Psyc 235: Introduction to StatisticsGraded AssessmentSlide 3Quiz on this ThursdayIntersection & UnionIndependent vs. Dependent EventsConditional ProbabilityBaye’s TheoremLaw of Total ProbabilitiesRandom VariablesSlide 11Data World vs. Theory WorldBut First…4 Standard ScalesWhat kind of scale is this?Discrete vs. Continuous Random VariablesProbability Density DistributionsNext:Central Tendency in Random VariablesProperties of ExpectationProperties of VarianceContingency Tables for 2 random variablesRememberPsyc 235:Introduction to StatisticsDON’T FORGET TO SIGN IN FOR CREDIT!(and check out the lunar eclipse on Thursday from about 9-10)Graded Assessment AL1: Feb 25th & BL1: Feb 27th•In Psych 289: anytime between 9-5•Can sign up for guaranteed spot:9am, 11:30am, 2pm, 4:30pmSign up in lab or Office Hours (Thurs Rm 25)•Bring ID and notes.Graded Assessment•ALEKS will be unavailable:AL1: 8am Mon - 11:59pm WedBL1: 8am Wed - 11:59pm Fri•Conflict/Makeup exams:must be within that windowlet us know ASAP (as in TODAY)Quiz on this Thursday•Use this quiz as practice exam for the assessment.•Get your notes ready beforehand.•Complete like an assessment•Make note of trouble areas, additional notes you would like, etc.•Can do the quiz in office hours and then ask Jason questionsQuestions?Intersection & Union•Intersection:P(A  B) = P(A)*P(B)(If mutually exclusive = 0)•Union:P(A U B) =P(A)+P(B)- P(AB) •Compliment: p(A)=1-p(A)Independent vs. Dependent Events•Independent Events: unrelated events that intersect at chance levels given relative probabilities of each event•Dependent Events: events that are related in some way-Concepts of union and intersection are the sameHowever, P(A B)  P(A)*P(B)•Do you think mutually exclusive events are dependent or independent?Conditional Probabilityp(BA) p(A)p(B|A) =Conceptually this means:A BBaye’s Theoremp(A|B)p(B) + p(A|B)p(B)p(A|B)p(B)p(B|A) =A B• Can we break this down a little to understand it better?• p(A|B)*p(B)=p(AB) • p(A|B)*p(B) + p(A|B)*p(B)= p(A B) + p(AB) = p(A)•So, this is just:p(BA) p(A)p(B|A) =Law of Total Probabilities•p(A) = p(AB) + p(AB)•p(A) = p(A|B)p(B) + p(A|B)p(B)AB_BRandom Variables•Where are we?•In set theory, we were talking about theoretical variables that only took on two values: either a 0 or 1. They were in the group or not.•Now we’re going to talk about variables that can take on multiple values.Random Variables•But wait, didn’t we already talk about variables that had multiple values?•When we were talking about central tendancy and dispersion, we were talking about specific distributions of data…now we’re going to start discussing theoretical distributions.Data World vs. Theory World•Theory World: Idealization of reality (idealization of what you might expect from a simple experiment)Theoretical probability distribution•Data World: data that results from an actual simple experimentFrequency distributionBut First… •Before we get into random variables, we need to spend a little bit of time thinking about: the kinds of values variables can take on what those values mean how we can combine them4 Standard Scales•Categorical (Nominal) ScaleNumbers serve only as labelsOnly relevant info is frequency •Ordinal ScaleThings that are rankedNumbers give you order of items, but not distance between/relation between•Interval ScaleScale with arbitrary 0 point and arbitrary unitsHowever, units give you proportional relationship between values•Ratio ScaleScale has an absolute 0 pointIntervals between units is constantWhat kind of scale is this?•Temperature•Grades•Number Scale•Terror Alert Scale•Class Rank•What are other scales you are familiar with?Discrete vs. Continuous Random Variables•DiscreteFinite number of outcomes (x = sum of dice)Countable infinite number of outcomesNumbers from 1 to infinity•ContinuousUncountably Infinite(x=number of flips to get a head)(Convergent series: the sum of 1-infinity approaches some value)Probability Density Distributions•Discrete: draw on boardProbability mass function•Continuous (x= spot where pointer lands)Probability mass funtionNext:•Now that we know more about random variables, we can apply everything that we’ve learned so far.•Graphing and displaying data•Central tendency & dispersion•Transformations of mean and variance•Contingency TablesCentral Tendency in Random Variables•E(x)=∑(X*p(x))•Var(x)=∑((X-E(x))2*p(x))Properties of Expectation•E(a)=a•E(aX)=a*E(X)•E(X+Y)=E(X)+E(Y)•E(X+a)=E(X)+a•E(XY)=E(X) * E(Y)Properties of Variance•Var(aX)=a2Var(X)•Var(X+a)=Var(X)•Var(X-a)=Var(X)•Var(X+Y)= Var(X) + Var(Y)•Var(X2)=E(X)+Var(X)2Contingency Tables for 2 random variables•A is facilitative of B when p(B|A)>P(B)•A is inhibitory for B when p(B|A)<P(B)Remember•1st Exam Feb 25/27Sign up for exam timeslots in lab Wed or Office Hours Thurs(or also first-come-first-served on exam day)•Quiz on