Kenny's Condition A #2

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Kenny's Condition A #2

E. Bernardo
Do you have articles than used Condition A # 2 of Kenny? 
 
Condition A #2 of Kenny (http://davidakenny.net/cm/identify.htm) is as follows:
 
Condition A:  Scaling the Latent Variable
    Because a latent variable is unmeasured, its units of measurement must be fixed by the researcher.  This condition concerns how the units of measurement of each latent variable are fixed.  Each construct must have either
1.  one fixed nonzero loading (usually 1.0),
2.  for causal factors, fixed factor variance (usually 1.0), or for factors that are caused, fixed factor disturbance variance (usually 1.0), or
3.  in some rare cases (see an example), a fixed causal path (usually 1.0), leading into or out of the latent variable.  Some computer programs, require that only strategy 1 be used, but both of the other strategies are perfectly legitimate.  For pure measurement model situations or confirmatory factor analysis (no causation between latent variables), strategy 2 is often used and it reduces to the standard factor analysis model.
 
Thank you for your help.
 

Tom
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Chi Square test and a posteriori multiple comparison

Tom

Hello

 

I got a 6x3 table with this descriptive result:

Funktion * G4 Kreuztabelle

 

G4

Gesamt

No

Yes

Funktion

1

Anzahl

8

12

20

% innerhalb von Funktion

40.0%

60.0%

100.0%

% innerhalb von G4

1.4%

2.0%

1.7%

% der Gesamtzahl

.7%

1.0%

1.7%

2

Anzahl

41

129

170

% innerhalb von Funktion

24.1%

75.9%

100.0%

% innerhalb von G4

7.2%

21.6%

14.5%

% der Gesamtzahl

3.5%

11.0%

14.5%

3

Anzahl

524

456

980

% innerhalb von Funktion

53.5%

46.5%

100.0%

% innerhalb von G4

91.4%

76.4%

83.8%

% der Gesamtzahl

44.8%

39.0%

83.8%

Gesamt

Anzahl

573

597

1170

% innerhalb von Funktion

49.0%

51.0%

100.0%

% innerhalb von G4

100.0%

100.0%

100.0%

% der Gesamtzahl

49.0%

51.0%

100.0%

 

 

The chi-square-test gives a significant result:

 

Chi-Quadrat-Tests

 

Wert

df

Asymptotische Signifikanz (2-seitig)

Chi-Quadrat nach Pearson

50.600a

2

.000

Likelihood-Quotient

52.878

2

.000

Zusammenhang linear-mit-linear

39.583

1

.000

Anzahl der gültigen Fälle

1170

 

 

a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale erwartete Häufigkeit ist 9.79.

 

If I’m right, chi-square test is a sort of omnibus-test. How can I perform with PASW 18 an a posteriori test in order to compare the relative amount of Yes within the three categories of the variable “function” ? Or, in other words: which one are significant: 40:60, 24:76 or/and 54:46?

 

I appreciate any help.

Tom

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Automatic reply: Chi Square test and a posteriori multiple comparison

Salbod

Thank you for your email. I will be out of the office beginning  Friday, August 20th, returning on Monday, August 30th and will respond to your message when I return.

 

 

Stephen Salbod

Data Analyst

Pace University

Psychology Department, NYC

 

 

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Re: Chi Square test and a posteriori multiple comparison

Hector Maletta
In reply to this post by Tom

The percentages for the Yes response are already in the table, as row percentages:

Funktion=1 à %Yes=12/20=60%

Funktion=2 à %Yes=129/170=75.9%

Funktion=3 à %Yes=456/980=46.53%

Total à% Yes=597/1170=51.0%

The other percentages in the table refer to column totals and table total, and are irrelevant for your purposes.

Now for significance. Are these percentages significant? It depends on what you mean. Significantly different from zero? Probably yes because they are quite large, and sample sizes are large except for Funktion=1, but even in that case it may be sufficient. In general,  use a t-test to do that comparison, in SPSS (comparing two independent samples). Significantly different from the overall percentage, which is 51%? Use the same t-test procedure in SPSS, comparing percentages to the fixed value 51%. In both cases: For the first category of funktion, for which the sample is exceedingly small (20 cases) the normality assumption of the t-test may not be met; so you may want to use nonparametric tests instead.

 

Hector

 

De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Balmer Thomas
Enviado el: Friday, August 20, 2
010 11:57 AM
Para: [hidden email]
Asunto: Chi Square test and a posteriori multiple comparison

 

Hello

 

I got a 6x3 table with this descriptive result:

Funktion * G4 Kreuztabelle

 

G4

Gesamt

No

Yes

Funktion

1

Anzahl

8

12

20

% innerhalb von Funktion

40.0%

60.0%

100.0%

% innerhalb von G4

1.4%

2.0%

1.7%

% der Gesamtzahl

.7%

1.0%

1.7%

2

Anzahl

41

129

170

% innerhalb von Funktion

24.1%

75.9%

100.0%

% innerhalb von G4

7.2%

21.6%

14.5%

% der Gesamtzahl

3.5%

11.0%

14.5%

3

Anzahl

524

456

980

% innerhalb von Funktion

53.5%

46.5%

100.0%

% innerhalb von G4

91.4%

76.4%

83.8%

% der Gesamtzahl

44.8%

39.0%

83.8%

Gesamt

Anzahl

573

597

1170

% innerhalb von Funktion

49.0%

51.0%

100.0%

% innerhalb von G4

100.0%

100.0%

100.0%

% der Gesamtzahl

49.0%

51.0%

100.0%

 

 

The chi-square-test gives a significant result:

 

Chi-Quadrat-Tests

 

Wert

df

Asymptotische Signifikanz (2-seitig)

Chi-Quadrat nach Pearson

50.600a

2

.000

Likelihood-Quotient

52.878

2

.000

Zusammenhang linear-mit-linear

39.583

1

.000

Anzahl der gültigen Fälle

1170

 

 

a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale erwartete Häufigkeit ist 9.79.

