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SOC202H1 Chapter Notes -Normal Distribution, Standard Deviation, Human Behavior

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Scott Schieman

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PROBABILITY THEORY analysis & understanding of chance occurrences
o Physical nature cyclical, follow strict scientific laws predictable
o Human behavior less predictable
Social/behavioral scientists req. incl. degrees of accuracy
o Many statistic predication based on normal curve
What is a Probability?
A PROBABILITY (p) a specification of how frequently a particular event of
interest is likely to occur over a large number of trails
o Probability of Success probability of this interesting event occurring
 
o Probability of Failure probability of this interesting not event
o Observe “outcomes” of large # of trails, identify all possible outcomes
Probability can be considered as proportions
Basic Rules of Probability Theory
Rule 1: probability in range between 0 and 1
o 0 = event cannot happen, 1 = event must happen
Rule 2: Addition rule for Mutually Exclusive events the probability of
many mutually exclusive (alternative) events is equal to the sum of the
probabilities of the individual events
o P(A or B) = P(A) + P(B) iff A & B are independent (scales)
Rule 3: Adjust for joint occurrence (General addition rule)
o Joint Occurrence an event that double0counts success or joins two
aspects of success
o P(A or B) = P(A) + P(B) P(A and B) (doesn’t scale)
Rule 4: Multiplication rule for Compound of Independent events
probability of a compound of independent events is equal to the multiple
of the probabilities of the separate parts of the events
o Compound events multiple-part events
o P(A and B) = P(A)P(B) iff A & B are independent (scales)
Rule 5: Account for replacement with compound events
Using the Normal Curve as a Probability Distribution
Z-score how many standard deviation away from the mean a raw (X-
score) lies
Specific AUC of normal distribution = probability of occurrence of any
single score falling in its domain
For normal distribution: the follow are equivalent
o 1. Proportion of cases between two scores
o 2. The AUC between these two scores
o 3. Probability of randomly selecting a case between these scores
o 1. A distributional interpretation that describes the results in relations
to the distribution of scores in a population or sample
o 2. A graphical interpretation that describes the proportion of areas
under a normal curve (assuming the distribution is normal shape)
o 3. A probabilistic interpretation that describes the probability of a
single random drawing of a subject from this population
the curve and compute the proportion (p) of the total curve this part
o Using statistical table & Z-score
o Req. variable is normally distributed in the population
o Req. variable is interval/ratio measurement level
   
= proportion of area under the curve
= total sample size
Computing percentiles for normally distributed populations
o Percentile Ranks the percentage of a sample or population that falls
at or below a specific value of a variable
If normally distributed find value’s corresponding z-value to
quickly compute percentile ranks
o Percentile ranks possible for non-normal distributions
The Normal Curve as a Tool for Proportional Thinking
Equal differences btwn scores doesn’t always indicate the same thing
o Raw scores by themselves misleading
o use standard deviation as unit of measure w/ normal distributions for
accurate insight into significance of a raw score
The Gambler’s Fallacy: Independence of Probability Events
Common statistical mistake w/ probability: misunderstand independence
of part of compound events
o Gamblers fallacy Assume on losing streak, luck will eventually turn
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