Continuous Variable, Incremental Scale Mid-points

#1
Hi. First posting here, apologies for the beginner’s question.
I am using data that measures a continuous variable (how anxious did you feel yesterday) on an incremental (0 to 10) scale. Each scale increment records a range of anxiety feelings. For example, anxiety = 3 responses record levels of anxiety feelings between 2.5 and 3.5, assuming respondents’ use of the scale is perfectly precise.
I know from the shape of the score distribution, particularly the number of anxiety = 2 responses and the number of anxiety = 4 responses that
fewer than half of the anxiety = 3 respondents experience a level of anxiety feelings between 2.5 and 3, and
more than half of the anxiety = 3 respondents experience a level of anxiety feelings between 3 and 3.5.
So the mean level of anxiety across all anxiety = 3 respondents appears to be (a little) more than 3.
This doesn’t present a data analysis problem for me, but I didn’t expect it and would like to read about it.
Am I confused, or is there a name for this effect? Did I miss a STATS101 class?
Thanks for your help…!
Best wishes,
Glen
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
So each increase in score is incremental based on the prior score components? Can you provide the scoring key so we can better understand this phenomenon.

Thanks.
 
#3
So each increase in score is incremental based on the prior score components? Can you provide the scoring key so we can better understand this phenomenon.

Thanks.
Hi HL, Thanks for your response.
The survey item is "On a scale of 0 to 10, where: 0 is ‘not at all’ and 10 is ‘completely’, overall, how anxious did you feel yesterday?". The scoring uses a 0 to 10 scale. The respondent's feeling of anxiety is the continuous variable, that is to say when a person becomes more anxious as their driving test approaches the person doesn't experience their anxiety stepping up from a baseline (say 2) to 3, then 4, then 5 etc. Their felt sense of anxiety creeps up smoothly . The scale that measures this continuous variable is an integer, 0 to 10, scale with 11 possible values.
Any thoughts?
Best wishes, Glen