 

If I’m right, chi-square test is a sort of omnibus-test. How can I perform with PASW 18 an a posteriori test in order to compare the relative amount of Yes within the three categories of the variable “function” ? Or, in other words: which one are significant: 40:60, 24:76 or/and 54:46?

 

I appreciate any help.

Tom

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Re: Chi Square test and a posteriori multiple comparison

Burleson,Joseph A.
In reply to this post by Tom
Thomas:

I would do another procedure rather than the one Hector suggests. The reason is that the data are di- and tri-chotomous, and t-tests require that the raw data be continuous for the test variable.

Instead: run a logistic regression with the Yes/No as the dependent, dichotomous outcome variable. Put in one independent variable, the tri-chotomous (1,2,3) variable.

If you have some a priori hypotheses as to which of the three rows are different, consider using them instead. The a priori comparisons number k -1 = 3 - 1 = 2, so that you are only allowed 2 of the 3 comparisons you mentioned. This allows for orthogonal comparisons, with no need to adjust the p-level such as in the 3 post-hoc tests you suggested.

There are two basic patterns as to how to compare the 3 cells this way:
A. Compare the hypothesized most different cell to the other two combined, then contrast the two that were first combined against each other.
B. Pick a "control" cell and do direct comparisons of it with EACH of the other 2, respectively.

Procedure A uses all the data on the first test, but is robust on that first test.
Procedure B uses 2/3 of the data on each test, but is more specific.

the trick is judging whether you want more robustness or more specificity.

The names of the orthogonal a priori test is logistic regression are the same as in general linear models. Note that some of them are NOT orthogonal.

Joe Burleson

________________________________
From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Balmer Thomas [[hidden email]]
Sent: 20 August 2010 10:56
To: [hidden email]
Subject: Chi Square test and a posteriori multiple comparison

Hello

I got a 6x3 table with this descriptive result:
Funktion * G4 Kreuztabelle



G4

Gesamt

No

Yes

Funktion

1

Anzahl

8

12

20

% innerhalb von Funktion

40.0%

60.0%

100.0%

% innerhalb von G4

1.4%

2.0%

1.7%

% der Gesamtzahl

.7%

1.0%

1.7%

2

Anzahl

41

129

170

% innerhalb von Funktion

24.1%

75.9%

100.0%

% innerhalb von G4

7.2%

21.6%

14.5%

% der Gesamtzahl

3.5%

11.0%

14.5%

3

Anzahl

524

456

980

% innerhalb von Funktion

53.5%

46.5%

100.0%

% innerhalb von G4

91.4%

76.4%

83.8%

% der Gesamtzahl

44.8%

39.0%

83.8%

Gesamt

Anzahl

573

597

1170

% innerhalb von Funktion

49.0%

51.0%

100.0%

% innerhalb von G4

100.0%

100.0%

100.0%

% der Gesamtzahl

49.0%

51.0%

100.0%



The chi-square-test gives a significant result:

Chi-Quadrat-Tests



Wert

df

Asymptotische Signifikanz (2-seitig)

Chi-Quadrat nach Pearson

50.600a

2

.000

Likelihood-Quotient

52.878

2

.000

Zusammenhang linear-mit-linear

39.583

1

.000

Anzahl der gültigen Fälle

1170





a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale erwartete Häufigkeit ist 9.79.


If I’m right, chi-square test is a sort of omnibus-test. How can I perform with PASW 18 an a posteriori test in order to compare the relative amount of Yes within the three categories of the variable “function” ? Or, in other words: which one are significant: 40:60, 24:76 or/and 54:46?

I appreciate any help.
Tom

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
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For a list of commands to manage subscriptions, send the command
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Re: Chi Square test and a posteriori multiple comparison

Hector Maletta
What Joseph Burleson proposes is right, but it requires entering the much
more complicated field of logistic regression. For the case at hand I tilt
to the view that one can use t-test nonetheless. For one thing, dichotomous
yes/no variables can be treated as interval measures: the percentage of
cases with the value 1 (if the other value is 0) equals the mean of the
variable considered as an interval scale. T-tests are, besides, frequently
used to assess percentage differences. However, CROSSTABS provides other
tests for contingency tables that may be more adequate, such as those based
on chi square.

Hector


-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de
Burleson,Joseph A.
Enviado el: Friday, August 20, 2010 2:22 PM
Para: [hidden email]
Asunto: Re: Chi Square test and a posteriori multiple comparison

Thomas:

I would do another procedure rather than the one Hector suggests. The reason
is that the data are di- and tri-chotomous, and t-tests require that the raw
data be continuous for the test variable.

Instead: run a logistic regression with the Yes/No as the dependent,
dichotomous outcome variable. Put in one independent variable, the
tri-chotomous (1,2,3) variable.

If you have some a priori hypotheses as to which of the three rows are
different, consider using them instead. The a priori comparisons number k -1
= 3 - 1 = 2, so that you are only allowed 2 of the 3 comparisons you
mentioned. This allows for orthogonal comparisons, with no need to adjust
the p-level such as in the 3 post-hoc tests you suggested.

There are two basic patterns as to how to compare the 3 cells this way:
A. Compare the hypothesized most different cell to the other two combined,
then contrast the two that were first combined against each other.
B. Pick a "control" cell and do direct comparisons of it with EACH of the
other 2, respectively.

Procedure A uses all the data on the first test, but is robust on that first
test.
Procedure B uses 2/3 of the data on each test, but is more specific.

the trick is judging whether you want more robustness or more specificity.

The names of the orthogonal a priori test is logistic regression are the
same as in general linear models. Note that some of them are NOT orthogonal.

