Experimental design and analysis for psychology:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 538 S. graph. Darst. |
| ISBN: | 9780199299881 |
Internformat
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| 245 | 1 | 0 | |a Experimental design and analysis for psychology |c Hervé Abdi .... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XX, 538 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Psychology / Research | |
| 650 | 4 | |a Psychology / Research / Methodology | |
| 650 | 4 | |a Psychology / Statistical methods | |
| 650 | 4 | |a Experimental design | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Abdi, Hervé |e Sonstige |0 (DE-588)1232083887 |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017693692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1825494927533932544 |
|---|---|
| adam_text |
Contents
1
Introduction
to experimental design
1
1.1
Introduction
1
1.2
Independent and dependent variables
2
1.3
Independent variables
4
1.3.1
Independent variables manipulated by the experimenter
4
1.3.2
Randomization
5
1.3.3
Confounded independent variables
5
1.3.4
'Classificatory' (or 'tag') and 'controlled' independent variables
8
1.3.5
Internal versus external validity
11
1.4
Dependent variables
12
1.4.1
Good dependent variables
13
1.5
Choice of subjects and representative design of experiments
14
1.6
Key notions of the chapter
15
2
Correlation
16
2.1
Introduction
16
2.2
Correlation: overview and example
16
2.3
Rationale and computation of the coefficient of correlation
18
2.3.1
Centering
19
2.3.2
The four quadrants
20
2.3.3
The rectangles and their sum
22
2.3.4
Sum of the cross-products
23
2.3.5
Covariance
24
2.3.6
Correlation: the rectangles and the squares
26
2.3.6.1
For experts: going from one formula to the other one
26
2.3.7
Some properties of the coefficient of correlation
27
2.3.8
For experts: why the correlation takes values between
—1
and
+1 27
2.4
Interpreting correlation and scatterplots
28
2.5
The importance of scatterplots
28
2.5.1
Linear and non-linear relationship
28
2.5.2
Vive la différence?
The danger of outliers
28
2.6
Correlation and similarity of distributions
30
2.6.1
The other side of the mirror: negative correlation
30
2.7
Correlation and Z-scores
32
2.7.1
Computing with Z-scores: an example
34
2.7.2
Z-scores and perfect correlation
34
2.8
Correlation and causality
36
2.9
Squared correlation as common variance
37
2.10
Key notions of the chapter
37
2.11
Key formulas of the chapter
38
2.12
Key questions of the chapter
38
3
Statistical test: the
F
test
39
3.1
Introduction
39
viii Contents
3.2
Statistical test
40
3.2.1
The null hypothesis and the alternative hypothesis
40
3.2.2
A decision rule: reject Ho when it is 'unlikely'
41
3.2.3
The significance level: specifying the
'improbable'
42
3.2.4
Type I and Type II errors: a and
β
42
3.2.5
Sampling distributions: Fisher's
F
44
3.2.5.1
Empirical (Monte-Carlo) approach
45
3.2.5.2
Theoretical (traditional) approach
47
3.2.6
Region of rejection, region of suspension of judgment,
and critical value
50
3.2.7
Using the table of critical values of Fisher's
F
52
3.2.8
Summary of the procedure for a statistical test
53
3.2.9
Permutation tests: how likely are the results?
53
3.3
Not zero is not enough!
