Categorical Data Analysis Midterm Review - PowerPoint Presentation

Slide1

Categorical Data Analysis Midterm Review

Val & AlyApril 2014Slide2

Overview

Regression Analysis: Mediation

Moderation

Non-parametric tests

When? Why? How?Slide3

Example 1

Bumble wants to know whether the relationship between children’s negative affect and self esteem can be explained by children’s bad behavior. Unfortunately, he had to take another vacation to Hawaii, so he left before he could check his results. It’s up to you to do it for him. What do you need to test for? Slide4

Mediation Model (Baron & Kenney)

X

M

Y

a

b

c

c

'Slide5

Mediation

Definition: The mediator (M)

explains

or

accounts for

the relationship between X &

Y

How to test (packet 2, p.3)

Baron & Kenney Procedure

Sobel

test (obsolete)

Bootstrapping

Interpretation

Avoid causal language, instead say:

“The pattern of correlations is consistent with mediation.”

“The association between X & Y is mediated by M.Slide6

Mediation

•Is there evidence for mediation?•Path A: Negative affect 

Bad behavior

B

=.024,

p

< .001

•

Path B: Bad behavior



Self Esteem

B

= -.649, p

= .024•Path C: Negative affect

 Self Esteem

C: B = -.111,

p < .001 C

' :

B

= -.096,

p

< .001Slide7

Moderation Model

X

Moderator

YSlide8

Moderation

Definition

The strength of the relationship between X on Y depends on the level of “Z (Moderator)”

.

How to test (

packet 3

, p

. 6

)

Multiple regression analysis with an interaction term (X*Moderator

)

Interpretation

The association between X and Y is stronger for

Z

=0 than for Z=1

Direction and magnitudeSlide9

Would the association between stress and anxiety differ depending on self-concept complexity?

(not complex=0, complex=1)

Coefficients

a

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Correlations

Collinearity

Statistics

B

Std. Error

Beta

Zero-order

Partial

Part

Tolerance

VIF

1

(Constant)

-.650

.297

-2.190

.030

GPA

.339

.072

.370

4.700

.000

.375

.371

.370

.996

1.004

SelfEsteem

-.062

.063

-.078

-.985

.326

-.100

-.084

-.077

.996

1.004

2

(Constant)

-1.435

.393

-3.648

.000

GPA

.154

.074

.168

2.082

.039

.375

.176

.149

.789

1.268

SelfEsteem

-.031

.058

-.039

-.545

.587

-.100

-.047

-.039

.987

1.013

Stress

.181

.056

.246

3.256

.001

.364

.269

.233

.900

1.112

Complexity

-.284

.068

-.327

-4.152

.000

-.446

-.335

-.297

.829

1.207

3

(Constant)

-1.057

.411

-2.572

.011

GPA

.123

.073

.134

1.677

.096

.375

.143

.118

.768

1.302

SelfEsteem

-.028

.056

-.035

-.490

.625

-.100

-.042

-.034

.986

1.014

Stress

.103

.062

.140

1.664

.098

.364

.142

.117

.694

1.442

Complexity

-.648

.154

-.746

-4.207

.000

-.446

-.340

-.295

.156

6.395

StressxComplexity

.078

.030

.442

2.625

.010

-.230

.220

.184

.174

5.755

a. Dependent Variable: Anxiety level during examSlide10

Anxiety level during exam =

-1.057 + .123GPA -.028self-esteem +.103 stress -.648

complexity

+ .078

stress*complexity

Interpretation:

Two-way interaction of stress and self-concept complexity was significant. (beta=

.442,

p

=.010)

This suggests that while holding GPA and self-esteem constant, higher stress is associated with more test anxiety for people with a complex self-concept than those with a simple self-concept.