Joe Burleson

________________________________
From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Balmer
Thomas [[hidden email]]
Sent: 20 August 2010 10:56
To: [hidden email]
Subject: Chi Square test and a posteriori multiple comparison

Hello

I got a 6x3 table with this descriptive result:
Funktion * G4 Kreuztabelle



G4

Gesamt

No

Yes

Funktion

1

Anzahl

8

12

20

% innerhalb von Funktion

40.0%

60.0%

100.0%

% innerhalb von G4

1.4%

2.0%

1.7%

% der Gesamtzahl

.7%

1.0%

1.7%

2

Anzahl

41

129

170

% innerhalb von Funktion

24.1%

75.9%

100.0%

% innerhalb von G4

7.2%

21.6%

14.5%

% der Gesamtzahl

3.5%

11.0%

14.5%

3

Anzahl

524

456

980

% innerhalb von Funktion

53.5%

46.5%

100.0%

% innerhalb von G4

91.4%

76.4%

83.8%

% der Gesamtzahl

44.8%

39.0%

83.8%

Gesamt

Anzahl

573

597

1170

% innerhalb von Funktion

49.0%

51.0%

100.0%

% innerhalb von G4

100.0%

100.0%

100.0%

% der Gesamtzahl

49.0%

51.0%

100.0%



The chi-square-test gives a significant result:

Chi-Quadrat-Tests



Wert

df

Asymptotische Signifikanz (2-seitig)

Chi-Quadrat nach Pearson

50.600a

2

.000

Likelihood-Quotient

52.878

2

.000

Zusammenhang linear-mit-linear

39.583

1

.000

Anzahl der gültigen Fälle

1170





a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale
erwartete Häufigkeit ist 9.79.


If I’m right, chi-square test is a sort of omnibus-test. How can I perform
with PASW 18 an a posteriori test in order to compare the relative amount of
Yes within the three categories of the variable “function” ? Or, in other
words: which one are significant: 40:60, 24:76 or/and 54:46?

I appreciate any help.
Tom

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD
Se certificó que el correo entrante no contiene virus.
Comprobada por AVG - www.avg.es
Versión: 8.5.441 / Base de datos de virus: 271.1.1/3081 - Fecha de la
versión: 08/20/10 06:35:00

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
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Re: Chi Square test and a posteriori multiple comparison

Bruce Weaver
Administrator
In reply to this post by Burleson,Joseph A.
My notes on categorical data (http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf, section 2.8) show how to partition the overall likelihood ratio chi-square into orthogonal components.  I've not checked, but because I'm using the likelihood ratio chi-square, I expect the method shown in my notes will give identical results to two orthogonal contrasts carried out via logistic regression, as proposed by Joe.

By the way, the example in the notes also uses a 3x2 table, so it should be fairly easy to adapt to Thomas's problem.

HTH.


Burleson,Joseph A. wrote
Thomas:

I would do another procedure rather than the one Hector suggests. The reason is that the data are di- and tri-chotomous, and t-tests require that the raw data be continuous for the test variable.

Instead: run a logistic regression with the Yes/No as the dependent, dichotomous outcome variable. Put in one independent variable, the tri-chotomous (1,2,3) variable.

If you have some a priori hypotheses as to which of the three rows are different, consider using them instead. The a priori comparisons number k -1 = 3 - 1 = 2, so that you are only allowed 2 of the 3 comparisons you mentioned. This allows for orthogonal comparisons, with no need to adjust the p-level such as in the 3 post-hoc tests you suggested.

There are two basic patterns as to how to compare the 3 cells this way:
A. Compare the hypothesized most different cell to the other two combined, then contrast the two that were first combined against each other.
B. Pick a "control" cell and do direct comparisons of it with EACH of the other 2, respectively.

Procedure A uses all the data on the first test, but is robust on that first test.
Procedure B uses 2/3 of the data on each test, but is more specific.

the trick is judging whether you want more robustness or more specificity.

The names of the orthogonal a priori test is logistic regression are the same as in general linear models. Note that some of them are NOT orthogonal.

Joe Burleson

________________________________
From: SPSSX(r) Discussion [SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of Balmer Thomas [Thomas.Balmer@phbern.ch]
Sent: 20 August 2010 10:56
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Chi Square test and a posteriori multiple comparison

Hello

I got a 6x3 table with this descriptive result:
Funktion * G4 Kreuztabelle



G4

Gesamt

No

Yes

Funktion

1

Anzahl

8

12

20

% innerhalb von Funktion

40.0%

60.0%

100.0%

% innerhalb von G4

1.4%

2.0%

1.7%

% der Gesamtzahl

.7%

1.0%

1.7%

2

Anzahl

41

129

170

% innerhalb von Funktion

24.1%

75.9%

100.0%

% innerhalb von G4

7.2%

21.6%

14.5%

% der Gesamtzahl

3.5%

11.0%

14.5%

3

Anzahl

524

456

980

% innerhalb von Funktion

53.5%

46.5%

100.0%

% innerhalb von G4

91.4%

76.4%

83.8%

% der Gesamtzahl

44.8%

39.0%

83.8%

Gesamt

Anzahl

573

597

1170

% innerhalb von Funktion

49.0%

51.0%

100.0%

% innerhalb von G4

100.0%

100.0%

100.0%

% der Gesamtzahl

49.0%

51.0%

100.0%



The chi-square-test gives a significant result:

Chi-Quadrat-Tests



Wert

df

Asymptotische Signifikanz (2-seitig)

Chi-Quadrat nach Pearson

50.600a

2

.000

Likelihood-Quotient

52.878

2

.000

Zusammenhang linear-mit-linear

39.583

1

.000

Anzahl der gültigen Fälle

1170





a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale erwartete Häufigkeit ist 9.79.


If I’m right, chi-square test is a sort of omnibus-test. How can I perform with PASW 18 an a posteriori test in order to compare the relative amount of Yes within the three categories of the variable “function” ? Or, in other words: which one are significant: 40:60, 24:76 or/and 54:46?

I appreciate any help.
Tom

=====================
To manage your subscription to SPSSX-L, send a message to
LISTSERV@LISTSERV.UGA.EDU (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
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--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

PLEASE NOTE THE FOLLOWING: 
1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above.
2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/).
Tom
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AW: Re: Chi Square test and a posteriori multiple comparison

Tom
In reply to this post by Tom
AW: Re: Chi Square test and a posteriori multiple comparison

Ok - a lot of informations, thank you all!

