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Impact of Gender and Marital Status on Depression: Factorial ANOVA Analysis, Lecture notes of Descriptive statistics

An in-depth analysis of a factorial anova study using spss glm to examine the relationship between gender, marital status, and depression. Descriptive statistics, parameter estimates, tests of between-subjects effects, and model summaries. It explains the differences between effect coding and dummy coding and their impact on the results.

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

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Something to Remember About Factorial ANOVA using SPSS GLM
Descriptive Statistics
Dependent Variable: DEP
5.3432 5.91411 169
7.8402 7.12801 194
6.6777 6.69899 363
GENDER
male
female
Total
Mean Std. Deviation N
Tests of Between-Subjects Effects
Dependent Variable: DEP
563.148a1563.148 12.964 .000
15697.727 115697.727 361.359 .000
563.148 1563.148 12.964 .000
15682.141 361 43.441
32432.000 363
16245.289 362
Source
Corrected Model
Intercept
GENDER
Error
Total
Corrected Total
Type III Sum
of Squares df Mean Square FSig.
R Squared = .035 (Adjusted R Squared = .032)
a.
Parameter Estimates
Dependent Variable: DEP
7.840 .473 16.568 .000
-2.497 .694 -3.600 .000
0a. . .
Parameter
Intercept
[GENDER=1]
[GENDER=2]
BStd. Error tSig.
This parameter is set to zero because it is redundant.
a.
For the regression parameter estimates SPSS computes a dummy
code for the fixed factor, using the largest coded group (here
female) as the comparison group.
Notice that, as expected, the b weight matches the mean
difference
male mean is 2.497 larger than the female mean.
Also, the F the effect of gender is t² for the gender parameter.
Model Summary
.186a.035 .032 6.59097
Model
1
RR Square
Adjusted
R Square
Std. Error of
the Estimate
Predictors: (Constant), GENC
a.
Coefficients
a
7.840 .473 16.568 .000
-2.497 .694 -.186 -3.600 .000
(Constant)
GENC
Model
1
BStd. Error
Unstandardized
Coefficients
Beta
Standardized
Coefficients
tSig.
Dependent Variable: DEPa.
ANOVA
b
563.148 1563.148 12.964 .000a
15682.141 361 43.441
16245.289 362
Regression
Residual
Total
Model
1
Sum of
Squares df Mean Square FSig.
Predictors: (Constant), GENCa.
Dependent Variable: DEPb.
We get the same thing all 3 ways …
Same df, SS & F
Same effect size
Same b
Same F = t²
GLM provides both “traditional ANOVA output” and “regression output” for the same analysis.
Here’s an example, using the relationship between Gender and depression.
Also, the results are the same as if we computed a dummy code with
females as the comparison group ourselves and then used
regression to perform the analysis.
if (gender = 1) genc = 1.
if (gender = 2) genc = 0.
pf3

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Something to Remember About Factorial ANOVA using SPSS GLM

Descriptive Statistics

Dependent Variable: DEP

GENDER

male

female

Total

Mean Std. Deviation N

Tests of Between-Subjects Effects Dependent Variable: DEP

563.148a^1 563.148 12.964. 15697.727 1 15697.727 361.359. 563.148 1 563.148 12.964. 15682.141 361 43. 32432.000 363 16245.289 362

Source Corrected Model Intercept GENDER Error Total Corrected Total

Type III Sum of Squares df Mean Square F Sig.

a.R Squared = .035 (Adjusted R Squared = .032)

Parameter Estimates

Dependent Variable: DEP

0 a^...

Parameter

Intercept

[GENDER=1]

[GENDER=2]

B Std. Error t Sig.

a.This parameter is set to zero because it is redundant.

For the regression parameter estimates SPSS computes a dummy

code for the fixed factor, using the largest coded group (here

female) as the comparison group.

Notice that, as expected, the b weight matches the mean

difference – male mean is 2.497 larger than the female mean.

Also, the F the effect of gender is t² for the gender parameter.

Model Summary

.186a^ .035 .032 6.