For people who have complex self-concept,

Anxiety level during exam

=

-1.057 + .123GPA -.028self-esteem

+.103

stress

-.648

(1)

+ .078

stress*(1)

=

-1.705

+ .123GPA -.028self-esteem

+

.181

stress

For people have simple self-concept,

Anxiety level during exam

=

-1.057 + .123GPA -.028self-esteem

+.103

stress

-.648

(0)

+ .078

stress*(0)

=

-1.057

+ .123GPA -.028self-esteem

+ .103

stressSlide11

Non-parametric vs. Parametric tests

Assumptions for parametrics/non-

parametrics

Evaluating different measures

Weakness & Benefits

You

should argue why you choose one test over the other test

(

c

ompare

two tests &

reasons for choice

)Slide12

Non-parametric analysis

Why & When is non-parametric analysis used?

(1)When data & distribution do not meet the assumptions of parametric analysis,

normality violation (outlier or skew)

Homogeneity of Variances (check skew & kurtosis, don’t trust

Levene

)

Issues with

Levene’s

test

as a test of homogeneity of variances:

Levene’s

test is not sensitive enough with small N; even though

Levene

is

n.s

., variances might actually differ enough to be a problem. With very large N,

Levene

may be significant but the difference in variance may not matter.

with small N, we cannot be confident that the sample represents the population well and cannot assess assumption of normality in the population

.

(2) When parametric tests are not appropriate

non-parametric tests

may

be more powerfulSlide13

Non-parametric tests

Comparing two independent

groups (p. 8 – 9, 16 – 17)

Wilcoxon

Ws

Mann-Whitney U

Median

Test

Comparing two

dependent

groups (p. 18 – 22)

Wilcoxon

T

Contingency Table Statistics (p. 24)

Pearson Chi-squared

Fisher’s exact Test

McNemar’s

test

Variety of Statistics of Effect Size & Correlations (p. 25 – 26)

Kappa

Lambda

Phi

Gamma

Spearman : r :: Wilcoxon :

t

Other non-parametric tests (p. 38)

Run’s TestSlide14

Which test would you use?

To test if 2 variables are independent Non parametric test: Chi Square, Fisher’s exact test (

fe

<5)

Parametric equivalent: Pearson’s

r

2

.

To test the difference between 2 independent groups

Non parametric: Wilcoxon W, Mann Whitney U

Parametric equivalent: Independent t-

test

3. To test the difference between 2 matched

groups

Non parametric: Wilcoxon T

Parametric equivalent: Matched samples t-

testSlide15

Example

Intervention to improve academic performanceRandomly assign CGU students to:

Control: No smart cookie (4, 6, 6, 9, 5

)

Experimental

: A batch of smart cookies (8, 10, 12, 15, 25

)

5

students in each

group

How

do we test if

these

cookies

really work?Slide16

Wilcoxon W

Why do we use it?Want to compare two independent groups

t-test assumptions have been

violated

H

o

:

The average rank of scores is the same for each

population

How do you use it?

Based on ranks of scores

Ws

is always the smallest sum of ranks

SPSS does not always reports correct

Ws

, but it will always report the correct Mann-Whitney USlide17

Mann Whitney U

Why do we use it?Similar circumstances for Wilcoxon

W

H

o

: p(E>C) =

0.50

How do you use it?

Based on number of pairs that need to be reversed to get perfect separation of groups

On SPSS, use the “Exact sig.” because “Asymptotic sig.” assumes a normal approximation

See page 8 for calculating probability of superioritySlide18

Example

• Intervention: Eating a smart cookie• Academic Performance for 7 students

–Pre {5,6,12,9,10,13,59}

–Post {5,7,14,12,12,13,21}

• Bumble

decided to use paired samples

t

-test. Would you accept Bumble’s analysis? Why or why not?Slide19

Issues?

Fails to meet the assumptions of paired samples t-test.Non-normal distribution of difference scores

Also

, small sample size makes parametric test more vulnerable to effects of violations of assumptionsSlide20

Wilcoxon T

Why do we use it?