So then, I did what Martin suggested (splitting the file), which gave me:

Funktion        G4
1       Chi-Quadrat     .800a
        df      1
        Asymptotische Signifikanz       .371
        Exakte Signifikanz      .503
        Punkt-Wahrscheinlichkeit        .240
2       Chi-Quadrat     45.553b
        df      1
        Asymptotische Signifikanz       .000
        Exakte Signifikanz      .000
        Punkt-Wahrscheinlichkeit        .000
3       Chi-Quadrat     4.718c
        df      1
        Asymptotische Signifikanz       .030
        Exakte Signifikanz      .032
        Punkt-Wahrscheinlichkeit        .005
a. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die kleinste erwartete Zellenhäufigkeit ist 10.0.
b. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die kleinste erwartete Zellenhäufigkeit ist 85.0.
c. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die kleinste erwartete Zellenhäufigkeit ist 490.0.

This means, if I’m right, that the proportions of function 2 and 3 are significantly different from equal (50:50), which is just a comparison within the category/group, not of the PROPORTION of the Yes/No between the groups. Or: does these results let me say, that group/ function 1 (with 60% Yes) does not answer significantly less “Yes” than group/ function 2 (with 75%)? I suppose, rather no…

If I got Bruce right, the Maximum Likelihood chi-square would be a possibility. Along with his paper I produced this: First, all the three functions, then, second, a comparison of function 1 and 2 only:
L2          Observed              E     ln(0/E) O*ln(O/E)
1yes    8       10      -0.22314355     -1.78514841
2       129     86      0.40546511      52.3049989
3       456     497     -0.08609722     -39.2603308
1no     12      10      0.18232156      2.18785868
2       41      84      -0.71724473     -29.407034
3       524     483     0.08147503      42.6929161
                                        26.7332605
                        L2              53.466521
                        df=2            highly sign.
Which means, that the three groups differ significantly from each other.


        O       E       ln(O/E) O*ln(O/E)
1 yes   8       14      -0.55961579     -4.4769263
2 yes   129     123     0.04762805      6.14401832
1 no    12      6       0.69314718      8.31776617
2 no    41      47      -0.13657554     -5.59959694
                                        4.38526125
                        L2              8.7705225
                        df=1            **


Which means, that function 1 and 2 are signficantly different answering “Yes”.              

Am I right, that this second solution gives me the desired comparison for two of the three independent groups, which the first solution doesn’t?
Is the expected frequency (funktion 1 no) of only 6 a problem?
And: How can I do this with PASW/SPSS?



[hidden email]
http://www.phbern.ch/weiterbildung
-----Ursprüngliche Nachricht-----
Von: SPSSX(r) Discussion [[hidden email]] Im Auftrag von Bruce Weaver
Gesendet: Freitag, 20. August 2010 21:21
An: [hidden email]
Betreff: Re: Chi Square test and a posteriori multiple comparison

My notes on categorical data
(http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf, section 2.8)
show how to partition the overall likelihood ratio chi-square into
orthogonal components.  I've not checked, but because I'm using the
likelihood ratio chi-square, I expect the method shown in my notes will give
identical results to two orthogonal contrasts carried out via logistic
regression, as proposed by Joe.

By the way, the example in the notes also uses a 3x2 table, so it should be
fairly easy to adapt to Thomas's problem.

HTH.



Burleson,Joseph A. wrote:
>
> Thomas:
>
> I would do another procedure rather than the one Hector suggests. The
> reason is that the data are di- and tri-chotomous, and t-tests require
> that the raw data be continuous for the test variable.
>
> Instead: run a logistic regression with the Yes/No as the dependent,
> dichotomous outcome variable. Put in one independent variable, the
> tri-chotomous (1,2,3) variable.
>
> If you have some a priori hypotheses as to which of the three rows are
> different, consider using them instead. The a priori comparisons number k
> -1 = 3 - 1 = 2, so that you are only allowed 2 of the 3 comparisons you
> mentioned. This allows for orthogonal comparisons, with no need to adjust
> the p-level such as in the 3 post-hoc tests you suggested.
>
> There are two basic patterns as to how to compare the 3 cells this way:
> A. Compare the hypothesized most different cell to the other two combined,
> then contrast the two that were first combined against each other.
> B. Pick a "control" cell and do direct comparisons of it with EACH of the
> other 2, respectively.
>
> Procedure A uses all the data on the first test, but is robust on that
> first test.
> Procedure B uses 2/3 of the data on each test, but is more specific.
>
> the trick is judging whether you want more robustness or more specificity.
>
> The names of the orthogonal a priori test is logistic regression are the
> same as in general linear models. Note that some of them are NOT
> orthogonal.
>
> Joe Burleson
>
> ________________________________
> From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Balmer
> Thomas [[hidden email]]
> Sent: 20 August 2010 10:56
> To: [hidden email]
> Subject: Chi Square test and a posteriori multiple comparison
>
> Hello
>
> I got a 6x3 table with this descriptive result:
> Funktion * G4 Kreuztabelle
>
>
>
> G4
>
> Gesamt
>
> No
>
> Yes
>
> Funktion
>
> 1
>
> Anzahl
>
> 8
>
> 12
>
> 20
>
> % innerhalb von Funktion
>
> 40.0%
>
> 60.0%
>
> 100.0%
>
> % innerhalb von G4
>
> 1.4%
>
> 2.0%
>
> 1.7%
>
> % der Gesamtzahl
>
> .7%
>
> 1.0%
>
> 1.7%
>
> 2
>
> Anzahl
>
> 41
>
> 129
>
> 170
>
> % innerhalb von Funktion
>
> 24.1%
>
> 75.9%
>
> 100.0%
>
> % innerhalb von G4
>
> 7.2%
>
> 21.6%
>
> 14.5%
>
> % der Gesamtzahl
>
> 3.5%
>
> 11.0%
>
> 14.5%
>
> 3
>
> Anzahl
>
> 524
>
> 456
>
> 980
>
> % innerhalb von Funktion
>
> 53.5%
>
> 46.5%
>
> 100.0%
>
> % innerhalb von G4
>
> 91.4%
>
> 76.4%
>
> 83.8%
>
> % der Gesamtzahl
>
> 44.8%
>
> 39.0%
>
> 83.8%
>
> Gesamt
>
> Anzahl
>
> 573
>
> 597
>
> 1170
>
> % innerhalb von Funktion
>
> 49.0%
>
> 51.0%
>
> 100.0%
>
> % innerhalb von G4
>
> 100.0%
>
> 100.0%
>
> 100.0%
>
> % der Gesamtzahl
>
> 49.0%
>
> 51.0%
>
> 100.0%
>
>
>
> The chi-square-test gives a significant result:
>
> Chi-Quadrat-Tests
>
>
>
> Wert
>
> df
>
> Asymptotische Signifikanz (2-seitig)
>
> Chi-Quadrat nach Pearson
>
> 50.600a
>
> 2
>
> .000
>
> Likelihood-Quotient
>
> 52.878
>
> 2
>
> .000
>
> Zusammenhang linear-mit-linear
>
> 39.583
>
> 1
>
> .000
>
> Anzahl der gültigen Fälle
>
> 1170
>
>
>
>
>
> a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale
> erwartete Häufigkeit ist 9.79.
>
>
> If I’m right, chi-square test is a sort of omnibus-test. How can I perform
> with PASW 18 an a posteriori test in order to compare the relative amount
> of Yes within the three categories of the variable “function” ? Or, in
> other words: which one are significant: 40:60, 24:76 or/and 54:46?
>
> I appreciate any help.
> Tom
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>


