single Likert scale question analysis

#1
I work for a holiday company which uses a 7 grade Likert scale questionnaire to collect feedback from our guests.
This is my first foray into statistics and my first post here (hope I'm in the right place!) although I find it fascinating, it's also confusing!
My company uses the formula below to calculate an average.
1 2 3 4 5 6 7
23 16 3 2 0 1 3 48
23 32 9 8 6 21 99
2.06
The top line is the scale 1 to 7, 1 being completely satisfied, 7 being completely unsatisfied.
The 2nd line contains the responses from our guests (23 are completely satisfied, 16 are very satisfied and so on)
The 3rd line is the formula 1 x 23, 2 x 16, 3 x 3, 4 x 2 and so on.
The end numbers in the 2nd and 3rd lines are the sum of each line.
The figure (which I take to be an "average") 2.06 is arrived at by dividing the sum of the bottom line (99) by the sum of the 2nd line (48).
My question is;
Is this a valid way of evaluating the responses? I don't understand why it's negatively weighted (1 response in the worst category equals 7 points in comparison to 1 in the best which gives only 1 point.
I would really appreciate any help on this, as I'm pretty sure my company is doing creative statistics!
Best regards
 

drewmac

New Member
#2
Hi

I'm not sure how useful it will be, but the following thread has some likert analysis related info; http://www.talkstats.com/showthread.php/17243-Likert-scale-statistical-analysis

You need to bear in mind that 1) the data isn't really interval i.e. equidistant. In other words, saying "really enjoyed my holiday" and "really really really enjoyed my holiday" isn't the same as e.g. a question like "how many cars do you own", "I own 3 cars...4 cars" etc. People can and often do treat likert as interval, but they lose something in their analysis.

The method the company uses seems odd to me.

This is a good link providing some useful likert analysis info too:

http://asq.org/quality-progress/2007/07/statistics/likert-scales-and-data-analyses.html

I think you would want to put this data into some form of vector and run a mann-whitney on it. Hopefully other uses will have a more detailed answer for you.
 
#3
Thanks for your reply.
I read up on Mann-Whitney in Wikipedia and, quite frankly, I have no idea where to begin! I am now in contact with the head of our statistics department who actually devised this system, but I would really appreciate some more outside input.
She can't seem to explain why the system is negatively weighted.
Surely a "1" should have the same positive value as a "7" has at the negative end of the scale. Her explanation was, that if we reversed the scale we would not arrive at a "high score", but I want to understand why it isn't simply neutrally measured. Meaning 10 x "1" responses = "10" and 10 x "7" responses = 10 (not 70).
Also, is it valid to even create an "average" score given that the intervals can't be precisely measured?
Thanks for any help.