Model 1

R R Square

Adjusted R Square

Std. Error of the Estimate

a.Predictors: (Constant), GENC

Coefficientsa

(Constant) GENC

Model 1

B Std. Error

Unstandardized Coefficients Beta

Standardized Coefficients t Sig.

a.Dependent Variable: DEP

ANOVAb

563.148 1 563.148 12.964 .000a 15682.141 361 43. 16245.289 362

Regression Residual Total

Model 1

Sum of Squares df Mean Square F Sig.

a.Predictors: (Constant), GENC b.Dependent Variable: DEP

We get the same thing all 3 ways …

Same df, SS & F

Same effect size

Same b

Same F = t²

GLM provides both “traditional ANOVA output” and “regression output” for the same analysis.

Here’s an example, using the relationship between Gender and depression.

Also, the results are the same as if we computed a dummy code with

females as the comparison group ourselves and then used

regression to perform the analysis.

if (gender = 1) genc = 1.

if (gender = 2) genc = 0.

Descriptive Statistics Dependent Variable: DEP

MARITAL

single married Total single married Total single married Total

GENDER

male

female

Total

Mean Std. Deviation N

Parameter Estimates Dependent Variable: DEP

0 a^... 3.150 .961 3.276. 0 a^... -4.207 1.474 -2.855.

0

a

...

0

a

...

0

a

...

Parameter Intercept [GENDER=1] [GENDER=2] [MARITAL=1] [MARITAL=2] [GENDER=1] * [MARITAL=1] [GENDER=1] * [MARITAL=2] [GENDER=2] * [MARITAL=1] [GENDER=2] * [MARITAL=2]

B Std. Error t Sig.

a.This parameter is set to zero because it is redundant.

Tests of Between-Subjects Effects Dependent Variable: DEP

1055.189a^3 351.730 8.313. 13262.668 1 13262.668 313.447. 278.122 1 278.122 6.573. 85.324 1 85.324 2.017. 344.868 1 344.868 8.151. 15190.100 359 42. 32432.000 363 16245.289 362

Source Corrected Model Intercept GENDER MARITAL GENDER * MARITAL Error Total Corrected Total

Type III Sum of Squares df Mean Square F Sig.

a.R Squared = .065 (Adjusted R Squared = .057)

YIKES!

Neither the gender main effect, nor the marital main effect match for the ANOVA and parameter estimates -- F? t² and the b values don’t reflect the marginal mean differences!

However, the interaction does match -- 2.855² = 8.151, and the interaction b (-4.207) reflects the difference between the simple effect of marital for males (-1.0562) and for females (3.1498) ‡ 4.207.

However, watch what happens when we switch to a factorial design – here with the fixed effects of gender and marital status and the outcome variable depression.

Why does this happen? The confluence of two things…

The ANOVA summary table reflects the use of “effects coding” (the highest coded group for each IV is the comparison group and is weighted -1 and the interaction term is the product of the two main effect codes), whereas the parameter estimates reflect the use of dummy coding (the highest coded group for each IV is the comparison group and is

weighted 0 and the interaction term is the product of the two main effect codes),

Effect codes and dummy codes are not linear transformations of each other, and so using them leads to different

patterns of colinearity between the main effects terms of the model, and so, different expressions of the main effects.

Two things to notice:

  1. The interaction term is the same for both effect coded and dummy coded versions. This may be why some folks suggest ignoring main effects if you have an interaction – because the interaction term is the same for various coding schemes. However, even if you delete a non-contributing interaction term, the main effects will still appear different for a dummy and effect coded analysis.
  2. This effect won’t show up if there is =n for the factorial design. If so, the main effects are orthogonal and so there’s

no colinearity to be partitioned differently by the different coding schemes. Some folks base upon this the suggestion that factorial analyses should be reserved for =n designs. Others counter that this is an artificial simplification of the patterns of “real colinearity” among variables. These folks suggest that differences between the main effects results using dummy vs. effect coding is no more “troublesome” than the differences between the main effects results when using alternative operational differences (manipulation or measurement) of the IVs. In either case you select your “preferred” operationalization and judiciously interpret the results.