55
3.3.1
Shrunken and adjusted
г
values
56
3.3.2
Confidence interval
57
3.3.2.1
Fisher's
Ζ
transform
58
3.3.3
How to transform
r
to Z: an example
58
3.3.4
Confidence intervals with the bootstrap
59
3.4
Key notions of the chapter
61
3.5
New notations
61
3.6
Key formulas of the chapter
61
3.7
Key questions of the chapter
62
Simple linear regression
63
4.1
Introduction
63
4.2
Generalities
63
4.2.1
The equation of a line
63
4.2.2
Example of a perfect line
64
4.2.3
An example: reaction time and memory set
65
4.3
The regression line is the 'best-fit' line
67
4.4
Example: reaction time and memory set
68
4.5
How to evaluate the quality of prediction
70
4.6
Partitioning the total sum of squares
72
4.6.1
Generalities
72
4.6.2
Partitioning the total sum of squares
73
4.6.3
Degrees of freedom
75
4.6.4
Variance of regression and variance of residual
75
4.6.5
Another way of computing
F
75
4.6.6
Back to the numerical example
76
4.6.6.1
Index
F
77
4.7
Mathematical digressions
77
4.7.1
Digression
1 :
finding the values of a and
b
77
4.7.2
Digression
2:
the mean of
Y
is equal to the mean of V
80
4.7.3
Digression
3:
the residuals (Y
-
Y) and the predicted values
Ϋ
are uncorrelated
80
4.7.4
Digression
4:
Γψγ = Γχ.γ
82
4.8
Key notions of the chapter
84
4.9
New notations
84
4.10
Key formulas of the chapter
84
4.11
Key questions of the chapter
85
Contents ix
Orthogonal multiple
regression
86
5.1
Introduction
86
5.2
Generalities
87
5.2.1
The equation of a plane
87
5.2.2
Example of a perfect plane
88
5.2.3
An example: retroactive interference
90
5.3
The regression plane is the 'best-fit' plane
92
5.4
Back to the example: retroactive interference
93
5.5
How to evaluate the quality of the prediction
96
5.5.1
How to evaluate the importance of each independent variable
in the prediction
98
5.5.2
How to evaluate the importance of each independent variable for
the dependent variable
99
5.5.3
From the
rç
coefficients to the /y coefficients
Ì00
5.6
F
tests for the simple coefficients of correlation
100
5.7
Partitioning the sums of squares
101
5.7.1
What is a score made of?
102
5.7.2
The score model
102
5.7.3
Life is simple when X and
Τ
are orthogonal: partitioning the sum
of squares regression
103
5.7.4
Degrees of freedom
104
5.7.5
Mean squares
104
5.7.6
The return of
F
104
5.7.7
Back to the example
105
5.8
Mathematical digressions
107
5.8.1
Digression
1:
finding the values of a, b, and
с
107
5.9
Key notions of the chapter
110
5.10
New notations
110
5.11
Key formulas of the chapter
110
5.12
Key questions of the chapter
111
Non-orthogonal multiple regression
112
6.1
Introduction
112
6.2
Example: age, speech rate and memory span
112
6.3
Computation of the regression plane
113
6.4
How to evaluate the quality of the prediction
116
6.4.1
How to evaluate the importance of each independent variable
in the prediction
117
6.4.2
The specific contribution of each independent variable:
the semi-partial contribution
118
6.5
Semi-partial correlation as increment in explanation
121
6.5.1
Alternative formulas for the semi-partial correlation coefficients
123
6.6
F
tests for the semi-partial correlation coefficients
124
6.7
What to do with more than two independent variables
125
6.7.1
Computing semi-partial correlation with more than two
independent variables
125
6.7.2
Multicollinearity: a specific problem with non-orthogonal
independent variables
126
6.8
Bonus: partial correlation
127
6.9
Key notions of the chapter
128
6.10
New notations
128
Contents
6.11 Key
formulas
of the chapter
128
6.12
Key questions of the chapter
129
ANOVA one factor: intuitive approach and computation of
F
130
7.1
Introduction
130
7.2
Intuitive approach
130
7.2.1
An example: mental "imagery
130
7.2.2
An index of effect of the independent variable
131
7.3
Computation of the
F
ratio
133
7.3.1
Notation, etc.
133
7.3.2
Distances from the mean
135
7.3.3
A variance refresher
136
7.3.4
Back to the analysis of variance
137
7.3.5
Partition of the total sum of squares
138
7.3.5.1
Proof of the additivity of the sum of squares
139
7.3.5.2
Back to the sum of squares
140
7.3.6
Degrees of freedom
140
7.3.6.1
Between-group degrees of freedom
141
7.3.6.2
Within-group degrees of freedom
141
7.3.6.3
Total number of degrees of freedom
142
7.3.7
Index
F
142
7.4
A bit of computation: mental imagery
142
7.5
Key notions of the chapter
144
7.6
New notations
144
7.7
Key formulas of the chapter
145
7.8
Key questions of the chapter
146
ANOVA, one factor: test, computation, and effect size
147
8.1
Introduction
147
8.2
Statistical test: a refresher
147
8.2.1
General considerations
147
8.2.2
The null hypothesis and the alternative hypothesis
148
8.2.3
A decision rule: reject Ho when it is'unlikely'
148
8.2.4
Sampling distributions: the distributions of Fisher's
F
148
8.2.5
Region of rejection, region of suspension of judgment,
critical value
149
8.3
Example: back to mental imagery
149
8.4
Another more general notation:
Λ
and S(A)
152
8.5
Presentation of the ANOVA results
153
8.5.1
Writing the results in an article
154
8.6
ANOVA with two groups:
F
and
t
154
8.6.1
For experts: Fisher and Student .Proof
155
8.6.2
Another digression:
F
is an average
156
8.7
Another example: Romeo and Juliet
157
8.8
How to estimate the effect size
161
8.8.1
Motivation
161
8.8.2
R
and
η
162
8.8.2.1
Digression:
Я^л
isa
coefficient of correlation
163
8.8.2.2
FandR^A
164
8.8.3
How many subjects? Quick and dirty power analysis
165
8.8.4
How much explained variance? More quick and dirty power
analysis
166
Contents xi
8.9
Computational
formulas
167
8.9.1
Back to
Romeo
and Juliet
167
8.9.2
The'numbers
¡η
the squares'
168
8.9.2.1
Principles of construction
168
8.9.2.2
'Numbers in the squares' and the Universe
. 169
8.10
Key notions of the chapter
170
8.11
New notations
170
8.12
Key formulas of the chapter
170
8.13
Key questions of the chapter
171
9
ANO VA,
one factor: regression point of view
172
9.1
Introduction
172
9.2
Example
1:
memory and imagery
173
9.3
Analysis of variance for Example
1 173
9.4
Regression approach for Example
1:
mental imagery
176
9.5
Equivalence between regression and analysis of variance
180
9.6
Example
2:
Romeo and Juliet
182
9.7
If regression and analysis of variance are one thing, why
keep two different techniques?
185
9.8
Digression: when predicting
У
from
Mg.,
b —
λ,
and
Згедгеѕѕјоп
= 0 185
9.8.1
Remember.
185
9.8.2
Rewriting SSX
186
9.8.3
Rewriting SCPYX
186
9.8.4
agression
=0 187
9.8.5
Recap
187
9.9
Multiple regression and analysis of variance
187
9.10
Key notions of the chapter
189
9.11
Key formulas of the chapter
189
9.12
Key questions of the chapter
190
10
ANOVA, one factor: score model
191
10.1
Introduction
191
10.1.1
Motivation: why do we need the score model?
191
10.1.2
Decomposition of a basic score
191
10.1.3
Fixed effect model
192
10.1.4
Some comments on the notation
194
10.1.5
Numerical example
194
10.1.6
Score model and sum of squares
195
10.1.7
Digression: why
ů\
rather than
σ|?
196
10.2
ANOVA with one random factor (Model II)
197
10.2.1
Fixed and random factors
197
10.2.2
Example: S[A) design with A random
198
10.3
The score model: Model II
198
10.4
F
< 1
or the strawberry basket
199
10.4.1
The strawberry basket
200
10.4.2
A hidden factor augmenting error
200
10.5
Size effect coefficients derived from the score model:
ω2
and p2
201
10.5.1
Estimation of
ω2ΑΎ
202
xii Contents
10.5.2
Estimating
ρ%γ 203
10.5.3
Negative values for
ω
and
ρ
203
10.5.4
Test for the effect size 203
10.5.5
Effect size: which one to choose?
