PROTEUS

              

 

 

 

 

 

 

 

 

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Solution to #20
 
recept   theatre   pool   field-trip   dinner  
  ill well tot     ill well tot     ill well tot     ill well tot     ill well tot  
exp 8 10 18   exp 5 5 10   exp 16 4 20   exp 6 10 16   exp 5 10 15  
n 16 30 46   n 19 35 54   n 8 36 44   n 18 30 48   n 19 30 49  
tot 24 40 64   tot 24 40 64   tot 24 40 64   tot 24 40 64   tot 24 40 64  

OR: 1.50

  OR: 1.84  

OR: 18.0

  OR: 1.00  

OR: 0.789

(1.27 PROT)

  

The analysis must be done on the exposure having the highest odds ratio.  This is the pool  (OR:18).    ChiSq is valid due to all the expected cell sizes being >5.  The chi-sq value is 22.42,  P<0.000005*   The null hypothesis (of no association) can be rejected.  The probability of seeing the data arranged as presented in the absence of any association is 5 in a million!. the swimming pool exposure was strongly associated with the illness. Those who were exposed to the pool had 18 times the risk of illness compared to those who were not so exposed.

NOTE: the question structured as an exam question only asks for a test of the null hypothesis on the exposure with the strongest odds ratio.   For practice, you are encouraged to complete the analysis for all the exposures.  The answers are given below:

    reception: - a weak association: those exposed to the reception were about 50% more likely to be ill than those not exposed.   chi-sq: 0.52,  P>0.05

    theatre: - a weak association: those exposed to the theatre visit were 84% more likely to be ill than those who did not attend. FET:  P: 0.293,     

    field trip: No association at all.   chi-sq: 0.00,  P=1.00   

    Those who attended the dinner were less likely (0.79) to be ill than those who did not attend. In other words, those NOT attending had more chance (27%) of being ill: chi-sq: 0.15,   P>0.05

* Note: report only the highest level of significance you can determine with the tables available.