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# CH 6 textbook notes

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University of Toronto St. George

Sociology

SOC202H1

Scott Schieman

Winter

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CH6 – PROBABILITY THEORY AND THE NORMAL PROBABILITY DISTRIBUTION
PROBABILITY THEORY – analysis & understanding of chance occurrences Using the Normal Curve as a Probability Distribution
o Physical nature cyclical, follow strict scientific laws predictable Z-score – how many standard deviation away from the mean a raw (X-
o Human behavior less predictable score) lies
Social/behavioral scientists req. incl. degrees of accuracy
Specific AUC of normal distribution = probability of occurrence of any
o Many statistic predication based on normal curve single score falling in its domain
For normal distribution: the follow are equivalent
What is a Probability? o 1. Proportion of cases between two scores
A PROBABILITY (p) – a specification of how frequently a particular event of o 2. The AUC between these two scores
interest is likely to occur over a large number of trails o 3. Probability of randomly selecting a case between these scores
o Probability of Success – probability of this interesting event occurring WAYS TO INTERPRET P
o 1. A distributional interpretation that describes the results in relations
( ) to the distribution of scores in a population or sample
o Probability of Failure – probability of this interesting not event o 2. A graphical interpretation that describes the proportion of areas
under a normal curve (assuming the distribution is normal shape)
occurring o 3. A probabilistic interpretation that describes the probability of a
o Observe “outcomes” of large # of trails, identify all possible outcomes single random drawing of a subject from this population
Probability can be considered as proportions
PARTITIONING AREAS UNDER THE NORMAL CURVE – to identify part of
the curve and compute the proportion (p) of the total curve this part
Basic Rules of Probability Theory represents
Rule 1: probability in range between 0 and 1 o Using statistical table & Z-score
o 0 = event

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