Examples on how to calculate “mean of means”

Attached is a spec GENERATEMEANS.SPX that shows 3 different ways to calculate the “mean of means”.

When creating a “mean of means” there are three different approaches you can take to get that information. If there are missing values in the fields (blanks or DKs), then the 3 different approaches can produce different values for the “mean of means”.

Approach 1 is to create what we call a “grand” mean. A ‘grand’ mean adds up the sum of all the ratings and divides by the number of ratings.Survox in general recommends this approach as it weights each mean by the number of ratings that make up that mean.

In order to calculate this mean, you must use an Overlay structure with every item that will be used in the mean. Every overlay other than the first one will consist of only valid information for the category where the overall mean is being calculated. All the other caterories should be based on DUD keyword so no data will be used from those definitions.

Approach 2 is to created an Average rating for each respondent and then take the mean of that. This is the easist one to calculate, but it can be skewed if you have a lot of respondents who only answered a small number of items.

In order to calculate this mean, you can just use the AVG function on all the individual means.

Approach 3 is to add up the mean of each of the items and then divide by the number of items. This is the only one that you could check by looking at the printed output, however the result can be skewed by a single rating with a low number of mentions.

In order to calculate this mean, you must use table manipulation to add up the other means and divide by the number of means. This result cannot

be stat tested either. Create an extra row using the DUD option. Then in table manipulation add each row into your dud row and then divide that row by the number of means you added in.

To illustrate the difference in the 3 approaches assume you have 10 respondents who rated 3 brands as follow:

ID   1   2  3  SUM    AVG==   =   =  =  ===   ====01   3   4  5   12      402   -   2  2    4      203   -   4  -    4      404   4   4  4   12      405   -   3  -    3      306   1   5  1    7   2.3307   4   -  1    5    2.5 08   -   -  -    0      - 09   5   5  5   15      510   -   3  1    4      2Sum 17  30 19   66  28.83Mean 3.4  3.75  2.71  9.86Grand Mean =   Sum of all items/Number of items=         66        /  20=    3.30Use Average Rating =  sum of all avg for respondent / number of resondents=           28.83                /     9=  3.20

Notice that all 3 approaches give a different value. No conclusions can or should be drawn from the fact that the 3rd approach happens to be closer tothe 1st one than the 2nd one. Different numbers could be plugged in the above responses and all 3 numbers will change possibly in different directions.

The only thing you could say for sure is that if you raised a value they would all increase. The good thing about approach 1 is that if you raise any number by 1, the final mean would go to 3.35. However, the same cannot be said about either of the other two means. Depending uponwhich number you changed the value will change differently.

This setup assumes that there are 5 attributes in positions 4-8 of the data record. They are coded 1 to 5 and 9 is don’t know.

Tabset One is for approach 1, Tabset Two is for approach 2, and Tabset Three is for approach 3.

The Base row is printed in this example to clarify the differences in the bases for each question. The Base row may not make any sense for approach 3.

>PurgeSame>Prtfile GenerateMeans~In GenerateMeans.Dat,ASCII=80>Createdb GenerateMeans,Dup=Warn~Def'These settings can/should be the same regardless of the approachTabset=Global:Edit=: -Coltna Cwid=10 Swid=20 Sdec=2 -Vper }Stub_Preface=:[Sup] Total[Sup] No Answer }Col=: TotalBanner=: