Psy 232 Class notes GW06:  Probability                           

P(Event) = (# occurrences of E) /( total # of possible occurrences)

Note: P(Event) is usually simply called p.

The p distribution range is always 0 to 1.00; p can never be larger than 1.00 or smaller than 0,

    hence no negative values are possible. 

        Examples . . .

Note:  p can be expressed in any of three ways:  fraction; proportion; or per cent.

        Examples . . .

One can determine probability from a frequency distribution:  p = f/N. 

    That is, the probability of a particular score occurring in a set of data

    is simply the frequency of that score divided by the total number of scores.

Important assumption regarding probability:  independent random sampling:

     Outcomes mutually exclusive (e.g. a coin toss cannot be both heads & tails)

     Outcomes exhaustive (e.g., there aren't any other possibilities than heads, tails, or edge)

     Outcomes independent (e.g., the occurrence of heads does not affect whether tails occurs on the next toss)

     Random sampling has two criteria, both of which must be met:

           - all members of a population have an equal chance of being selected

           - for samples with more than one individual, all selections must have a constant probability

Normal distribution & probability:

            Recall that for z-score distributions µ = 0 and σ = +1 

            Using z-scores to mark off sections of a normal distribution, we can state the p-value (usually in

            terms of percentages) for any area under the curve.  The three commonly noted areas, marked by

            z-scores of 0, 1, 2, and 3, are

            0 - 1:  34.13%         1 - 2:  13.59%         2 - 3 :  2.28%          3 - infinity:  .0013

            (Note:  percentages don't add exactly to 50 because of rounding.)

            Remember that the left & right sides of the normal distribution are exactly mirrored,

                so the percentages are the same on both sides of the mean.

            The foregoing percentages are true for all normal distributions, regardless of the original mean

            & standard deviation.

In graphical form - areas under the normal curve, marked off by Std Devs:
                  red =  0 to 1 s.d., green = 1 to 2 s.d., blue = 2 to 3 s.d., black = 3 to infinity

   s.d.  =              -3               -2             -1              0             +1            +2            +3              
     p  =    .0013       .0228        .1359        .3413        .3413        .1359       .0228         .0013
    % =    .13%        2.28%      13.59%     34.13%     34.13%    13.59%     2.28%       .13% 

Using the Unit Normal Table to determine probabilities via z-scores.

            In-class practice exercises . . .