203
10.5.6
Interpreting the size of an effect
204
10.6
Three exercises
204
10.6.1
Images. 204
10.6.2
Thefat man and not so very nice numbers.
205
10.6.3
How to choose between fixed and random-taking off with
Elizabeth Loftus.
206
10.7
Key notions of the chapter
208
10.8
New notations
208
10.9
Key formulas of the chapter
209
10.10
Key questions of the chapter
210
11
Assumptions of analysis of variance
211
11.1
introduction
211
11.2
Validity assumptions
211
11.3
Testing the homogeneity of variance assumption
213
11.3.1
Motivation and method
213
11.4
Example
214
11.4.1
One is a bun.
214
11.5
Testing normality: Lilliefors
217
11.6
Notation
218
11.7
Numerical example
219
11.8
Numerical approximation
220
11.9
Transforming scores
220
11.9.1
Ranks
221
11.9.2
The log transform
221
11.9.3
Arcsine transform
221
11.10
Key notions of the chapter
222
11.11
New notations
222
11.12
Key formulas of the chapter
222
11.13
Key questions of the chapter
223
12
Analysis of variance, one factor: planned orthogonal
comparisons
224
12.1
Introduction
224
12.2
What is a contrast?
225
12.2.1
How to express a research hypothesis as a contrast
227
12.2.1.1
Example: rank order
228
12.2.1.2
A bit harder
228
12.3
The different meanings of alpha
228
12.3.1
Probability in the family
229
12.3.2
A Monte-Carlo illustration
230
12.3.3
The problem with replications of a meaningless
experiment: 'alpha and the captain's age'
231
12.3.4
How to correct for multiple comparisons:
Šidak
and
Bonferroni, Boole, Dunn
232
12.4
An example: context and memory
234
12.4.1
Contrasted groups
235
Contents xiii
12.5
Checking the independence of two contrasts
236
12.5.1
For experts: orthogonality of contrasts and correlation
236
12.6
Computing the sum of squares for a contrast
237
12.7
Another view: contrast analysis as regression
238
12.7.1
Digression: rewriting the formula of R\ ^
238
12.8
Critical values for the statistical index
240
12.9
Back to the context
. 241
12.10
Significance of the omnibus
F vs
significance of specific
contrasts
244
12.11
How to present the results of orthogonal comparisons
245
12.12
The omnibus
F
is a mean!
246
12.13
Sum of orthogonal contrasts: sub-design analysis
246
12.13.1
Sub-design analysis: an example
247
12.14
Trend analysis
248
12.15
Key notions of the chapter
251
12.16
New notations
251
12.17
Key formulas of the chapter
251
12.18
Key questions of the chapter
252
13
ANOVA, one factor: planned non-orthogonal comparisons
253
13.1
Introduction
253
13.2
The classical approach
254
13.2.1
Šidak
and Bonferonni, Boole, Dunn tests
254
13.2.2
Splitting up a[PF] with unequal slices
255
13.2.3
Bonferonni
er
al.: an
example
256
13.2.4
Comparing all experimental groups with the same control
group: Dunnett's test
257
13.3
Multiple regression: the return!
258
13.3.1
Multiple regression: orthogonal contrasts for Romeo
and Juliet
258
13.3.2
Multiple regression vs classical approach: non-orthogonal
contrasts
262
13.3.3
Multiple regression: non-orthogonal contrasts for Romeo
and Juliet
263
13.4
Key notions of the chapter
266
13.5
New notations
266
13.6
Key formulas of the chapter
267
13.7
Key questions of the chapter
267
14
ANOVA, one factor: post hoc or a posteriori analyses
268
14.1
Introduction
268
14.2
Scheffé's test:
all possible contrasts
270
14.2.1
Justification and general idea
270
14.2.2
An example:
Scheffé test
for Romeo and Juliet
272
14.3
Pairwise comparisons
273
14.3.1
Tukeytest
273
14.3.1.1
Digression: What is Frange?
