Individual Differences & Correlations Psy 425 Tests & Measurements Furr & Bacharach Ch 3, Part 1

Nature of Variability Assumption: –Differences exist among people –A diagnostic measure is capable of detecting those differences Two kinds of differences 1.Interindividual (between people) 2.Intraindividual (within a single person)

Questions… Who will be admitted? Who will benefit? Who should be hired? Who meets criteria for diagnosis?

Crucial assumption Psychological differences exist AND the differences can be detected through well-designed measurement processes

Psychometric Concepts of Reliability & Validity Are entirely dependent on differences among people

Individual Differences & Psychological Tests Research –Exposing people to different experimental conditions (experiences) & measuring effects of these conditions on behavior –Determine the extent to which differences are a function of experimental conditions Clinical settings –Diagnosis –Change over time

Variability Differences among the scores within a distribution of scores

Assessment of Test Scores For a single test: –Detect and describe individual differences within the distribution of scores Central tendency Variability Shape of the distribution

TEST SCORES

Central Tendency “typical” score in a distribution of scores Mean = Arithmetic Mean

 30 = 17.2 X = MEAN

 30 = 17.2 X = MEAN

Variability Variance Standard Deviation

Computing Variance

Mean = MEAN  VARIANCE

(X – X ) 1  9 – =  26 – = . Mean = DEVIATION

= SS = S(X - X)2 = Variance (s2) = Standard Deviation (s) Squared Deviation

= SS = S(X - X)2 = Variance (s2) = Standard Deviation (s) s 2 = = 29 VARIANCE

Computing Standard Deviation

= SS = S(X - X)2 = Variance (s2) = Standard Deviation (s) = 856/30 STDEV

Assessing the Distribution of Scores Frequency count –For each score or band of scores, count the number of individuals who received that score or who are within that band of scores –Plot the frequency distribution of scores Ideal distribution? –Normal = theoretically ideal What do you usually get?

Types of Distributions Normal –Symmetric on either side of the mean –For psychological tests, Often assume that scores are normally distributed Important assumption… Skewed

Distribution (2 wide) Number of Participants

Distribution (5 wide) Number of Participants

Normal Distribution Number of Participants

Other Examples

Worksheet #1 Enter scores Determine central tendency and variability Graph frequency distribution of scores

Association between Distributions Covariability –Degree to which two distributions of scores vary in a corresponding manner What scores might co-vary? –Depression & anxiety –Schizotypy & autism –IQ & GPA

TEST SCORES

What do you want to know about these scores?

Direction & Magnitude

Direction of Relationship Positive or direct association –High on one, high on the other Negative or inverse association –High on one, low on the other

Magnitude of Relationship Strong or weak association? Strong –Consistency between variables Weak –Inconsistency between variables

LOOK!

For each test: –Central tendency –Variability

Covariance & Correlation

Covariance Useful –Direction of association 1.Positive 2.Negative Limited information –Magnitude? Size of covariance effected by size of scales… –Covariance between two small scale variables different than that between two large scale variables

Covariance

Correlation INDEX OF CONSISTENCY OF INDIVIDUAL DIFFERENCE SCORES Easy to interpret Range between -1.0 and +1.0 Reflects direction and magnitude of association “Bounded” quality is obtained by dividing the covariance by the standard deviations of the two variables.

Correlation

Worksheet #2 Enter scores Determine central tendency and variability Determine cross-products Determine covariance Determine correlation