PSYC2009 Study Guide - Final Guide: Decision Theory, Statistical Inference, Human Science
Introduction to Probability
Why we need to know about probability?
1. Inferential statistics involves probabilities.
2. Assessments of risk are based on probabilities of events. Key concept: conditional probability,
for instance, the risk of suffering a heart attack within the year is not the same if you're 25 vs
75yo.
3. Co-occurrence of uncertain events - consider the probability of a child developing ADHD, and
the probability of a child developing aggression problems, and the probability of a child
developing both. What if the two things are connected - compound and conditional
probabilities are needed to know this.
Types of Probability
A Priori or
Theoretical
• The number of distinct ways in which that event could occur divided by the total number of
distinct occurrences.
• Theoretical probabilities are assumed or defined in human science research and we'll
encounter some of these.
• When can one do this - it's an issue of some controversy: for instance, it can be quite
dangerous to assume that two events are equally probable simply because we don't know
what their probabilities are (principle of indifference).
Frequentist
or
Empirical
• The no. of times that event has occurred divided by the total number of opportunities for
that event to occur. Also known as relative frequency.
• Eg: If you want to find out whether a coin is unbiased or not, then throw it many time and
record. If you get 125 heads in 260 tosses then your best estimate of the probability of
getting a head is 125/260.
• The greater the number of tosses, the more stable and therefore valid the result. This is one
of the key concepts in probabilistic sampling - the bigger the sample the more precise (i.e.
less variable) the resulting estimate of a population parameter.
Bayesian
or
Subjective
• A judgeet aout the likelihood of a evet that is oheret i the sese that it oeys the
rules of probability judgement.
• Suppose the ABS has found that unemployment among Australians in your age-group in
Canberra is 23%. Does that mean you have a 0.23 chance of being unemployed right now?
No: either you are now unemployed or you are not. The 23% figure refers only to the chance
of finding an unemployed person if you selected randomly from the Canberra population in
that age group right now.
• However, we do associate probability with unique events. Eg: What is the probability you'll
get a HD for this unit? Because they are unique events with no a priori justification for logical
probabilities, these probabilities are subjective degrees of belief.
• Such estimates are used in statistical decision theory, engineering, game theory, risk
assessment, and everyday life. The only requirement made of anyone using subjective
probabilities is that they obey the rules for probabilities.
Rules for Probability
• Total probability rule: probabilities must add up to 1 over all possible outcomes.
• Addition rule: P(A or B) = P(A) + P(B) - P(A and B)
• Events A and B are called mutually exclusive if they cannot co-occur. This implies that P(A and
B) = O since [P(A or B) = P(A) + P(O).
• To calculate compound probabilities, can use a contingency table.
Conditional Probabilities and Risk
• Risk factor - if people possessing a certain characteristic are more likely to suffer from a
disorder than those who don't possess it.
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Document Summary
Inferential statistics involves probabilities: assessments of risk are based on probabilities of events. Key concept: conditional probability, for instance, the risk of suffering a heart attack within the year is not the same if you"re 25 vs. 75yo: co-occurrence of uncertain events - consider the probability of a child developing adhd, and the probability of a child developing aggression problems, and the probability of a child developing both. What if the two things are connected - compound and conditional probabilities are needed to know this. Also known as relative frequency: eg: if you want to find out whether a coin is unbiased or not, then throw it many time and record. If you get 125 heads in 260 tosses then your best estimate of the probability of getting a head is 125/260: the greater the number of tosses, the more stable and therefore valid the result. Suppose the abs has found that unemployment among australians in your age-group in.
