Individual Differences

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Individual DifferencesCorrelations

• Psy 425
• Tests Measurements
• Furr Bacharach
• Ch 3, Part 1

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Nature of Variability

• Assumption
• Differences exist among people
• A diagnostic measure is capable of detecting
  those differences
• Two kinds of differences
• Interindividual (between people)
• Intraindividual (within a single person)

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Questions

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

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Crucial assumption

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

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Psychometric Conceptsof Reliability Validity

• Are entirely dependent on differences among
  people

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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

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Variability

• Differences among the scores within a
  distribution of scores

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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

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TEST SCORES
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Central Tendency

• typical score in a distribution of scores
• Mean
• Arithmetic Mean

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MEAN
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MEAN
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Variability

• Variance
• Standard Deviation

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Computing Variance
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MEAN ? VARIANCE
Mean 17.17
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DEVIATION
(X X) 1? 9 17.17 -8.17 2? 26 17.17
8.83 3? . . . . . .
Mean 17.17
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Squared Deviation
SS S(X - X)2 Variance (s2) Standard
Deviation (s)
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VARIANCE
856 30
s2
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SS S(X - X)2 Variance (s2) Standard
Deviation (s)
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Computing Standard Deviation
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STDEV
856/30
SS S(X - X)2 Variance (s2) Standard
Deviation (s)
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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?

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Types of Distributions

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

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Distribution (2 wide)
Number of Participants
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Distribution (5 wide)
Number of Participants
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Normal Distribution
Number of Participants
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Other Examples
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Worksheet 1

• Enter scores
• Determine central tendency and variability
• Graph frequency distribution of scores

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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

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TEST SCORES
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What do you want to know about these scores?
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Direction Magnitude
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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

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Magnitude of Relationship

• Strong or weak association?
• Strong
• Consistency between variables
• Weak
• Inconsistency between variables

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LOOK!
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• For each test
• Central tendency
• Variability

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Covariance Correlation
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Covariance

• Useful
• Direction of association
• Positive
• 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

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Covariance
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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.

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Correlation
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Worksheet 2

• Enter scores
• Determine central tendency and variability
• Determine cross-products
• Determine covariance
• Determine correlation