-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
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Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
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Re: AW: Re: Chi Square test and a posteriori multiple comparison

Bruce Weaver
Administrator
It's still not clear to me what question, or questions, you are trying to answer.  

The overall chi-square test is statistically significant.  This tells you that the row and column variables are not independent of each other -- i.e., the proportion of Yes's is not the same at each of the 3 levels.  

The SPLIT FILE analysis you show asks if the proportion of Yes's is significantly different from .5 at each level of the other variable, but it makes no comparisons across the 3 levels.

The orthogonal contrast method picks two rows from the table, and asks if the proportion of Yes's differs across those two rows.  Then it collapses those two rows together, and asks if the proportion of Yes's in those two rows combined differs from the proportion of Yes's in the 3rd row.

If the overall chi-square test is of interest, it seems to me that the questions addressed by the orthogonal contrast method are probably more interesting than the SPLIT FILE questions.  

Finally, now that you've shown us the counts, it's possible to do the analyses using the WEIGHT command.  E.g.,

* Read in the data.

data list list / r c kount (3f5.0).
begin data
1 1 8
1 2 12
2 1 129
2 2 41
3 1 456
3 2 524
end data.

weight by kount.
crosstabs r by c / stat = chisq /cells = count row.

* The likelihood ratio chi-square for the 3x2 table = 53.152 .

* Row 2 is the one that looks a lot different from the other two.
* So for the orthogonal contrasts, I'd like to compare rows 3 and 1,
* and then 3 and 1 pooled vs 2.  

* Row 1 vs Row 3 .
temporary.
select if any(r,1,3). /* Omit row 2 .
crosstabs r by c / stat = chisq /cells = count row.

* Rows 1 & 3 pooled vs Row 2 .
temporary.
recode r (3=1). /* Temporarily recode 3 to 1.
crosstabs r by c / stat = chisq /cells = count row.

* Likelihood ratio chi-square for first table =    .339 .
* Likelihood ratio chi-square for second table = 52.813 .
* The sum of the two = 53.152, which is the value for
* the overall table.  So the likelihood ratio chi-square
* values for the two orthogonal components add up to the
* total, as they should do.

* The SPLIT FILE method, which IMO, is probably not what you want.

split file by r.
NPAR TESTS
  /CHISQUARE=c
  /EXPECTED=EQUAL
  /MISSING ANALYSIS.
split file off.

HTH.


Balmer Thomas wrote
Ok - a lot of informations, thank you all!

So then, I did what Martin suggested (splitting the file), which gave me:

Funktion        G4
1       Chi-Quadrat     .800a
        df      1
        Asymptotische Signifikanz       .371
        Exakte Signifikanz      .503
        Punkt-Wahrscheinlichkeit        .240
2       Chi-Quadrat     45.553b
        df      1
        Asymptotische Signifikanz       .000
        Exakte Signifikanz      .000
        Punkt-Wahrscheinlichkeit        .000
3       Chi-Quadrat     4.718c
        df      1
        Asymptotische Signifikanz       .030
        Exakte Signifikanz      .032
        Punkt-Wahrscheinlichkeit        .005
a. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die kleinste erwartete Zellenhäufigkeit ist 10.0.
b. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die kleinste erwartete Zellenhäufigkeit ist 85.0.
c. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die kleinste erwartete Zellenhäufigkeit ist 490.0.

This means, if I’m right, that the proportions of function 2 and 3 are significantly different from equal (50:50), which is just a comparison within the category/group, not of the PROPORTION of the Yes/No between the groups. Or: does these results let me say, that group/ function 1 (with 60% Yes) does not answer significantly less “Yes” than group/ function 2 (with 75%)? I suppose, rather no…

If I got Bruce right, the Maximum Likelihood chi-square would be a possibility. Along with his paper I produced this: First, all the three functions, then, second, a comparison of function 1 and 2 only:
L2          Observed              E     ln(0/E) O*ln(O/E)
1yes    8       10      -0.22314355     -1.78514841
2       129     86      0.40546511      52.3049989
3       456     497     -0.08609722     -39.2603308
1no     12      10      0.18232156      2.18785868
2       41      84      -0.71724473     -29.407034
3       524     483     0.08147503      42.6929161
                                        26.7332605
                        L2              53.466521
                        df=2          highly sign.
Which means, that the three groups differ significantly from each other.


