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Date:         Mon, 10 Jul 2006 11:44:17 -0400
Reply-To:     "Luo, Peter" <>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Luo, Peter" <>
Subject:      comparison question
Comments: To: Lisa Stickney <>
Content-Type: text/plain

Thank Lisa for adding the subject line to my original message.

I totally agree with all the comments. However, we didn't have access to the raw data, so have to work with the aggregated numbers.

Let me re-phrase the situation:

A survey was conducted among 150 randomly selected customers; each customer was invited to express his/her opinion on 15 brands. For every brand, the option was: 1-'more likely', 2-'the same', 3-'less likely'. Naturally, not every customer answered all 15 questions.

The data come back and was tabulated; now our researcher has the report in front of her. What she saw on the report is: for every brand, the percent of customers selected 1, percent selected 2, percent 3, and the number of answers.

Then she 1. calculated a 'net gain' on each brand (net gain= % more likely - % less likely), ignoring % the same 2. calculated a weighted average net gain across all 15 brands

Her question: when comparing the brand specific net gain against the average net gain, can I tell which brand's net gain is significantly from the average?

Here is what I was thinking to solve her request

1. since brand specific 'net gain' is the difference between two proportions, I can calculate the standard deviation of that difference

2. assume the average net gain (cross 15 brands) is fixed

3. conduct a z or t test on the difference between the brand specific net gain and the average net gain, using mean comparison rather than proportion comparison since 'net gain' could be negative. The test will need the standard deviation derived from the 1st step.

Need comments and suggestions.

-----Original Message----- From: Lisa Stickney [] Sent: Thursday, July 06, 2006 12:02 PM To: Luo, Peter Cc: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: comparision question

Hi Peter,

I can understand why you're puzzled. Before I try to answer your question, I have a few of my own.

> For each brand she deducted a 'net' gain, which is the balance of the % of > consumers who answered "more likely' and % who answered 'less likely.' > It's > a 3 choice question: 1-less likely, 2-the same, 3-more likely. >

I'm not entirely sure what your friend did here:

Did she compute a net gain (% more likely - % less likely) or did she deduct

the "net gain" from something else? If so, what?

Assuming the former (% more likely - % less likely), the question becomes, why? I'm not sure what the point of this is. If you do this, you omit all repsondents who selected #2 (the same) from your data. What is she trying to find out about the brands? Why not just look at the average response for

the question?

> > > Then she took the average of the net gains cross all 15 brands. >

Again, why? Are all 15 brands releated in some way? Is there some theoretical reason for averaging the difference of the extremes in repsondent scores for 15 different brands? More information would help here.

> > > Her question is: to what extent one can determine if a particular brand > was > significantly more (or less) favored by these consumers, say if brand A > got > a net gain of +10%, but the average net gain is +15%, can I be confident > to > say the brand A is less favored? > > the number of consumers who answered each brand varied from 35 to 74.

I don't think so (your concern is valid). Since Brand A is in the average, this muddies already murky waters. Again, I'm not sure what the point is or

what would be gained by performing a comparison in this manner.

It's my understanding that in general & if possible, it's best to leave data

in it's original form. Not only are do you deal with the participants' actual responses, but it's much easier to interpret.

If your friend wants to see if there are significant differences between consumer's brand perceptions, then run an ANOVA on the original data. Plus,

if she did that she'd retain all participants' repsonses and not not just those who selected an extreme.

However, that said, the size of this sample is a major concern. I seriously

doubt there's enough power to pick up anything but the largest of differences (e.g. I strongly agree w/ 'I prefer to eat in a 5 star restaurant than a cafeteria'). Is there any way your friend can collect more data? Also, if she's going to recollect the data, she might want to consider expanding her response set to 5 or 6 possible answers (e.g. 1-much less likely, 2-less likely 3-the same, 4-more likely, 5-much more likely).

Good luck to your friend, and I hope this helps.

Best, Lisa

P.S. When e-mailing this list, it's generally good to include a brief description in the subject line -- I took the liberty of filling one in for you.

Lisa T. Stickney Ph.D. Candidate The Fox School of Business and Management Temple University

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