Statistical Methods for Psychology

Because there are only 2 dffor Moral, there is no dummy variable corresponding to the last

level of Moral. (Remember, all of this is done internally, and you won’t see the recoding.

Moreover, coding the levels as (2,1) will lead to different estimates than coding them as (1, 2),

though other statistics will be unchanged. You have to read the manual to see what the pro-

gram does.) Other programs, however, use a 1, 0, 2 1 type of coding, which we saw when

we discussed the analysis of variance. The net result is that SPSS GENLOG forces the co-

efficient for the highest level of a variable to be 0, whereas other programs force the sum

of the coefficients for that variable to be 0, making the last one equal to –1 times the sum

of the others. For this reason you may see very drastic differences between the parameter

estimates produced by different programs. The end result in terms of expected values will

be the same, but the solutions may look very different.

From Exhibit 17.5 we see that our model can be written as

Because SPSS codes an observation as 1 if it is the member of a particular treatment

or interaction level, and 0 if it is not, we can calculate expected frequencies by substitut-

ing 1s or 0s in the model and solving for ln(Fij). We then exponentiate the result to ob-

tain the expected frequency. The easiest case is an observation in the (Not Guilty, High

Fault, Low Moral) cell, because it would be coded 0 on everything. That would lead us

to ln(F 113 ) 5 3.191 20 20 20 1... 10 5 3.191. Then e3.191 5 24.31, which, as we

will see in Exhibit 17.6, is the expected value for that cell.

Expected Cell Frequencies

Finally, let us look at how well our model predicts the observed cell frequencies. The

results are shown in Exhibit 17.6.

In this exhibit you see the observed and expected cell frequencies followed by a

statistical test on the residuals (deviates)—the difference between observed and expected

1 1.529VF 111 1.040VM 111 0.573VM 12

=3.191 2 1.153F 12 0.758M 11 0.505M 22 0.198V 1

ln (Fijk)=l1lF1lM1lV1lFV1lMV

Section 17.8 Treatment Effects 653

Cell Counts and Residualsb

Verdict Fault Moral

111

2

3

21

2

3

211

2

3

21

2

3

Observed

Count

42

79

32

23

65

17

4

12

8

11

41

24

%

11.7%

22.1%

8.9%

6.4%

18.2%

4.7%

1.1%

3.4%

2.2%

3.1%

11.5%

6.7%

Count

38.547

85.395

29.058

26.453

58.605

19.942

3.600

12.720

7.680

11.400

40.280

24.320

%

10.8%

23.9%

8.1%

7.4%

16.4%

5.6%

1.0%

3.6%

2.1%

3.2%

11.3%

6.8%

Residual

3.453

• 6.395
  2.942


• 3.453
  6.395


• 2.942
  .400
  –.720
  .320
  –.400
  .720
  –.320

Standardized

Residual

.556

–.692

.546

–.671

.835

–.659

.211

–.202

.115

–.118

.113

–.065

Adjusted

Residual

1.008

–1.632

.950

–1.008

1.632

–.950

.262

–.338

.161

–.262

.338

–.161

Deviance

.548

–.701

.537

–.687

.821

–.676

.207

–.204

.115

–.119

.113

–.065

Expected

aModel: Poisson

bDesign: Constant 1 Fault 1 Moral 1 Verdict 1 Verdict*Fault 1 Verdict*Moral

Exhibit 17.6 Estimated cell frequencies for optimal model