Drug Abuse Screening Test -20 are answered with No and Yes and is coded with 0,1 called dichotomous but as a whole scale this scale has also been classified like ordinal scale i.e. Low drug abused 1-5 scores, Intermediate drug abused 6-10 scores, Substantial drug abused 11-15 scores, Severe drug abused 16-20 scores but again this was converted into as a whole scale as Likert Scale.Can we consider it interval scale and consider it for Parametric Statistics.
The screening test response (yes/no) is a binomial, so you should use a binomial model.
The scores are bound in (0; 20). For such variables I suggest to re-scale them into (0;1) and use a beta model.
Given that the binomial is well approximated by a normal distribution, I would use this as justification for using statistics that make assumptions of normality. Most of the time, those are weak assumptions, anyway and the Central Limit theorem and Chebychev inequality justify the assumptions you are going to make regarding normality.
I would not reduce the resolution by rescoring the data into the categories you mentioned. You may want to retain them for interpretive purposes and nothing is lost if you keep everything in its original metric (0-20). Whether those labels are justified as different categories is a very different matter. From the point of view of classical test theory (true-score-error score theory) estimating parameters and using this test to conduct parametric analyses would be justified.
A more modern treatment of measurement might give you a different picture, however. No assumptions need to be made about the location of the item's difficulty on an underlying latent scale. Distributional assumptions can be relaxed. The only real assumptions made are that the item can be located on an underlying difficulty scale, as can the ability or level of drug abuse of the respondent, and the probability of endorsing an item is a function only of the difficulty of the item and the ability of the person. Examination and testing of any number of hypotheses are possible because of guaranteed properties when the model fits the data, including test bias, equal intervals, etc.) See the following for some examples.
Engelhard, G. (2012). Invariant measurement: Using Rasch models in the social, behavioral, and health sciences. New York, N.Y. : Psychology Press
Wright, B. D., & Stone, M.H. (1969). Best Test Design, Chicago: Mesa Press.
The answer to you question is "yes" for all practical purposes.
Best wishes,
David Drehmer
Dear Jochen Wilhelm and David E Drehmer thanks a lot for your answering
Even for small samples and yes or no questions, you can use a log linear model.
Dear Nelson Kautzner Marques Junior and Firdouse RAHMAN Khan thanks for your answer.
When I use ordinal data I employed analisis with not parametric statistics; as Wilcoxon. Most of the data obteined in psychology and other disciplines not employ data of a range of interval actually.
Good luck
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