Nonparametric version of the matched samples t-test

Concerned about extreme outliers messing with

data

H

o

: The sum of ranks of the positive difference scores = The sum of ranks of the negative difference

scores

How do you use it?

Based on score ranking, and then summing scores for positive and negative differences, use smallest to get your T.

Remember to ignore difference scores of zero.

Outliers are based on difference scores, not actual scores.Slide21
Slide22

Chi-Square (

χ2)

Why?

Tests whether the data that we observe (

frequencies

) differ from our expectation based on a model such as independent of two variables

.

When?

f

e

>5 →

χ

2

test

H

0

: independence between the row and column variables in the

population

How?

χ

2

=∑(

fo-fe

)

2

/

fe

df

=(#rows-1)*(#columns-1)

Critical

χ

2

=3.84 when

2x2

Yates correction for continuity

χ

2

=∑(|

fo-fe

|-0.5)

2

/

fe

when

df

=1 and margins are fixed before collecting data

Slide23

Fisher’s exact Test

When?f

e

<5

If

fe

is small, it may distort a

χ

2

value (check the denominator of formula!

)

How?

Prob

=(

a+b

)!(

c+d

)!(

a+c

)!(

b+d

)!

N!a!b!c!d

!

P

robability of the exact outcome, sum with more extreme outcomesSlide24

Example

Bumble and Bimble were auditors for the IRS. One task was to review tax returns to determine whether the return should be audited. Bumble and Bimble each reviewed the same sample of 150 returns.

Bumble

selected 120 that should be reviewed and

Bimble

selected 115 to be reviewed, but there were only 110 returns they both reviewed. Do they differ significantly in their selection rates? Slide25

McNemar

Why?

To tests the likelihood of an event:

Is Rater 1 more likely to say + (or -)

than

Rater 2?

Do more people Pass (or Fail)

test

after training

?

Null hypothesis

H

0

: p(+| X)=p(+| Y), (

a+b

)/N=(

a+c

)/N;

Are marginal distributions same?

H

0

can be boiled down to… b=c

∴

McNemar

uses

disagreement

cells

to answer these questions

!

How?

(1)

χ

2

approximation

χ

2

= (|b-c|-1)

2

/(

b+c

) if

Npq

>5, Always

df

=1, critical

χ

2

.05=3.84

N is not total N, but total of two cell (

b+c

)

(2) Binomial test (p.34 Siegel’s Table D)

+

-

+

a

b

a+b

-

c

d

c+d

a+c

b+d

NSlide26
Slide27
Slide28

Cohen’s Kappa

To test extent of agreement

Percent observed (Po) and Percent chance (Pc) agreement

Test significance with chi squareSlide29
Slide30
Slide31
Slide32
Slide33

Example

• People are waiting in line at the Apple store to purchase the iPhone 5. Its an exclusive offer and its 3 am, but people are already there!• MMMFFFFMMMMMFFF

• Are people of the same gender lining

up in clusters more than we would

expect by chance?Slide34

Runs test

Why?Test for Serial Randomness of Nominal Data  

Q: Is the order of two mixed groups more (or less)

scrambled than would be expected by chance?

H

0

: random dispersion of nominal data

How?

Use Siegel’s table F1&2 (p.38)

If R < the lower R

Critical

(“too few” table) then the data are non-random due to clustering.

If R > the upper R

Critical

(“too many” table) then the data are non-random due to uniformity.

If R falls between the lower and upper R

Critical

then the data are consistent with random mixing of cases.

Slide35

Runs

•In our example, bigger clusters = less runs• Are there too few runs?

• MMM, FFFF, MMMMM, FFF

• N

1

= 7, N

2

= 8, R = 4

• Siegel (1956) table on p. 36,

p

< .05

• Value shown on table or smaller is sig.Slide36

Happy Studying!

Read Question carefullycreate a table with the numbersthink about which test is most appropriate

Recall some of the basicsAssumptions

Null hypotheses

P-values