Cozby And Bates: Methods In Behavioral Research Chapter 12 .

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Mark Van SelstSan Jose State UniversityCozby and Bates:Methods in Behavioral ResearchChapter 12Understanding Research Results: Descriptionand CorrelationSummer 2014

Approaches to ResearchDESCRIPTIVE Describes situational or personal characteristics at a particular place andtimeCORRELATIONAL (Quasi-Experimental) GOAL: TO UNCOVER SYSTEMATIC RELATIONS Statistical analysis: correlation coefficient (pearsons r) r 1 r 0 r -1 Make predictions Test predictions (theory) Causal relations cannot be inferred on basis of correlation (requires temporalorder, causal path, association)EXPERIMENTAL Manipulate variables of interest (manipulate a given situation or experiencefor two or more groups of individuals, followed by a measurement of theeffect of those experiences on thoughts, feelings, or behavior). Establishes Causality

Approaches to -Experimental) Current state snapshot Not about relations Often “Real World”(e.g., focus group) Allows complexity 2 variables Is there a relationship Not causal- prediction (e.g.,gpa/SAT/GRE) Can test theory 2 variables Causal relations Manipulate variables Often “lab”-based Predict, understand,explain, control Can lose complexity

Scales of Measurement NominalOrdinalIntervalRatioDifferent scales of measurement allow different typesof comparisons to be performed. (e.g., frequencytotals vs. group means)

Representing Frequency Distributions Frequency Distribution TablePie Charts (proportions)Bar Graphs (categories)Frequency Polygons (line graphs)Frequency HistogramsScatterplots (Individual Score Pairings)

Descriptive vs. Inferential Statistics Descriptive Statistics DESCRIBE (the sample) Inferential Statistics allow INFERENCES to bedrawn from the SAMPLE about thePOPULATION

Descriptive Statistics Describe the sample Measures of Central Tendency; Mean Median Mode, Measures of Dispersion; Skew Kurtosis, Variability (variance, standard deviation, range)

Correlation Coefficient Strength (0 1) and Direction ( / - ) of therelationship Constraints: Restriction of range Could reflect floor or ceiling effects or just theselection of a very restricted sample Non-linear relationships

Meaning, Strength (0 1), & Direction ( /-)of the Correlational Relationship

Effect SizeEffect size is a (important!) general term that refers to thestrength of association between variables. In its mostgeneric sense, the effect size indicates how much of thevariability in one variable is attributable to its relation withparticular other variables. Pearson’s r is a measure ofthe effect size (recall: -1.0 r 1.0).Small:Medium:Large:/r/ 0 to .20/r/ .20 to .30/r/ .30 to .40 r2 is “variance accounted for”; that is how much (%) of thevariation across Variable A is associated with variation inVariable B. The technical term is that r2 is the “coefficientof determination”.

Statistical Significance (Inferential Statistics) Would the relationship be present if we tested a differentsample? Does this sample indicate a relationship in thelarger population? (p-value) Whereas the correlation coefficient indicates the strengthof the relationship, the regression equation provides thebest linear fit (point estimation) for the data. Regression equations use the known value(s) (X) topredict the unknown value(s) (Y') Y' a bX Y' a b1X1 b2X2(standard two-variable prediction equation)(Multiple Correlation / Multiple Regression equation)

Partial Correlation Partial correlation allow one to “factor out” other variablesby statistically “correcting” for their effects. Partialcorrelations approximate keeping the “undesired” variableconstant (i.e., not influencing the result) without actuallykeeping the undesired variable constant.The Third Variable Problem Partial correlations (correlations having removed theeffect of third variables) can indicate whether or not thethird variable is “responsible” for the relationship.

(fictional) Partial Correlation ExampleThe overlap in variability(covariation) between thetwo variables (green,purple) that is notassociated with the thirdvariable (gray) yeilds thepartial correlation of r .01The effect of a third variablecan be “partialed out” of therelationship between twoother variables.

SEM (Structural Equation Modeling) General term for techniques that assess predictedrelationships across variables Path Analysis depicts the relationships described in themodels and show the “path” of the purported causalinfluences

Chapter 12 Terminology Bar graphCentral tendency Mean, median, modeCorrelation coefficientCriterion variableDescriptive statisticsEffect sizeFrequency distributionFrequency polygonsMeasurement scales Nominal, ordinal, interval,ratioMultiple correlationPartial correlation Path analysisPie chartPredictor variableOutcome measureRegression equationRestriction of rangeScatterplotStandard deviationStatistical significanceStructural equation modelingVariabilityVariance

www.calstate.eduwww.sjsu.edu/psych

Chapter 12 Terminology Bar graph Central tendency Mean, median, mode Correlation coefficient Criterion variable Descriptive statistics Effect size Frequency distribution Frequency polygons Measurement scales Nominal, ordinal, interval, ratio Multiple correlation

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