Statistics for the Social Sciences Psychology 340 Spring 2010 Introductions & Review of some basic research methods

PSY 340 Statistics for the Social Sciences This course How is this course different from PSY 138? –Format: Longer lectures, but no separate lab times –Content: review of PSY 138 and beyond (remember the “beyond 138” in the decision tree) Dealing with more complex situations (more than 2 variables) Hypothesis testing with: –Correlation and regression –Multiple regression –Tests for differences with more than two groups

PSY 340 Statistics for the Social Sciences PSY 138

PSY 340 Statistics for the Social Sciences This course

PSY 340 Statistics for the Social Sciences Course Format Syllabus: Blackboard – try logging in now Lectures - will take up most of class time Homework (30%) - practice items, ARE collected for credit (typically due Tuesdays) Exams (50%) –three cumulative mid-semester exams (10% each) –1 final exam (20%) Quizzes (5%) - on-line Blackboard quizzes, based primarily on textbook readings (typically due Thurs) Final project (15%) – large data set, multiple analyses, write up a “results” section Labs – additional practice items, NOT collected for credit –Two parts: By hand step-by-step example(s) Large SPSS dataset practice question(s)

PSY 340 Statistics for the Social Sciences Variability is key A the heart of research methodology and statistics is variability –Variables - characteristics with values that aren’t constant (across individuals, time, place, etc.) –We’re interested in explaining (predicting) the variability of variables –We use research methods (like experimental control) to try to constrain variability to make it easier to see how different variables affect each other –We use statistical procedures to examine which variables vary together (and which don’t)

PSY 340 Statistics for the Social Sciences Statistical analysis follows design Statistical analysis follows from the design of a study Our decision tree helps us ask the right design questions which will lead us to the appropriate statistical test

PSY 340 Statistics for the Social Sciences Statistical analysis follows design Vs. Decide if there is a difference Decide if there is a relationship between variables Observational studies Experimental & Quasi-experimental studies Testing for differences between groups (conditions) Testing for similarities between variables This is a generality, there are exceptions. Towards the end of the course we’ll see that the two may be considered essentially the same kinds of analyses

PSY 340 Statistics for the Social Sciences Basic Research Methods Observational study –Researcher observes and measures variables of interest to find relationships between the variables –No attempt is made to manipulate or influence responses Experimental methodology –One (or more) independent variable(s) is manipulated while changes are observed in another variable (dependent) –Used to establish cause-and-effect relationships between variables –Uses extensive methods of control to minimize extraneous sources of variability Quasi-experimental methodology –One (or more) of the independent variables is a pre-existing characteristic (e.g., sex, age, etc.)

PSY 340 Statistics for the Social Sciences Different basic methods Experimental versus Observational methods –Experiments involve manipulation of variables –Observational methods involve examining things as they already are

PSY 340 Statistics for the Social Sciences ObservationalExperimental Example –Randomly select individuals –Watch their study habits –See how they do on a test –Randomly select individuals –Randomly assign to groups Crammed study group Distributed study group –See how they do on a test Issue: What’s the best way to study for a test?

PSY 340 Statistics for the Social Sciences Experimental Control Our goal: –to test the possibility of a relationship between the variability in our IV and how that affects our DV. –Control is used to minimize excessive variability. –To reduce the potential of confounds.

PSY 340 Statistics for the Social Sciences Imprecision in manipulation (IV) & measurement (DV) & random varying extraneous variables Imprecision in manipulation (IV) & measurement (DV) & random varying extraneous variables Logic of experimental control Sources of Total (T) Variability: T = NonRandom exp + NonRandom other + Random variables which covary with IV (condfounds) variables which covary with IV (condfounds) Manipulated independent variables (IV) Manipulated independent variables (IV) Study method: –Crammed –Distributed Distributed studiers never get to practice problmems Different study times, different study methods, etc. Variability in Test Performance

PSY 340 Statistics for the Social Sciences Logic of experimental control Experimental procedures are used to reduce R and NR other so that we can detect NR exp. That is, so we can see the changes in the DV that are due to the changes in the independent variable(s). Sources of Total (T) Variability: T = NonRandom exp + NonRandom other + Random Constrain variability by carefully levels of IV Eliminate counfounds Use good measures

