hoc tests for Friedman s ANOVA
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15.6.6. Calculating an effect size
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15.67. Writing and interpreting the results
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What have I discovered about statistics?
<D
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
16 MuLtivariate anaLysis of variance MANOVA
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What will this chapter tell me?
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When to use MANOVA
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Introduction similarities and differences to ANOVA
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16.3.1. Words of warning
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16.3.2. The example for this chapter
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Theory of MANOVA
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16.4.1. Introduction to matrices
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16.4.2. Some important matrices and their functions
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16.4.3. Calculating MANOVA by hand a worked example
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16.4.4. Principle of the MANOVAtest statistic
@
Practical issues when conducting MANOVA
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16.5.1. Assumptions and how to check them
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16.5.2. Choosing a test statistic
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16.5.3. Follow up analysis ®
MANOVA on SPSS ®
16.6.1. The main analysis
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16.6.2. Multiple comparisons in MANOVA
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16.6.3. Additional options
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Output from MANOVA
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16.7.1. Preliminary analysis and testing assumptions
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16.7.2. MANOVA test statistics
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16.7.3. Univariate test statistics
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16.7.4. SSCP Matrices
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16.7.5. Contrasts
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DISCDVERING STATISTICS USING SPSS
16 8
eporting results from MANOVA ®
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ollowing up MANOVA with discriminant analysis ®
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he linai interpretation @
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nivariate ANOVA or discriminant analysis?
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xplor tory f ctor n lysis
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hat will this chapter tell me?
<D
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hen to use factor analysis ®
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actors ®
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raphical representation
1
lactors ®
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athematical representation
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lactors ®
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actor scores ® 633
iscovering factors ®
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hoosing a method ®
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ommunality ®
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actor analysis vs. principai component analysis ®
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heory behind principai component analysis ®
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actor extraction: eigenvalues and the scree plot ®
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mproving interpretation: factor rotation ®
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esearch example ®
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efore you begin ®
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unning the analysis ®
65actor extraction on SPSS® 65otation®
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cores ®
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ptions®
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nterpreting output from SPSS ®
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reliminary analysis ®
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actor extraction ® 66actor rotation ®
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actor scores ®
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ummary®
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ow to report factor analysis
<D
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eliability analysis ®
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easures of reliability®
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nterpreting Cronbach s some cautionary tales ...) ®
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leliability analysis on SPSS®
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nterpreting the output ®
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CONTENTS
What have I discovered about statistics? ®
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
CategoricaL data
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18 1
18 2
18 3
18 4
18 5
18 6
18 7
18 8
18 9
18 1
18 11
18 12
What will this chapter tell me? eD
Analysing categorical data eD
Theory of analysing categorical data eD
18 3 1 Pearson s chi square test eD
18 3 2 Fisher s exact test eD
18 3 3 The Iikelihood ratio ®
18 3 4
Yates correction
®
Assumptions of the chi square test eD
Doing chi square on SPSS eD
18 5 1 Entering data raw scores eD
18 5 2 Entering data weight cases eD
18 5 3 Running the analysis eD
18 5 4 Output for the chi square test eD
18 5 5 Breaking down a significant chi square test with standardized residuals
®
18 5 5 Calculating an effect size
®
18 5 7 Reporting the results of chi square eD
Several categorical variables: loglinear analysis
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18 5 1 Chi square as regression @
18 5 2 Loglinear analysis
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Assumptions in loglinear analysis
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Loglinear analysis using SPSS ®
18 8 1 Initial considerations ®
18 8 2 The loglinear analysis ®
Output from loglinear analysis ®
Following up loglinear analysis
®
Effect sizes in loglinear analysis
®
Reporting the results of loglinear analysis
®
What have I discovered about statistics? eD
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
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9 MuLtiLeveLLinear modeLs 725
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19 2
19 3
What will this chapter tell me? eD
Hierarchical data
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19 2 1 The iJ;1traclasscorrelation ®
19 2 2 Benefits of multilevel modeis ®
Theory of multilevellinear modeis
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DISCOVERING STATISTICS USING SPSS
19.3.1. An example
19.3.2. Fixed and random coefficients
9 4
The multilevel model
19.4.1. Assessing the fit and comparing multilevel modeis
19.4.2. Typesof covariance structures @
9 5
Some practical issues
19.5.1. Assumptions @
19.5.2. Sampie size and power
19.5.3. Centring variables
9 6
Multilevel modelling on SPSS
19.6.1. Entering the data
19.6.2. Ignoring the data structure ANOVA
19.6.3. Ignoring the data structure ANCOVA
19.6.4. Factoring in the data structure: random intercepts @
19.6.5. Factoring in the data structure: random intercepts and slopes
19.6.6. Adding an interaction to the model
9 7 Growth modeis
@
19.7.1. Growth curves polynomials) @
19.7.2. An example: the honeymoon period
19.7.3. Restructuring the data @
19.7.4. Running a growth model on SPSS
19.7.5. Further analysis @
9 8 How to report a multilevel model
What have I discovered about statistics?
Key terms that I ve discovered
Smart Alex s tasks
Further reading
Online tutorial
Interesting real research
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Epilogue
Glossary
Appendix
A l
A 2
A 3
A 4
References
Index
Table of the standard normal distribution
Critical values of the t-distribution
Critical values of the F-distribution
Critical values of the chi-square distribution
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8 6