7. RESULTS DUE TO CHANCE?
                                       

    Eight Rules

1. False Precision

2. Base Rate Fallacy

3. Correlation Not Causation

4. Single Variable

5. Substantial Differences

6. Longitudinal Study

8. Dose-Response 		 
FLIP A MILLION COINS

  •   Flip each coin twenty times

  •   Probability of heads or tails on each flip = 50%

  •   (1/2)10   =   1/1024

          —   In first ten flips, expect 1000 coins to be all heads

          —   In first ten flips, expect 1000 coins to be all tails

  •   (1/2)20   =   10-6

          —   In 20 flips, expect one coin to be all heads

          —   In 20 flips, expect one coin to be all tails
    •  
    This happens even if all coins are fair.

    How to determine if they aren't?

    Results will not be reproducible.

    After ten flips, suspect some coins are not fair.

    Flip them again; after ten more flips most will have "normal" behavior.

    		 
     
    SAMPLE SIZE PROBLEMS
     
     
  •   A construction company employs ten people

  •   Has been in business five years

  •   No lost-time injuries (LTI)

  •   Must follow OSHA procedures

          —   Why require this?

          —   Why not exempt companies with good records?
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  •   Good safety record (mining, construction):   one LTI per 100 workers/year

  •   Ten employees, 5 years:   50 worker-years

  •   What is probability achieve zero LTI by chance?

          —   Assume actual rate of LTI = R

          —   Probability worker will NOT be injured: 1 - R

          —   Probability N workers will NOT be injured: (1 - R)N
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    R
    1   -   R
    (1   -   R)50   (%)
         		If the true lost-time injury risk per year R is .1, one can achieve, by chance, no injuries in 50 employee-years only .5% of the time. If the rate is .05, this can happen 7.7% of the time. It can happen 36% of the time when the rate is .02.

    So when the true LTI risk per year is .05 (on average, one of every twenty workers suffers a LTI every year), there is a 7.7% chance no injuries will occur in a fifty-worker force.   When the risk is .02 (one out of fifty), no injuries will occur in that fifty-worker force 36% of the time.     		 
        .10     .90           .5154  
        .09     .91           .8955
        .08     .92           1.547
        .07     .93           2.656
        .06     .94           4.533
        .05     .95           7.700
        .04     .96           12.99
        .03     .97           21.81
        .02     .98           36.42
      TOP Table 1. Probability No LTI Occur In A Year As A Function Of Probability R of LTI.  
     
     
    In the first row of Table 2 below, when the true probability of an LTI during the year is R = .05 (one in twenty), the probability that there will be no LTI for a N-employee company is   (1   -   R)N.   The probability that there will be at least one LTI is 1 minus that number.   Columns two through five of the Table show the results for N   =   5, 10, 15, and 20.

    So for companies with 5, 10, 15, and 20 employees, respectively, the probability that there will be AT LEAST ONE LTI in the coming year is 22%, 40%, 54%, and 64%.   (When the probability of an LTI = .05)   When the LTI probability is .01 (a typical rate for the construction or mining industries), the probability of at least one LTI during a year is 5%, 10%, 14%, and 18%.   So a company with twenty employees, even if their safety processes are good (and at a rate of one in a hundred would expect no LTI during the coming year), would have a significant chance of having at least one LTI.

    Even if a company's safety is double the usual (so that R = .005), there is almost a ten percent chance (actually, 9.5%) they will have an LTI this year (if they have 20 employees).   This is large enough that it could have significant financial impact if the company assumes they will have no LTIs.

    		 
     
    R
    1   -   (1   -   R)5
    1   -   (1   -   R)10
    1   -   (1   -   R)15
    1   -   (1   -   R)20
    		 
     
    .050
    0.226
    .401
    .537
    .642
    		  
     
    .020
    .096
    .183
    .261
    .332
    		  
     
    .010
    .049
    .096
    .140
    .182
    		  
     
    .005
    .025
    .049
    .072
    .095
    		  
     
    .003
    .015
    .030
    .044
    .058
    		  
     
    .002
    .010
    .020
    .030
    .039
    		  
     
    .001
    .005
    .010
    .015
    .020
    		  
     
    Table 2.         		Probability Of At Least One LTI Per Year As A Function Of R and Number of Employees N = 5, 10, 15, and 20.  
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    CONCLUSIONS
     
  •   Small Co:   Short-term safety record may deviate from long-term

            —   If fewer LTIs, false sense of security

            —   If more LTIs, may lead to financial ruin

            —   Need for mandatory rules

            —   Protects employees

            —   Protects company

  •   Large Co:   short-term safety record will equal long-term

            —   Will have constant year-to-year costs

            —   No surprises

            —   No need for mandatory rules

            —   Can charge (workman's comp) according to experience
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