ordinal data question

[Angela Shartrand]

We have a survey (with ~100 items) that asks students to indicate
their level of familiarity with various terms and concepts. It is on
an 5 point ordinal scale - NONE to VERY HIGH. The survey was given at
the beginning and end of a semester or academic year, so we have pre
and post test data (unmatched, but drawn from the same population at
10 different schools). Based on the pretest data, the survey has high
reliability (~.962 Cronbach's Alpha).

I have two questions:

A colleague has conducted a principal components factor analysis but
SPSS warns this is not appropriate for ordinal data (I know it's
common to treat this type of scale as interval, though). I do know
there is another type of factor analysis for categorical data but I
don't think I have that option (I have SPSS 13 Base for Mac)

What is the best way to graphically represent comparisons between the
pre and post test results in this situation? I have seen means
computed and then pre and post results can be presented in bar
graphs, but again, this is somewhat controversial for ordinal data.
To avoid this, I tried creating clustered pie charts which illustrate
how the response patterns change from pre to post (an increase in %
of VERY HIGH responses and a decline in NONE responses for example).
This works nicely for individual items, obviously with 100+ of them
it becomes very tedious and I would like to summarize results by
factor (groups of similar items) in some way.

What is the best way to aggregate responses to several items given
the ordinal scale? What is an easy way to graphically present changes
from pre to post by factor (We have 5 sections of the survey, and the
factors in each range from 1 to 4 with a grand total of 12, so
obviously it would be nice to present 12 figures instead of 100!

Thanks for any help you can provide.

Angela

[Kooij, A.J. van der]

I'm from the Data Theory Group at Leiden University and we have developed the other "type of factor analysis for categorical data " you mention (CATPCA).
I have often compared results from interval and ordinal analyses; if all variables are Likert-type and reliability is high, as in your case, there is usually very little difference between analyzing as interval and analyzing as oridinal. So, I would use the factor scores for graphical representations.
 
CATPCA is indeed not in Base, but in the CATEGORIES package. I would recommend to obtain CATEGORIES if possible, because CATPCA has some analysis options (that are not available in standard PCA) that can be used for data measured at multiple time points, resulting in very nice graphical representations of the effect of time (CATPA can also perform analysis at interval level).
 
Regards,
Anita
 
________________________________

From: SPSSX(r) Discussion on behalf of Angela Shartrand
Sent: Thu 21/06/2007 15:48
To: [hidden email]
Subject: ordinal data question



We have a survey (with ~100 items) that asks students to indicate
their level of familiarity with various terms and concepts. It is on
an 5 point ordinal scale - NONE to VERY HIGH. The survey was given at
the beginning and end of a semester or academic year, so we have pre
and post test data (unmatched, but drawn from the same population at
10 different schools). Based on the pretest data, the survey has high
reliability (~.962 Cronbach's Alpha).

I have two questions:

A colleague has conducted a principal components factor analysis but
SPSS warns this is not appropriate for ordinal data (I know it's
common to treat this type of scale as interval, though). I do know
there is another type of factor analysis for categorical data but I
don't think I have that option (I have SPSS 13 Base for Mac)

What is the best way to graphically represent comparisons between the
pre and post test results in this situation? I have seen means
computed and then pre and post results can be presented in bar
graphs, but again, this is somewhat controversial for ordinal data.
To avoid this, I tried creating clustered pie charts which illustrate
how the response patterns change from pre to post (an increase in %
of VERY HIGH responses and a decline in NONE responses for example).
This works nicely for individual items, obviously with 100+ of them
it becomes very tedious and I would like to summarize results by
factor (groups of similar items) in some way.

What is the best way to aggregate responses to several items given
the ordinal scale? What is an easy way to graphically present changes
from pre to post by factor (We have 5 sections of the survey, and the
factors in each range from 1 to 4 with a grand total of 12, so
obviously it would be nice to present 12 figures instead of 100!

Thanks for any help you can provide.

Angela



**********************************************************************
This email and any files transmitted with it are confidential and
intended solely for the use of the individual or entity to whom they
are addressed. If you have received this email in error please notify
the system manager.
**********************************************************************

[Robert Marshall-7]

Hi Angela,

You will get some more responses, so you can compare them, as I am not the most expert on this list.    In my Ph.D. studies, I ran accross the Chi Square statistic that may work for you as a way to examine relationships between categorical variables.  Essentially, that is what you have, I think, with your scale.  It is not in the Likert format for continuous data.  You may want to check that out.   Also, I think your idea of the bar charts for ordinal data was OK.

Compare my answers with others, to be sure.

Robert

-------------- Original message --------------
From: Angela Shartrand <[hidden email]>

> We have a survey (with ~100 items) that asks students to indicate
> their level of familiarity with various terms and concepts. It is on
> an 5 point ordinal scale - NONE to VERY HIGH. The survey was given at
> the beginning and end of a semester or academic year, so we have pre
> and post test data (unmatched, but drawn from the same population at
> 10 different schools). Based on the pretest data, the survey has high
> reliability (~.962 Cronbach's Alpha).
>
> I have two questions:
>
> A colleague has conducted a principal components factor analysis but
> SPSS warns this is not appropriate for ordinal data (I know it's
> common to treat this type of scale as interval, though). I do know
> there is another type of factor analysis for categorical data but I
> don't think I have that option (I have SPSS 13 Base for Mac)
>
> What is the best way to graphically represent comparisons between the
> pre and post test results in this situation? I have seen means
> computed and then pre and post results can be presented in bar
> graphs, but again, this is somewhat controversial for ordinal data.
> To avoid this, I tried creating clustered pie charts which illustrate
> how the response patterns change from pre to post (an increase in %
> of VERY HIGH responses and a decline in NONE responses for example).
> This works nicely for individual items, obviously with 100+ of them
> it becomes very tedious and I would like to summarize results by
> factor (groups of similar items) in some way.
>
> What is the best way to aggregate responses to several items given
> the ordinal scale? What is an easy way to graphically present changes
> from pre to post by factor (We have 5 sections of the survey, and the
> factors in each range from 1 to 4 with a grand total of 12, so
> obviously it would be nice to present 12 figures instead of 100!
>
> Thanks for any help you can provide.
>
> Angela