274
14.3.1.2
An example: Tukey test for Romeo and Juliet
275
14.3.2
The Newman-Keuls test
276
14.3.3
An example: taking off
. 277
14.3.4
Duncan test
279
xiv Contents
14.4 Key
notions
of the chapter
280
14.5
New notations
280
14.6
Key questions of the chapter
281
15
More on experimental design: multi-factorial designs
282
15.1
Introduction
282
15.2
Notation of experimental designs
283
15.2.1
Nested factors
284
15.2.2
Crossed factors
285
15.3
Writing down experimental designs
285
15.3.1
Some examples
285
15.4
Basic experimental designs
286
15.5
Control factors and factors of interest
287
15.6
Key notions of the chapter
289
15.7
Key questions of the chapter
289
16
ANOVA, two
f
actors:
Α χ
В
or S{
Α χ
В)
290
16.1
Introduction
290
16.2
Organization of a two-factor design:
Αχ Β
292
16.2.1
Notations
293
16.3
Main effects and interaction
294
16.3.1
Main effects
294
16.3.2
Interaction
295
16.3.3
Example without interaction
295
16.3.4
Example with interaction
296
16.3.5
More about the interaction
297
16.4
Partitioning the experimental sum of squares
297
16.4.1
Plotting the pure interaction
299
16.5
Degrees of freedom and mean squares
299
16.6
The score model (Model I) and the sums of squares
301
16.7
Example: cute cued recall
303
16.8
Score model II: A and
В
random factors
306
16.8.1
Introduction and review
306
16.8.2
Calculating
F
when A and
В
are random factors
307
16.8.3
Score model when
Л
and
ß
are random
307
16.8.4
A and
В
random: an example
308
16.9
ANOVA
Αχ Β
(Model III): one factor fixed,
one factor random
310
16.9.1
Score model for
Л
χ
Б
(Model III)
310
16.10
Index of effect size
311
16.10.1
Index
Я2
'global'
311
16.10.2
The regression point of view
312
16.10.2.1
Digression: the sum equals zero
313
16.10.2.2
Back from the digression
314
16.10.3
F
ratios and coefficients of correlation
316
16.10.3.1
Digression: two equivalent ways of computing
the
F
ratio
317
16.10.4
Index R2 'partial'
317
16.10.5
Partitioning the experimental effect
319
16.11
Statistical assumptions and conditions of validity
319
16.12
Computational formulas
320
Contents xv
16.13
Relationships between the names of the sources of
variability, df and
SS
321
16.14
Key notions of the chapter
322
16.15
New notations
322
16.16
Key formulas of the chapter
323
16.17
Key questions of the chapter
323
17
Factorial designs and contrasts
324
17.1
Introduction
324
17.2
Vocabulary
324
17.3
Fine-grained partition of the standard decomposition
325
17.3.1
An example: back to cute cued recall
325
17.3.1.1
The same old story: computing the sum of
squares for a contrast
326
17.3.1.2
Main effect contrasts
326
17.3.1.3
Interaction contrasts
327
17.3.1.4
Adding contrasts: sub-design analysis
327
17.4
Contrast analysis in lieu of the standard decomposition
328
17.5
What error term should be used?
