# Sum of questionnaire score - ordinal vs interval? and choosing an inference test

#### krisjb

##### New Member
Hello there,

I'm doing a module in research methods and we are required to analyse some data (provided to us) from a randomised control trial.

I'm having some difficulty deciding on what stats analysis to do...

Background: the primary outcome measure is the sum of scores from a 36 item 'disability questionnaire' (the dependent variable). Each item on the questionnaire asks participants to rate the difficulty they have performing an everyday task. They have 3 options which are attributed a score - no difficulty (0), some difficulty (1), unable to do (2). They end up with a score out of 72. This is done at baseline (time 0). Participants are then randomised to receive an intervention group or a control group (independent variable). After a couple of days, both groups repeat the questionnaire (time 1).

The main research question is, does the intervention reduce disability (which would be evidenced by a significantly greater decrease in questionnaire score in the intervention group than in the control group).

My questions are:

1) what type of variable is the sum of the scores of the questionnaire? Reading around this I can't find any clear guidance. Some sources say Likert-type scales are strictly ordinal data but then could the sum of Likert-type scale scores be classed as interval data?

2) what test should be used to assess for a between-group difference in disability score between time 0 and time 1? My stats textbooks aren't very clear on this!

#### ondansetron

##### TS Contributor
I think ordinal, generally speaking, although some people argue with enough levels to an ordinal variable you may approximate an interval scale (I don’t necessarily agree).

I think it’s inappropriate to pretend a bunch of ordinal items suddenly become interval scale because we summed them. The relative loss of efficiency by using an ordinal (and more conservative) method is better than the inappropriate assumptions and ailments that may come from using a method that assumes a variable is at least interval scaled when the variable is really ordinal.

#### krisjb

##### New Member
Thanks. That's what I suspected.

The difficulty is then which non-parametric statistical test to do for ordinal data. I had thought an ANCOVA was best with group (intervention vs control) as independent variable, final disability questionnaire score as dependent variable and baseline disability questionnaire as covariate. However, this is really only for a parametric dependent variable right?

If the control and intervention groups are matched on baseline disability score, is it then just acceptable to do a Wilcoxon Signed Rank Test using final disability score as dependent variable and group as the independent variable?

#### ondansetron

##### TS Contributor
Rather than matching I would read up on either a rank regression or a proportional odds (ordinal logistic model) so you can just include covariates (Baseline score and others) directly in a multiple regression with the treatment variable as a dummy.