PSY 340 Statistics for the Social Sciences Weight analogy Imagine the different sources of variability as weights R NR exp NR other R NR other Treatment groupcontrol group

PSY 340 Statistics for the Social Sciences Weight analogy If NR other and R are large relative to NR exp then detecting a difference may be difficult R NR exp NR other R NR other

PSY 340 Statistics for the Social Sciences Weight analogy But if we reduce the size of NR other and R relative to NR exp then detecting gets easier R NR other R NR exp NR other

PSY 340 Statistics for the Social Sciences Logic of observational approaches  Suppose that you wish to predict exam performance using an observational method Sources of Total (T) Variability: Variables that don’t covary with test performance Variables that don’t covary with test performance Variables that do covary with test performance Variables that do covary with test performance Observe and record variables, but don’t know which group they’ll fit into T = NonRandom other + Random Total study time Study topic Test time Breakfast food Hours of sleep That’s what we’ll use statistics to find out

PSY 340 Statistics for the Social Sciences Logic of observational approaches Total variability it test performance Unexplained variance 64% Total study time r =.6 Some co-variance between the two variables If we know the total study time, we can predict 36% of the variance in test performance

PSY 340 Statistics for the Social Sciences Logic of observational approaches Total variability it test performance Unexplained variance 51% Test time r =.1 Total study time r =.6 A little co-variance between these test performance and test time If we add it to study time, then we can explain more the of variance in test performance

PSY 340 Statistics for the Social Sciences Logic of observational approaches Total variability it test performance Unexplained variance 51% breakfast r =.0 Test time r =.1 Total study time r =.6 No co-variance between these test performance and breakfast food If we add it to the other two, then we can NOT explain more the of variance in test performance

PSY 340 Statistics for the Social Sciences Logic of observational approaches Total variability it test performance Unexplained variance 40% Test time r =.1 Total study time r =.6 breakfast r =.0 Hrs of sleep r =.45 Some co-variance between these test performance and hours of sleep If we add it to study time, then we can explain more the of variance in test performance (but notice what happens with the overlap)

PSY 340 Statistics for the Social Sciences Statistical analysis follows design Statistical analysis follows from the design of a study The next question in the tree

PSY 340 Statistics for the Social Sciences Statistical analysis follows design Decide if there is a difference How many separate samples? 1 Testing for a difference between a sample and a known population value Or within-groups designs Testing for a difference between two samples Various “t-tests” 2 >2 Testing for a difference between two samples Various “ANOVA” designs

PSY 340 Statistics for the Social Sciences What are samples? Who do we test? –Population The set of all individuals of interest – Sample A subset of the population from whom data is collected Typically we don’t have access to all of the population We test these folks and then generalize the results to the population as a whole

PSY 340 Statistics for the Social Sciences What are samples? – “Sample” may also be used to refer to the participants (randomly) assigned to a particular condition of the experiment condition A condition B condition C condition D

PSY 340 Statistics for the Social Sciences Statistical analysis follows design Statistical analysis follows from the design of a study Next question in the tree

PSY 340 Statistics for the Social Sciences Statistical analysis follows design … Are the samples related or independent? related There is a pre-existing relationship between the groups –“non-independent groups” –“matched samples” Or the same subjects participate in multiple conditions –“within-groups” –“repeated-measures” independent There is no pre-existing relationship between the groups “between-groups”

PSY 340 Statistics for the Social Sciences Example Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)? Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)?

PSY 340 Statistics for the Social Sciences Example Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)? Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)?

PSY 340 Statistics for the Social Sciences Example Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)? Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)?

PSY 340 Statistics for the Social Sciences Example Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)? Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)?

PSY 340 Statistics for the Social Sciences Example Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)? Dr. Charles investigated the impact of three types of video taped teaching programs for two types of subjects (math and Spanish). 12 participants were randomly assigned to one type of teaching program and one subject. After two weeks of training Dr. Charles assessed their learning. What test should he use to analyze his data (which program works best for which subject)?