330
17.5.1
The easy case: fixed factors
330
17.5.2
The harder case: one or two random factors
330
17.6
Example: partitioning the standard decomposition
330
17.6.1
Testing the contrasts
331
17.7
Example: a contrast non-orthogonal to the
standard decomposition
332
17.8
A posteriori comparisons
333
17.9
Key notions of the chapter
334
17.10
Key questions of the chapter
334
18
ANOVA, one-factor repeated measures design:
S x
A
335
18.1
Introduction
335
18.2
Advantages of repeated measurement designs
335
18.3
Examination of the
F
ratio
337
18.4
Partition of the within-group variability: S(A) = S + AS
338
18.5
Computing
F
in an
S
χ
A design
340
18.6
Numerical example:
S
χ
A design
340
18.6.1
An alternate way of partitioning the total sum of squares
342
18.7
Score model: Models I and II for repeated
measures designs
343
18.8
Effect size: R, R, and
R
343
18.9
Problems with repeated measures
344
18.9.1
Carry-over effects
345
18.9.2
Pre-test and post-test
345
18.9.3
Statistical regression, or regression toward the mean
346
18.10
Score model (Model \)SxA design: A fixed
346
18.11
Score model {Model
II) S
x
A design: A random
347
18.12
A new assumption: sphericity (circularity)
348
18.12.1
Sphericity: intuitive approach
348
18.12.2
Box's index of sphericity:
ε
349
18.12.3
Greenhouse-Geîsser
correction
350
xvi Contents
18.12.4 Extreme Greenhouse-Geisser
correction
351
18.12.5 Huynh-Feldt
correction
351
18.12.6
Stepwise strategy for sphericity
351
18.13 An
example with computational formulas
352
18.14
Another example: proactive interference
353
18.15
Key notions of the chapter
354
18.16
New notations
355
18.17
Key formulas of the chapter
355
18.18
Key questions of the chapter
357
19
ANOVA, two-factor completely repeated measures: <S
χ Λ χ
В
358
19.1
Introduction
358
19.2
Example: plungin'!
358
19.3
Sum of squares, means squares and
F
ratios
359
19.4
Score model (Model I),
S x
Ax
В
design: A and
В
fixed
361
19.5
Results of the experiment: plungin'
362
19.6
Score model (Model II): <Sx
Λ χ
В
design, A and
В
random
367
19.7
Score model (Model 111):
S
χ Αχ Β
design, A fixed,
В
random
368
19.8
Quasi-F
:
F'
369
19.9
A cousin F"
370
19.9.1
Digression: what to choose?
371
19.10
Validity assumptions, measures of intensity,
key notions, etc.
371
19.11
New notations
371
19.12
Key formulas of the chapter
372
20
ANOVA, two factor partially repeated measures: S[A)
χ Β
373
20.1
Introduction
373
20.2
Example: bat and hat
375
20.3
Sums of squares, mean squares, and
F
ratios
377
20.4
The comprehension formula routine
378
20.5
The 13-point computational routine
380
20.6
Score model (Model I), S(A)
χ
В
design: A and
В
fixed
381
20.7
Score model (Model II), S(A)x
В
design: A and
В
random
382
20.8
Score for Model III, S(A)
χ Β
design: A fixed and
В
random
383
20.9
Coefficients of intensity
384
20.10
Validity of S(A)
χ Β
designs
384
20.11
Prescription
385
20.12
Key notions of the chapter
385
20.13
Key formulas of the chapter
385
20.14
Key questions of the chapter
386
21
ANOVA, nested factorial design:
S
χ Α(Β)
387
21.1
Introduction
387
21.2
Example: faces in space
388
21.2.1
A word of caution: it is very hard to be random
388
Contents xvii
.1,3
How to analyze an
S x
A(B) design
389
21.3.1
Sums of squares
389
21.3.2
Degrees of freedom and mean squares
390
21.3.3
F
and quasi-F ratios
391
21.4
Back to the example: faces in space
392
21.5
What to do with A fixed and
В
fixed
393
21.6
When
Л
and
В
are random factors
394
21.7
When A is fixed and
В
is random
394
21.8
New notations
394
21.9
Key formulas of the chapter
394
21.10
Key questions of the chapter
395
22
How to derive expected values for any design
396
22.1
Introduction
396
22.2
Crossing and nesting refresher
397
22.2.1
