Question

1. A rehabilitation center researcher was interested in ex- amining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and the time required in physical therapy until successful reha- bilitation. Data on the number of days required for a suc- cessful completion of physical therapy and the prior phys- ical fitness status (below average, average, above average), and the doctor they were randomly paired with (out of 3 possible doctors) were collected.

(a) Is this an experimental, observation, or mixed study? Explain.

(b) What is the primary variable of interest (the response variable)?

(c) What are the explanatory variables? Identify all levels of the explanatory variables (factor-levels) if appropriate.

(d) Identify all combinations of the explanatory variables.

Answer 1

a.

Experimental Study : Where the researcher has the control over the variables and can manipulate those

Observational Study : Where the researcher has no control over the variables and take the observations randomly

number of days required for a successful completion of physical therapy is observational variable ( researcher has no control ) also the prior physical fitness status is also observational

but the choice of doctor can vary according to the researcher

hence the study is of mixed type

b. primary variable of interest (the response variable) is : time required in physical therapy until successful rehabilitation after going through a corrective knee surgery

c. explanatory variables :

Doctor : 1, 2 and 3

prior physical fitness status : below average, average, above average

d. combinations of the explanatory variables :

below average prior physical fitness status and doctor 1

average prior physical fitness status and doctor 1

above average prior physical fitness status and doctor 1

below average prior physical fitness status and doctor 2

average prior physical fitness status and doctor 2

above average prior physical fitness status and doctor 2

below average prior physical fitness status and doctor 3

average prior physical fitness status and doctor 3

above average prior physical fitness status and doctor 3