Hello friend.
The following is my proposed methodology for analyzing survey data for a
professor in criminology at Florida State University.
I'd like someone experienced in categorical data analysis to review it and
email me comments, or criticisms, or suggestions.
Thank you.
Kermit Rose
[EMAIL PROTECTED]
The dependent variable is a multivalued categorical variable. The model
dependent variable is an interaction variable. It is the interaction of
some subset of the 10 two-valued dummy variables representing the dependent
variable. The 10 values of the dependent variable are choices of
preferential treatment for affirmative action.
The model independent variable is also an interaction variable. It is
the interaction of two-valued dummy variables representing some subset
of the predicting variables.
The raw data variables are either categorical variables or ordinal level
variables.
Suppose V is a categorical varible with values v1,v2,v3.
Then V is converted to two variables X1,X2 with
X1 = 1 if V = v1, and X1 = 0 otherwise.
X2 = 1 if V = v2, and X2 = 0 otherwise.
Suppose R is an ordinal level variable with values r1 < r2 < r3 < r4.
Then R is converted to three variables S1,S2,S3 with
S1 = 1 if R = r1 and S1 = 0 otherwise.
S2 = 1 if R = r1 or r2 and S2 = 0 otherwise.
S3 = 1 if R = r1 or r2 or r3 and S3 = 0 otherwise.
We say the model independent variable is true for a case if all the
independent variable values are present in the case. Otherwise the
mocel independent variable is false for that case.
We say the model dependent variable is true for a case if all the dependent
variable values are present in the case. Otherwise the dependent variable
is false for that case.
We define parameters t,I,D and N as follows.
t is the number of cases where both the model independent and model dependent
variable are true.
I is the number of cases where the model independent variable is true.
D is the number of cases where the model Dependent variable is true.
N is the total number of cases.
Model Model
Dependent Independent Count Expected Col pct
variable varible
true true t D*I/N t/D
true false D-t D(1-I/n) 1 - t/D
true total D D 1
false true I-t I(1-D/N) (I-t)/(n-D)
false false N-I-D+t N-I-D+D*I/N 1-(I-t)/(N-D)
false Total N-D N - D 1
Total true I I I/N
Total False N-I N - I 1 - I/N
Total Total N N 1
Covariance of model independent and model dependent variable =
(t - I^2/N - D^2/N + D * I/N)/(N-1)
variance of model independent variable =
I (1 - I/N)/(N-1)
Variance of model Dependent variable =
D (1 - D/N)/(N-1)
square of correlation between model independent variable and model dependent
variable is r-square =
[ t - I^2 /N - D^2 /N + D*I/N ]/ [I* D * (1 - I/N)* (1-D/N) ]
Chisquare of crosstab of model independent variable with model dependent
variable is
(t - D*I/N)*( N/[D*I] + N/[I*(N-D)] + N/[D*(N-I)] + N/[(N-I)*(N-D)] )
The significance number that is calculated for a statistic is the
predicted probability that the null hypothesis is true.
There are two different null hypotheses of interest.
null_1:
The dependent variable does not depend on independent variable.
The significance of null_1 is
(D - t)/N
null_2:
There is not a bidirectional relationship between the independent variable
and the dependent variable.
The significance of null_2 is (I+D-2*t)/N
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