Crossing
397
22.2.2
Nesting
397
22.2.2.1
A notational digression
397
22.2.2.2
Back to nesting
397
22.3
Finding the sources of variation
398
22.3.1
Sources of variation. Step
1 :
write down the
formula
398
22.3.2
Sources of variation. Step
2:
elementary factors
398
22.3.3
Sources of variation. Step
3:
interaction terms
399
22.4
Writing the score model
400
22.5
Degrees of freedom and sums of squares
401
22.5.1
Degrees of freedom
401
22.5.2
Sums of squares
401
22.5.2.1
Comprehension formulas
402
22.5.2.2
Computational formulas
402
22.5.2.3
Computing in a square
402
22.6
Example
403
22.7
Expected values
404
22.7.1
Expected value: Step
1 404
22.7.2
Expected value: Step
2 405
22.7.3
Expected value: Step
3 405
22.7.4
Expected value: Step
4 406
22.8
Two additional exercises
406
22.8.1
S(A
χ
B(O): A and
В
fixed,
С
and <S random
407
22.8.2
S{Ax BiC)): A fixed, B,C, and
S
random
407
Appendices
409
A Descriptive statistics
411
A.1 Introduction
411
A.2 Histogram
411
A.3 Some formal notation
414
A.3.1 Notations for a score
414
A.3.2 Subjects can be assigned to different groups
414
xviii Contents
A.3.3
The value of a score for subjects ¡n multiple groups is Vs,s
414
A.3.4 The summation sign is
Σ
414
A.4 Measures of central tendency
415
A.4.1 Mean
416
A.4.2 Median
416
A.4.3 Mode
417
A.4.4 Measures of central tendency recap
417
A.5 Measures of dispersion
417
A.5.1 Range
417
A.5.2 Sum of squares
417
A.5.3 Variance
419
A.5.4 Standard deviation
421
A.6 Standardized scores alias Z-scores
422
A.6.1 Z-scores have a mean of
0,
and a variance of
1 422
A.6.2 Back to the Z-scores
423
В
The sum sign:
£ 424
B.1 Introduction
424
B.2 The sum sign
424
С
Elementary probability: a refresher
426
C.1 Introduction
426
C.2 A rough definition
426
C.3 Some preliminary definitions
427
C.3.1 Experiment, event and sample space
427
C.3.2 More on events
428
C.3.3 Or, and, union and intersection
430
C.4 Probability: a definition
430
C.5 Conditional probability
432
C.5.1
Bayes'
theorem
434
C.5.2 Digression: proof of
Bayes'
theorem
435
C.6 Independent events
436
C.7 Two practical counting rules
438
C.7.1 The product rule
438
C.7.2 Addition rule
439
C.8 Key notions of the chapter
440
C.9 New notations
441
C.10 Key formulas of the chapter
441
C.1
1
Key questions of the chapter
442
D
Probability distributions
443
D.1 Introduction
443
D.2 Random variable
443
D.3 Probability distributions
444
D.4 Expected value and mean
446
D.5 Variance and standard deviation
447
D.6 Standardized random variable: Z-scores
449
D.7 Probability associated with an event
451
D.8 The binomial distribution
453
Contents xix
D.9
Computational shortcuts
456
D.9.1 Permutation, factorial, combinations and
binomial coefficient
456
D.10 The'normal approximation'
460
D.10.1
Digression: the equation of the normal distribution
460
D.1
1
How to use the normal distribution
462
D.12 Computers and Monte-Carlo
465
D.13 Key notions of the chapter
467
D.1
4
New notations
467
D.1
5
Key formulas of the chapter
468
D.16 Key questions of the chapter
468
The binomial test
470
E.1 Introduction
470
E.2 Measurement and variability in psychology
470
E.2.1 Kiwi and Koowoo: a binomial problem
471
Є.2.2
Statistical test
472
E,3 Coda: the formal steps of a test
475
E.4 More on decision making
476
E.4.1 Explanation of'tricky'wording
479
E.5 Monte-Carlo binomial test
479
E.5.1 A test for large N: normal distribution
480
E.6 Key notions of the chapter
483
E.7 New notations
483
E.8 Key questions of the chapter
484
Expected values
485
F.1 Introduction
485
F.2 A refresher
485
F.3 Expected values: the works for an S(A) design
488
F.3.1 A refresher
488
F.3.2 Another refresher: the score model
489
F.3.3 Back to the expected values
490
F.3.4 Evaluating