        O       E       ln(O/E) O*ln(O/E)
1 yes   8       14      -0.55961579     -4.4769263
2 yes   129     123     0.04762805      6.14401832
1 no    12      6       0.69314718      8.31776617
2 no    41      47      -0.13657554     -5.59959694
                                        4.38526125
                        L2              8.7705225
                        df=1          **


Which means, that function 1 and 2 are signficantly different answering “Yes”.              

Am I right, that this second solution gives me the desired comparison for two of the three independent groups, which the first solution doesn’t?
Is the expected frequency (funktion 1 no) of only 6 a problem?
And: How can I do this with PASW/SPSS?



thomas.balmer@phbern.ch
http://www.phbern.ch/weiterbildung
-----Ursprüngliche Nachricht-----
Von: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] Im Auftrag von Bruce Weaver
Gesendet: Freitag, 20. August 2010 21:21
An: SPSSX-L@LISTSERV.UGA.EDU
Betreff: Re: Chi Square test and a posteriori multiple comparison

My notes on categorical data
(http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf, section 2.8)
show how to partition the overall likelihood ratio chi-square into
orthogonal components.  I've not checked, but because I'm using the
likelihood ratio chi-square, I expect the method shown in my notes will give
identical results to two orthogonal contrasts carried out via logistic
regression, as proposed by Joe.

By the way, the example in the notes also uses a 3x2 table, so it should be
fairly easy to adapt to Thomas's problem.

HTH.



Burleson,Joseph A. wrote:
>
> Thomas:
>
> I would do another procedure rather than the one Hector suggests. The
> reason is that the data are di- and tri-chotomous, and t-tests require
> that the raw data be continuous for the test variable.
>
> Instead: run a logistic regression with the Yes/No as the dependent,
> dichotomous outcome variable. Put in one independent variable, the
> tri-chotomous (1,2,3) variable.
>
> If you have some a priori hypotheses as to which of the three rows are
> different, consider using them instead. The a priori comparisons number k
> -1 = 3 - 1 = 2, so that you are only allowed 2 of the 3 comparisons you
> mentioned. This allows for orthogonal comparisons, with no need to adjust
> the p-level such as in the 3 post-hoc tests you suggested.
>
> There are two basic patterns as to how to compare the 3 cells this way:
> A. Compare the hypothesized most different cell to the other two combined,
> then contrast the two that were first combined against each other.
> B. Pick a "control" cell and do direct comparisons of it with EACH of the
> other 2, respectively.
>
> Procedure A uses all the data on the first test, but is robust on that
> first test.
> Procedure B uses 2/3 of the data on each test, but is more specific.
>
> the trick is judging whether you want more robustness or more specificity.
>
> The names of the orthogonal a priori test is logistic regression are the
> same as in general linear models. Note that some of them are NOT
> orthogonal.
>
> Joe Burleson
>
> ________________________________
> From: SPSSX(r) Discussion [SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of Balmer
> Thomas [Thomas.Balmer@phbern.ch]
> Sent: 20 August 2010 10:56
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: Chi Square test and a posteriori multiple comparison
>
> Hello
>
> I got a 6x3 table with this descriptive result:
> Funktion * G4 Kreuztabelle
>
>
>
> G4
>
> Gesamt
>
> No
>
> Yes
>
> Funktion
>
> 1
>
> Anzahl
>
> 8
>
> 12
>
> 20
>
> % innerhalb von Funktion
>
> 40.0%
>
> 60.0%
>
> 100.0%
>
> % innerhalb von G4
>
> 1.4%
>
> 2.0%
>
> 1.7%
>
> % der Gesamtzahl
>
> .7%
>
> 1.0%
>
> 1.7%
>
> 2
>
> Anzahl
>
> 41
>
> 129
>
> 170
>
> % innerhalb von Funktion
>
> 24.1%
>
> 75.9%
>
> 100.0%
>
> % innerhalb von G4
>
> 7.2%
>
> 21.6%
>
> 14.5%
>
> % der Gesamtzahl
>
> 3.5%
>
> 11.0%
>
> 14.5%
>
> 3
>
> Anzahl
>
> 524
>
> 456
>
> 980
>
> % innerhalb von Funktion
>
> 53.5%
>
> 46.5%
>
> 100.0%
>
> % innerhalb von G4
>
> 91.4%
>
> 76.4%
>
> 83.8%
>
> % der Gesamtzahl
>
> 44.8%
>
> 39.0%
>
> 83.8%
>
> Gesamt
>
> Anzahl
>
> 573
>
> 597
>
> 1170
>
> % innerhalb von Funktion
>
> 49.0%
>
> 51.0%
>
> 100.0%
>
> % innerhalb von G4
>
> 100.0%
>
> 100.0%
>
> 100.0%
>
> % der Gesamtzahl
>
> 49.0%
>
> 51.0%
>
> 100.0%
>
>
>
> The chi-square-test gives a significant result:
>
> Chi-Quadrat-Tests
>
>
>
> Wert
>
> df
>
> Asymptotische Signifikanz (2-seitig)
>
> Chi-Quadrat nach Pearson
>
> 50.600a
>
> 2
>
> .000
>
> Likelihood-Quotient
>
> 52.878
>
> 2
>
> .000
>
> Zusammenhang linear-mit-linear
>
> 39.583
>
> 1
>
> .000
>
> Anzahl der gültigen Fälle
>
> 1170
>
>
>
>
>
> a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale
> erwartete Häufigkeit ist 9.79.
>
>
> If I’m right, chi-square test is a sort of omnibus-test. How can I perform
> with PASW 18 an a posteriori test in order to compare the relative amount
> of Yes within the three categories of the variable “function” ? Or, in
> other words: which one are significant: 40:60, 24:76 or/and 54:46?
>
> I appreciate any help.
> Tom
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> LISTSERV@LISTSERV.UGA.EDU (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>


-----
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Kenny-s-Condition-A-2-tp2641949p2642709.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
To manage your subscription to SPSSX-L, send a message to
LISTSERV@LISTSERV.UGA.EDU (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

PLEASE NOTE THE FOLLOWING: 
1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above.
2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/).
Tom
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AW: Re: AW: Re: Chi Square test and a posteriori multiple comparison

Tom
Thanks, Bruce, yes, these orthogonal contrast were what I've been looking for.

