1)Test the effects of IV on DV 2)Protects against threats to internal validity Internal Validity – Control through Experimental Design Chapter 10 – Lecture 10 Causation

Highest Constraint Comparisons btw grps Random sampling Random assignment Experimental Design Infer Causality

1)One or more hypothesis 2)Includes at least 2 “levels” of IV 3)Random assignment 4)Procedures for testing hypothesis 5)Controls for major threats to internal validity Experimental Design (5 characteristics)

Develop the problem statement Define IV & DV Develop research hypothesis Identify a population of interest Random sampling & Random assignment Specify procedures (methods) Anticipate threats to validity Create controls Specify Statistical tests Ethical considerations Experimental Design Clear Experimental Design…

1.between groups variance (systematic) Experimental Design 2 sources of variance 2. Within groups variance (nonsystematic) (error variance) drugno drug Remember… Sampling error Significant differences…variability btw means is larger than expected on the basis of sampling error alone (due to chance alone)

Variance Need it! Without it… No go Between Group Within Group Experimental Variance (Due to your treatment) + Extraneous Variance (confounds etc.) VARIANCE Error Variance (not due to treatment – chance) CONTX Subs “Partitioning of the variance”

between groups variance Within groups variance Variance: Important for the statistical analysis F = Systematic effects + error variance error variance F = 1.00 F = No differences btw groups

Variance Your experiment should be designed to Maximize experimental variance Control extraneous variance Minimize error variance

Maximize “Experimental” Variance At least 2 levels of IV (IVs really vary?) Manipulation check: make sure the levels (exp. conditions) differ each other Ex: anxiety levels (low anxiety/hi anxiety)  performance on math task anxiety scale

Control “Extraneous” Variance 1.Ex. & Con grps are similar to begin with 2.Within subjects design (carryover effects??) 3.If need be, limit population of interest (o vs o ) 4.Make the extraneous variable an IV (age, sex, socioeconomic) = factorial design MF Lo Anxiety Hi Anxiety M-low M-hi F-low F-hi Factorial design (2 IV’s) YOUR Proposals

1.Ex Post Facto 2.Single-group, posttest only 3.Single-group pretest-posttest 4.Pretest-Posttest natural control group Group A Naturally Occurring Event Measurement 1. Ex Post Facto – “after the fact” Control through Design – Don’ts No manipulation

Control through Design – Don’ts Single group posttest only Single group Pretest-posttest Group A TX Posttest Pretest Group A TX Posttest Compare

Control through Design – Don’ts Pretest-Posttest Naturalistic Control Group Group A Pretest TX Posttest Group B Pretestno TX Posttest Compare Natural Occurring

Manipulate IV Control Group Randomization Control through Design – Do’s – Experimental Design Testing One IV 4 Basic Designs 1. Randomized Posttest only, Control Group 2. Randomized Pretest-Posttest, Control Group 3. Multilevel Completely Randomized Between Groups 4. Solomon’s Four- Group

Randomized Posttest Only – Control Group (most basic experimental design) R Group A TX Posttest (Ex) R Group B no TX Posttest (Con) Compare

Randomized, Pretest-Posttest, Control Group Design R Group A Pretest TX Posttest (Ex) R Group B Pretest no TX Posttest (Con) Compare

Multilevel, Completely Randomized Between Subjects Design (more than 2 levels of IV) R Group A Pretest TX1 Posttest R Group B Pretest TX 2 Posttest R Group C Pretest TX3 Posttest R Group D Pretest TX4 Posttest Compare

Solomon’s Four Group Design (extension Multilevel Btw Subs) R Group A Pretest TX Posttest R Group B Pretest ---- Posttest R Group C TX Posttest R Group D Posttest Compare Powerful Design!

What stats do you use to analyze experimental designs? Depends the level of measurement Test difference between groups Nominal data  chi square (frequency/categorical) Ordered data  Mann-Whitney U test Interval or ratio  t-test / ANOVA (F test)

t-TestCompare 2 groups Independent Samples (between Subs) One sample (Within) Evaluate differences bwt 2 independent groups Evaluate differences bwt two conditions in a single groups

Assumptions to use t-Test 1.The test variable (DV) is normally distributed in each of the 2 groups 2.The variances of the normally distributed test variable are equal – Homogeniety of Variance 3. Random assignment to groups

Represents the distribution of t that would be obtained if a value of t were calculated for each sample mean for all possible random samples of a given size from some population t-distribution

Degrees of freedom (df) When we use samples we approximate means & SD to represent the true population Sample variability (SS = squared deviations) tends to underestimate population variability Restriction is placed = making up for this mathematically by using n-1 in denominator

Degrees of freedom (df): n-1 The number of values (scores) that are free to vary given mathematical restrictions on a sample of observed values used to estimate some unknown population = price we pay for sampling S 2 = variance ss (sum of squares) df (degrees of freedom) (x - ) 2 n-1 x

Degrees of freedom (df): n-1 Number of scores free to vary Data Set  you know the mean (use mean to compute variance) n=2 with a mean of 6 X8?6X8?6 In order to get a mean of 6 with an n of 2…need a sum of 12…second score must be 4… second score is restricted by sample mean (this score is not free to vary) =x

Analysis of Variance (ANOVA) Two or more groups ….can use on two groups… t 2 = F Variance is calculated more than once because of varying levels (combo of differences) Several Sources of Variance SS – between SS – Within SS – Total Sum of Squares: sum of squared deviations from the mean Partitioning the variance

Assumptions to use ANOVA 1.The test variable (DV) is normally distributed 2.The variances of the normally distributed test variable is equal – Homogeniety of Variance 3. Random assignment to groups

between groups variance Within groups variance F = Systematic effects + error variance error variance F = 1.00 F = No differences btw groups F = times as much variance between the groups than we would expect by chance

Planned comparisons & Post Hoc tests A Priori (spss: contrast) part of your hypothesis…before data are collected…prediction is made A Posteriori Not quite sure where differences will occur After Omnibus F…

2 types of errors that you must consider when doing Post Hoc Analysis Why not just do t-tests! 1.Per-comparison error (PC) 2.Family wise error (FW) Alpha Inflate Alpha!!!!

 FW = c(  c = # of comparisons made  = your PC Ex: IV ( 5 conditions) 1 vs 2 1 vs 3 1 vs 4 1 vs 5 2 vs 3 2 vs 4 2 vs 5 3 vs 4 3 vs 5 4 vs 5  FW = c(  10 (0.05) =.50

HSD