F.3.5 Evaluating
F.3.6 Evaluating
AS
490
492
493
F.3.7 Expected value of the sums of squares
494
F.3.8 Expected value of the mean squares
494
Statistical tables
495
Table
1
The standardized normal distribution
497
Table
2
Critical values of Fisher's
F
499
Table
3
Fisher's
Z
transform
502
Table
4
Lilliefors test of normality
505
Table
5
Sidàk's test
506
Table
6
Bonferroni's test
509
xx Contents
Table
7 Trend
analysis:
orthogonal
polynomials
512
Table
8
Dunnett'stest
513
Table
9
Frange
distribution
514
ТаЫеЮ
Duncan's test
515
References
518
Index
531 |
| any_adam_object | 1 |
| author_GND | (DE-588)1232083887 |
| building | Verbundindex |
| bvnumber | BV035638863 |
| callnumber-first | B - Philosophy, Psychology, Religion |
| callnumber-label | BF181 |
| callnumber-raw | BF181 |
| callnumber-search | BF181 |
| callnumber-sort | BF 3181 |
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| dewey-ones | 150 - Psychology |
| dewey-raw | 150.72/4 |
| dewey-search | 150.72/4 |
| dewey-sort | 3150.72 14 |
| dewey-tens | 150 - Psychology |
| discipline | Psychologie |
| edition | 1. publ. |
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| id | DE-604.BV035638863 |
| illustrated | Illustrated |
| indexdate | 2025-03-02T15:00:25Z |
| institution | BVB |
| isbn | 9780199299881 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017693692 |
| oclc_num | 276335964 |
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| physical | XX, 538 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Experimental design and analysis for psychology Hervé Abdi .... 1. publ. Oxford [u.a.] Oxford Univ. Press 2009 XX, 538 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Psychology / Research Psychology / Research / Methodology Psychology / Statistical methods Experimental design Experimentelle Versuchsforschung (DE-588)4488711-5 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Psychologie (DE-588)4047704-6 s Experimentelle Versuchsforschung (DE-588)4488711-5 s Datenanalyse (DE-588)4123037-1 s DE-604 Abdi, Hervé Sonstige (DE-588)1232083887 oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017693692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Experimental design and analysis for psychology Psychology / Research Psychology / Research / Methodology Psychology / Statistical methods Experimental design Experimentelle Versuchsforschung (DE-588)4488711-5 gnd Psychologie (DE-588)4047704-6 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4488711-5 (DE-588)4047704-6 (DE-588)4123037-1 |
| title | Experimental design and analysis for psychology |
| title_auth | Experimental design and analysis for psychology |
| title_exact_search | Experimental design and analysis for psychology |
| title_full | Experimental design and analysis for psychology Hervé Abdi .... |
| title_fullStr | Experimental design and analysis for psychology Hervé Abdi .... |
| title_full_unstemmed | Experimental design and analysis for psychology Hervé Abdi .... |
| title_short | Experimental design and analysis for psychology |
| title_sort | experimental design and analysis for psychology |
| topic | Psychology / Research Psychology / Research / Methodology Psychology / Statistical methods Experimental design Experimentelle Versuchsforschung (DE-588)4488711-5 gnd Psychologie (DE-588)4047704-6 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Psychology / Research Psychology / Research / Methodology Psychology / Statistical methods Experimental design Experimentelle Versuchsforschung Psychologie Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017693692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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