-----Ursprüngliche Nachricht-----
Von: SPSSX(r) Discussion [mailto:[hidden email]] Im Auftrag von Bruce Weaver
Gesendet: Montag, 23. August 2010 23:58
An: [hidden email]
Betreff: Re: AW: Re: Chi Square test and a posteriori multiple comparison

It's still not clear to me what question, or questions, you are trying to
answer.

The overall chi-square test is statistically significant.  This tells you
that the row and column variables are not independent of each other -- i.e.,
the proportion of Yes's is not the same at each of the 3 levels.

The SPLIT FILE analysis you show asks if the proportion of Yes's is
significantly different from .5 at each level of the other variable, but it
makes no comparisons across the 3 levels.

The orthogonal contrast method picks two rows from the table, and asks if
the proportion of Yes's differs across those two rows.  Then it collapses
those two rows together, and asks if the proportion of Yes's in those two
rows combined differs from the proportion of Yes's in the 3rd row.

If the overall chi-square test is of interest, it seems to me that the
questions addressed by the orthogonal contrast method are probably more
interesting than the SPLIT FILE questions.

Finally, now that you've shown us the counts, it's possible to do the
analyses using the WEIGHT command.  E.g.,

* Read in the data.

data list list / r c kount (3f5.0).
begin data
1 1 8
1 2 12
2 1 129
2 2 41
3 1 456
3 2 524
end data.

weight by kount.
crosstabs r by c / stat = chisq /cells = count row.

* The likelihood ratio chi-square for the 3x2 table = 53.152 .

* Row 2 is the one that looks a lot different from the other two.
* So for the orthogonal contrasts, I'd like to compare rows 3 and 1,
* and then 3 and 1 pooled vs 2.

* Row 1 vs Row 3 .
temporary.
select if any(r,1,3). /* Omit row 2 .
crosstabs r by c / stat = chisq /cells = count row.

* Rows 1 & 3 pooled vs Row 2 .
temporary.
recode r (3=1). /* Temporarily recode 3 to 1.
crosstabs r by c / stat = chisq /cells = count row.

* Likelihood ratio chi-square for first table =    .339 .
* Likelihood ratio chi-square for second table = 52.813 .
* The sum of the two = 53.152, which is the value for
* the overall table.  So the likelihood ratio chi-square
* values for the two orthogonal components add up to the
* total, as they should do.

* The SPLIT FILE method, which IMO, is probably not what you want.

split file by r.
NPAR TESTS
  /CHISQUARE=c
  /EXPECTED=EQUAL
  /MISSING ANALYSIS.
split file off.

HTH.



Balmer Thomas wrote:

