You can find risk reduction in the following epidemiology text books :

Gordis, Leon. (2000). Epidemiology. Fourth  Edition. W.B. Saunders Company.

Friedman Gary D.(2004). Premiere of Epidemiology. Fifth edition. McGraw Hill Professional

Jekel, J F., Katz, D L., Elmore, J G. (2001). Epidemiology Biostatistics and Preventive Medicine. Second edition. W.B Saunders Company.

Basically Absolute Risk reduction is

Absolute Risk Reduction = incidence among treatment group- incidence among control

                      AR            = a/a+b  -  c/ c+d

thank you.

I used the absolute risk reduction to compare the answers of two groups of professionals in a questionnaire. so I didn't compare treatment vs no treatment.this was suggested by a statistician at the school.

What is the background of these two groups?   Even if you didn't use the treatment & control, you can compare the response of one group with another group.

i asked dentists and dietitians multiple response questions about some food categories and i asked them to choose all that apply.

then the frequencies of each option was calculated and a response rate to each option was used to calculate relative and absolute risk. 

Take group for which RR is to computed as treatment group and other group which is to be served as reference group as control. Arrange this data in 2x2 table with groups in rows and food categories yes/no in column and calculate RR.

Question Dieticians Dentist       DI percent DE percent      ARR    RRR

                total=94       total=123

Chocolate   81            120          0.86            0.98              -11.39     -13.22

Yogurt        23            56            0.24            0.46              -21.06       -86.07

Fruits          67             60           0.71             0.49             22.50        31.56

Sweeties    93            123         0.99            1.00              -1.06         -1.08

The ARR & RRR are basically measures of potential impact. The measures of Potential Impact reflects the expected contribution of a study factor to the frequency of a disease in a particular population. A measure of potential impact quantifies the possible consequences of exposure to a risk factor for a population. Here either Dieticians or Dentists received any intervention to measure the impact of intervention? Please check the calculation of ARR & RRR.

my method of calculation ARR was (a/a+b)-(c/c+d). this was what the statistician suggested to do! the RRR was calculated the same way you suggested for RRR. I couldn't interpret the results of the analysis. I'll send you the statistician technique.

this all was to see if the specific answers of dentists were different from dieticians.

Risk analysis

E.g. chocolate

Dietician: 78 out of 91, thus p1=78/91=0.8571

Dentist: 120 out of 128, thus p2=120/128=0.9375

Absolute risk reduction: p1-p2=-0.0803=-8.03%

Relative risk reduction: 100*(p1-p2)/p1=-9.375%

E.g. fruits

Absolute risk reduction: 25.24%

Relative risk reduction: 35.37%

The positive and negative signs indicate that the a real risk is reduced (positive) or increased (negative).

I think the order I need to use is like this:

occupation            answer

                                 chocolate              no chocolate

dentist

dietician

Dieticians Dentist       DI percent DE percent                     ARR    RRR               

total=94       total=123

Chocolate   81            120          0.86            0.98              -11.39     -13.22

Yogurt        23            56            0.24            0.46              -21.06       -86.07

Fruits          67             60           0.71             0.49             22.50        31.56

Sweeties    93            123         0.99            1.00              -1.06         -1.08

First find RR, RR =0.88 for chocolates indicates dieticians are (1-0.88)% i.e 12 % percent less likely to consume chocolate compared to dentists.

The ARR is interpreted as the risk of developing the disease is increased by ARR for those individuals exposed to the risk factor. ARR of chocolate is -11.39%, thus if a person is  dietician, the  risk of chocolate consumption  reduced by 11.39% compared to dentists.

RRR measures what proportion of the risk in exposed persons is due to the exposure?

RRR of chocolates is -13.22 indicates that 13.22 % of the chocolate consumption among dietician may attributed to dieticians.

If the objective is to find  specific answers of dentists were different from dieticians, you can just use Relative Risk  with 95% CI (If study design is prospective) otherwise use OR with 95% CI. 

thanks for your answers but I still feel you didn't get my point.

chocolate and other foods were answers in a survey and the required is to find if the dieticians answers were different from the dentists answers. the question was which of the following foods put the patient at risk of dental caries? and I used risk analysis to see if the answers are different or not.

however, the statistician told me to do the following;

ARR= (a/a+b) - (c/c+d)*100

RRR= ((a/a+b) - (c/c+d))/(a/a+b)*100.

are these methods right? because they are different from what you sent me before.