Probability - Introduction to Statistics in Psychology - Lecture Slides, Slides of Statistics for Psychologists

Download Probability - Introduction to Statistics in Psychology - Lecture Slides and more Slides Statistics for Psychologists in PDF only on Docsity! Introduction to Statistics in Psychology PSY 201 Lecture 13 probability Why casinos make money. DESCRIPTIVE STATISTICS most of what we have discussed so far is called descriptive statistics • distributions • graphs • central tendency • variation • correlation describe sets of data 2 INFERENTIAL STATISTICS given a set of data from a sample we want to infer something about the entire population • mean • standard deviation • correlation • ... never with certainty with probability 3 PROBABILITY number between 0 and 1 probability of event A is written as P (A) if P (A) = 1.0 it indicates with certainty that event A will happen if P (A) = 0 it indicates with certainty that event A will not happen 4 PROBABILITY LAWS there are specific rules to probability we want to know the probability of many events, pairs of events, contingent events,... how to calculate probabilities depends upon • Complements • Mutually exclusive compound events • Nonmutually exclusive events • Statistically independent joint events • Statistically dependent joint events 5 SINGLE EVENTS precise definition requires high-level mathematics intuitive definition is that probability of a single event is the ratio of the number of possible outcomes that include the event to the total number of possible outcomes P (a die coming up 3) = Number of outcomes that include 3 Total number of outcomes P (a die coming up 3) = 1 6 ! 0.167 1 2 3 4 5 6 6 docsity.com COMPLEMENTS suppose we know the probability P (A), where A is some event then if A represents “not A” (called the complement of A) P (A) = 1.0" P (A) when A = turning up a 3 on a die A means turning up anything other than a 3 since P (A) = 0.167 P (A) = 1.0" 0.167 = 0.833 1 2 3 4 5 6 7 COMPOUND EVENTS sometimes we know the probability of two events A and B and we want to know the probability of event A or B e.g. P (turning up a 3 or a 4 on a die) these are mutually exclusive events one or the other 8 MUTUALLY EXCLUSIVE for mutually exclusive compound events, calculating the probability of the compound is easy consider probability of rolling numbers on a die P (3 or a 4) = P (3) + P (4) P (turning up a 3 or a 4 on a die) = 1 6 + 1 6 = 2 6 = 1 3 1 2 3 4 5 6 in general, if A and B are mutually exclusive P (A or B) = P (A) + P (B) 9 NONMUTUALLY EXCLUSIVE sometimes events are not mutually exclusive e.g. A = turning up a number # 3 on a die: P (A) = 12 B = turning up an odd number on a die: P (B) = 12 what is P (A or B)? 1 2 3 4 5 6 cannot just add probabilities because numbers common to A and B get counted twice! 10 NONMUTUALLY EXCLUSIVE subtract out common probability P (number # 3 or odd) = P (# 3) + P (odd)" P (# 3 and odd) = 1 2 + 1 2 " 2 6 = 3 6 + 3 6 " 2 6 = 4 6 = 2 3 in general P (A or B) = P (A)+P (B)"P (A and B) when the events are mutually exclusive, P (A and B) = 0. and we get the rule for mutually exclusive events 11 JOINT EVENTS if we know P (A) and P (B) what is P (A and B)? both events must occur (simultaneously or successively) e.g. P (3 on a die and HEAD on a coin flip) 12 docsity.com