How to interpret total % of cases in multiple response

[Jaime-27]

Hi: How do I interpret the total percentage of cases in a multiple
response output? For example, in  the table below, what can I say about
344.8%?

$SenAC Frequencies
    Responses Percent of Cases
  N Percent
 SAC1 21 10.5% 36.2%
 SAC2 16 8.0% 27.6%
 SAC3 25 12.5% 43.1%
 SAC4 49 24.5% 84.5%
 SAC5 39 19.5% 67.2%
 SAC6 8 4.0% 13.8%
 SAC7 16 8.0% 27.6%
 SAC8 22 11.0% 37.9%
 SAC9 4 2.0% 6.9%
Total  200 100.0% 344.8%
a Dichotomy group tabulated at value 1.

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[ViAnn Beadle]

The base is the number of cases, the numerator is the number of responses of
1 to items in the dichotomy group. So, the value 1 occurred on average 3.44
per case. A case is a line of data.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Jaime
Sent: Wednesday, October 22, 2008 1:12 PM
To: [hidden email]
Subject: How to interpret total % of cases in multiple response

Hi: How do I interpret the total percentage of cases in a multiple
response output? For example, in  the table below, what can I say about
344.8%?

$SenAC Frequencies
    Responses Percent of Cases
  N Percent
 SAC1 21 10.5% 36.2%
 SAC2 16 8.0% 27.6%
 SAC3 25 12.5% 43.1%
 SAC4 49 24.5% 84.5%
 SAC5 39 19.5% 67.2%
 SAC6 8 4.0% 13.8%
 SAC7 16 8.0% 27.6%
 SAC8 22 11.0% 37.9%
 SAC9 4 2.0% 6.9%
Total  200 100.0% 344.8%
a Dichotomy group tabulated at value 1.

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[Hector Maletta]

Responses can be divided by the total number of responses, or by the total
number of cases, yielding percentage of responses or percentage of cases
respectively. The percentage of cases tells you the percent of people giving
a particular response. The "total" percentage of cases tells you the percent
of people giving SOME or ANY (valid) response. The latter is often of no
use, except to indicate the average number of responses per 100 respondents.

Therefore, when each individual may give several responses, the "total"
percentage of cases may be above 100%. For instance, in your example
(difficult to interpret because of alignment and lack of information) a
total of 344% should indicate an average of 3.44 responses per individual
(or 344 per 100 individuals).



Hector



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Jaime
Sent: 22 October 2008 17:12
To: [hidden email]
Subject: How to interpret total % of cases in multiple response



Hi: How do I interpret the total percentage of cases in a multiple

response output? For example, in  the table below, what can I say about

344.8%?



$SenAC Frequencies

    Responses Percent of Cases

  N Percent

 SAC1 21 10.5% 36.2%

 SAC2 16 8.0% 27.6%

 SAC3 25 12.5% 43.1%

 SAC4 49 24.5% 84.5%

 SAC5 39 19.5% 67.2%

 SAC6 8 4.0% 13.8%

 SAC7 16 8.0% 27.6%

 SAC8 22 11.0% 37.9%

 SAC9 4 2.0% 6.9%

Total  200 100.0% 344.8%

a Dichotomy group tabulated at value 1.



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[Bob Schacht-3]

At 04:23 AM 10/23/2008, Hector Maletta wrote:
>Responses can be divided by the total number of responses, or by the total
>number of cases, yielding percentage of responses or percentage of cases
>respectively. The percentage of cases tells you the percent of people giving
>a particular response. The "total" percentage of cases tells you the percent
>of people giving SOME or ANY (valid) response. The latter is often of no
>use, except to indicate the average number of responses per 100
>respondents. . .

Hector's response is valuable because it reminds us that any percentage is
always relative.
It is always the percentage of ___________. Unless you can fill in the
blank, you don't know what you're dealing with.
And if you can fill in the blank, that should tell you what denominator to use.

It is commonplace in SPSS Crosstabs to include a percentage in each cell--
but you have to specify whether it is a row % (i.e., a % of the row total)
or a column % (i.e., % of column total). To fill in the blank above with
"row total" or "column total" is dangerous shorthand, however, because it
deflects attention away from what the row or column total represents.
Hector's language regarding "responses" or "cases" is better. Even better
would be to use another word for "case" which is more specific of your
particular context (is a case a customer? or a patient? or a voter?) Using
the more specific language will give the "percentage" more meaning.

In polling data, if a Gallup poll reported that 52% of cases favor Obama,
and 42% of cases favor McCain, you would immediately want to know what a
"case" represents, wouldn't you? Does it represent likely voters, or
registered voters? Does it refer to men, or to women, or both? Does it
include a stratified random sample of all age groups? Does it represent a
national cross-section, or a geographically limited region? Obviously, this
does not represent a multiple response situation, but the "percent" there
still has a referent, and Hector did a nice job of emphasizing that.

A more relevant example would be current national census information on
Race and Ethnicity, which is self-identified, and may refer to more than one
category. There, the relevant percentage is usually of "cases," i.e.
respondents. But since more than one "race" can now be specified, we need
an even more elaborate descriptor, such as "___% of respondents were
identified at least partly as Black" or some such, as well as an admonition
that the percentages may add up to more than 100 percent due to multiracial
responses. With multiple response items, the format for reporting results
must be more complex. Shortcuts generally result in misunderstandings.

Bob Schacht

Robert M. Schacht, Ph.D. <[hidden email]>
Pacific Basin Rehabilitation Research & Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814

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