>
> Ok - a lot of informations, thank you all!
>
> So then, I did what Martin suggested (splitting the file), which gave me:
>
> Funktion        G4
> 1       Chi-Quadrat     .800a
>         df      1
>         Asymptotische Signifikanz       .371
>         Exakte Signifikanz      .503
>         Punkt-Wahrscheinlichkeit        .240
> 2       Chi-Quadrat     45.553b
>         df      1
>         Asymptotische Signifikanz       .000
>         Exakte Signifikanz      .000
>         Punkt-Wahrscheinlichkeit        .000
> 3       Chi-Quadrat     4.718c
>         df      1
>         Asymptotische Signifikanz       .030
>         Exakte Signifikanz      .032
>         Punkt-Wahrscheinlichkeit        .005
> a. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die
> kleinste erwartete Zellenhäufigkeit ist 10.0.
> b. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die
> kleinste erwartete Zellenhäufigkeit ist 85.0.
> c. Bei 0 Zellen (.0%) werden weniger als 5 Häufigkeiten erwartet. Die
> kleinste erwartete Zellenhäufigkeit ist 490.0.
>
> This means, if I’m right, that the proportions of function 2 and 3 are
> significantly different from equal (50:50), which is just a comparison
> within the category/group, not of the PROPORTION of the Yes/No between the
> groups. Or: does these results let me say, that group/ function 1 (with
> 60% Yes) does not answer significantly less “Yes” than group/ function 2
> (with 75%)? I suppose, rather no…
>
> If I got Bruce right, the Maximum Likelihood chi-square would be a
> possibility. Along with his paper I produced this: First, all the three
> functions, then, second, a comparison of function 1 and 2 only:
> L2          Observed              E     ln(0/E) O*ln(O/E)
> 1yes    8       10      -0.22314355     -1.78514841
> 2       129     86      0.40546511      52.3049989
> 3       456     497     -0.08609722     -39.2603308
> 1no     12      10      0.18232156      2.18785868
> 2       41      84      -0.71724473     -29.407034
> 3       524     483     0.08147503      42.6929161
>                                         26.7332605
>                         L2              53.466521
>                         df=2          highly sign.
> Which means, that the three groups differ significantly from each other.
>
>
>         O       E       ln(O/E) O*ln(O/E)
> 1 yes   8       14      -0.55961579     -4.4769263
> 2 yes   129     123     0.04762805      6.14401832
> 1 no    12      6       0.69314718      8.31776617
> 2 no    41      47      -0.13657554     -5.59959694
>                                         4.38526125
>                         L2              8.7705225
>                         df=1          **
>
>
> Which means, that function 1 and 2 are signficantly different answering
> “Yes”.
>
> Am I right, that this second solution gives me the desired comparison for
> two of the three independent groups, which the first solution doesn’t?
> Is the expected frequency (funktion 1 no) of only 6 a problem?
> And: How can I do this with PASW/SPSS?
>
>
>
> [hidden email]
> http://www.phbern.ch/weiterbildung
> -----Ursprüngliche Nachricht-----
> Von: SPSSX(r) Discussion [mailto:[hidden email]] Im Auftrag von
> Bruce Weaver
> Gesendet: Freitag, 20. August 2010 21:21
> An: [hidden email]
> Betreff: Re: Chi Square test and a posteriori multiple comparison
>
> My notes on categorical data
> (http://www.angelfire.com/wv/bwhomedir/notes/categorical.pdf, section 2.8)
> show how to partition the overall likelihood ratio chi-square into
> orthogonal components.  I've not checked, but because I'm using the
> likelihood ratio chi-square, I expect the method shown in my notes will
> give
> identical results to two orthogonal contrasts carried out via logistic
> regression, as proposed by Joe.
>
> By the way, the example in the notes also uses a 3x2 table, so it should
> be
> fairly easy to adapt to Thomas's problem.
>
> HTH.
>
>
>
> Burleson,Joseph A. wrote:
>>
>> Thomas:
>>
>> I would do another procedure rather than the one Hector suggests. The
>> reason is that the data are di- and tri-chotomous, and t-tests require
>> that the raw data be continuous for the test variable.
>>
>> Instead: run a logistic regression with the Yes/No as the dependent,
>> dichotomous outcome variable. Put in one independent variable, the
>> tri-chotomous (1,2,3) variable.
>>
>> If you have some a priori hypotheses as to which of the three rows are
>> different, consider using them instead. The a priori comparisons number k
>> -1 = 3 - 1 = 2, so that you are only allowed 2 of the 3 comparisons you
>> mentioned. This allows for orthogonal comparisons, with no need to adjust
>> the p-level such as in the 3 post-hoc tests you suggested.
>>
>> There are two basic patterns as to how to compare the 3 cells this way:
>> A. Compare the hypothesized most different cell to the other two
>> combined,
>> then contrast the two that were first combined against each other.
>> B. Pick a "control" cell and do direct comparisons of it with EACH of the
>> other 2, respectively.
>>
>> Procedure A uses all the data on the first test, but is robust on that
>> first test.
>> Procedure B uses 2/3 of the data on each test, but is more specific.
>>
>> the trick is judging whether you want more robustness or more
>> specificity.
>>
>> The names of the orthogonal a priori test is logistic regression are the
>> same as in general linear models. Note that some of them are NOT
>> orthogonal.
>>
>> Joe Burleson
>>
>> ________________________________
>> From: SPSSX(r) Discussion [[hidden email]] On Behalf Of Balmer
>> Thomas [[hidden email]]
>> Sent: 20 August 2010 10:56
>> To: [hidden email]
>> Subject: Chi Square test and a posteriori multiple comparison
>>
>> Hello
>>
>> I got a 6x3 table with this descriptive result:
>> Funktion * G4 Kreuztabelle
>>
>>
>>
>> G4
>>
>> Gesamt
>>
>> No
>>
>> Yes
>>
>> Funktion
>>
>> 1
>>
>> Anzahl
>>
>> 8
>>
>> 12
>>
>> 20
>>
>> % innerhalb von Funktion
>>
>> 40.0%
>>
>> 60.0%
>>
>> 100.0%
>>
>> % innerhalb von G4
>>
>> 1.4%
>>
>> 2.0%
>>
>> 1.7%
>>
>> % der Gesamtzahl
>>
>> .7%
>>
>> 1.0%
>>
>> 1.7%
>>
>> 2
>>
>> Anzahl
>>
>> 41
>>
>> 129
>>
>> 170
>>
>> % innerhalb von Funktion
>>
>> 24.1%
>>
>> 75.9%
>>
>> 100.0%
>>
>> % innerhalb von G4
>>
>> 7.2%
>>
>> 21.6%
>>
>> 14.5%
>>
>> % der Gesamtzahl
>>
>> 3.5%
>>
>> 11.0%
>>
>> 14.5%
>>
>> 3
>>
>> Anzahl
>>
>> 524
>>
>> 456
>>
>> 980
>>
>> % innerhalb von Funktion
>>
>> 53.5%
>>
>> 46.5%
>>
>> 100.0%
>>
>> % innerhalb von G4
>>
>> 91.4%
>>
>> 76.4%
>>
>> 83.8%
>>
>> % der Gesamtzahl
>>
>> 44.8%
>>
>> 39.0%
>>
>> 83.8%
>>
>> Gesamt
>>
>> Anzahl
>>
>> 573
>>
>> 597
>>
>> 1170
>>
>> % innerhalb von Funktion
>>
>> 49.0%
>>
>> 51.0%
>>
>> 100.0%
>>
>> % innerhalb von G4
>>
>> 100.0%
>>
>> 100.0%
>>
>> 100.0%
>>
>> % der Gesamtzahl
>>
>> 49.0%
>>
>> 51.0%
>>
>> 100.0%
>>
>>
>>
>> The chi-square-test gives a significant result:
>>
>> Chi-Quadrat-Tests
>>
>>
>>
>> Wert
>>
>> df
>>
>> Asymptotische Signifikanz (2-seitig)
>>
>> Chi-Quadrat nach Pearson
>>
>> 50.600a
>>
>> 2
>>
>> .000
>>
>> Likelihood-Quotient
>>
>> 52.878
>>
>> 2
>>
>> .000
>>
>> Zusammenhang linear-mit-linear
>>
>> 39.583
>>
>> 1
>>
>> .000
>>
>> Anzahl der gültigen Fälle
>>
>> 1170
>>
>>
>>
>>
>>
>> a. 0 Zellen (.0%) haben eine erwartete Häufigkeit kleiner 5. Die minimale
>> erwartete Häufigkeit ist 9.79.
>>
>>
>> If I’m right, chi-square test is a sort of omnibus-test. How can I
>> perform
>> with PASW 18 an a posteriori test in order to compare the relative amount
>> of Yes within the three categories of the variable “function” ? Or, in
>> other words: which one are significant: 40:60, 24:76 or/and 54:46?
>>
>> I appreciate any help.
>> Tom
>>
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>
>
> -----
> --
> Bruce Weaver
> [hidden email]
> http://sites.google.com/a/lakeheadu.ca/bweaver/
>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
>
> --
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>
>


-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
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