Four Basic Types Of Measurement:

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Four Basic Types Of Measurement

• Categorizing
• Nominal
• Ranking
• Ordinal
• Determination of the size interval
• Interval
• Determination of the size of ratios
• Ratio

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CENTRAL TENDENCY AND VARIABILITY (NOMINAL SCALES)

• Information guessing game (ESP experiments)

• Background
• - Transmission of signals
• - How much is lost in channel?
• - How to measure the information transmitted in
  a message?

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CENTRAL TENDENCY AND VARIABILITY (NOMINAL SCALES)

• One word - no guesses
• Two words - one guess
• Four words - two guesses
• Eight words - three guesses

- of guesses - power to which two needs to be
raised to define of words, or log to base 2 of
of alternatives -Number of guesses called of
bits (binary units)
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Varying amounts of information
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• Nominal scales
• Name of category does not imply rank, even if it
  is a number.

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Nominal Scales

• Assignment to categories according to a rule
• e. g., manic - depressive
• paranoid - schizophrenic
• involutional - melancholic
• Starting point of science
• Chemists - elements
• Physicists - atoms and sub-atomic particles
• Lineaus - biological categories
• Freud - infantile sexuality - neurotic disorders
• Modern Psychology
• does it have reliable units of analysis?
• Reflexes?
• short term memory?
• behavior disorders?

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Frequency Distributions(Nominally Scaled Data)

• Bar graph - histogram
• Mode - summary statistic

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Ordinal Scales

• - Numbers convey relative magnitude.
• rank of one usually assigned to highest magnitude
• cant add or subtract ranks, e. g., ranks of
  weight

Rank Weight (lbs.) 1 200 2 20 3 3 4
2 5 .5
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Ordinal Scales Summary Statistics

• Central Tendency Median (as many observations
  above median as below it)
• Variability Range (difference between the
  smallest and highest values)

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• Interval scales
• Size of difference is known
• Units are of equal size
• Ratio scales
• True zero point exists
• Multiplication or division possible

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Magnitude of Psychological Judgments as a
Function of Physical Intensity
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CALCULATING THE MEAN

• Given the raw data 2, 4, 6, 8, 10

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Arithmetic Mean Center of Gravity
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Symmetrical Distributions
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Measures of Central Tendency in a Positively
Skewed Distribution
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Skewed (Asymmetrical) Distributions
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Symmetrical Distributions
Asymmetrical Distributions
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Binomial Distributions
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Calculating Deviations from the MeanGiven the
raw data 2, 4, 6, 8, 10
Mean Deviation

• Mean Absolute Deviation

Variance
Standard Deviation
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Calculating Deviations from the MeanGiven the
raw data 2, 4, 6, 8, 10
Mean Deviation

• Mean Absolute Deviation

Variance
Standard Deviation
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MEASURING WITH THE STANDARD DEVIATION Z-SCORES

• Given the raw data 2, 4, 6, 8, 10

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CORRELATION
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Normal Distribution
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r 1.0
Zy
Zx
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Example of Positive Correlation
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Examples of Positive, Negative and Minimal
Correlation
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• Effect of range on correlation

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Relationship between r2 and Predicted Variance

• Example measures of rainfall and corn height
• Suppose that r 0.8. This means that 64
  (0.8)2 of the variance of the height of corn
  height is accounted for by knowledge of how much
  rain fell.

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VALIDITY AND RELIABILITY

• Reliability To what extent will a test give the
  same set of results over repeated measurements?

• Validity To what extent does a test measure
  what it purports to measure?
• Validity and reliability are measured as
  correlation coefficients.

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Measuring reliability

• Odd-even or split-half method To what extent
  does one half of the test agree with the items of
  the second half of the test?
• Test-retest Results of test is given on two
  different occasions are compared. Assumes that
  there are no practice effects
• Alternative form Where there is a practice
  effect, an alternative form of the original test
  is given and the results are compared.
• A reliable test may not be valid.
• A valid test must be reliable may not be valid.
• A valid test must be reliable.

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HERITABILITY

• Heritability The proportion of variance of a
  phenotype that is attributable to genetic
  variance.

• Phenotype Observable trait
• Genotype What is transmitted from generation to
  generation
• What of a phenotype is genetic?
• Heritability is calculated by determining
  phenotypic variance and the magnitudes of its two
  components (genetic and environmental variance)

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Calculation of Heritability
Heritability The proportion of variance of a
phenotype that is attributable to genetic
variance.
?2p ?2g ?2e
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Which Contributes More to Area?Width or Length
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Heritability
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Example h2 of IQ 0.6. This does not mean
that 60 of an individuals IQ is genetic and 40
is environmental.
Heritability does not apply to individuals!
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Heritability
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Heritability is Specific to the Population in
which its Measured
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Minimum maximum values of h (coefficient of
heritability)
?2
G
h2
(h2 gt 0 lt 1)

h 0.00 None of the observed values of
phenotype is due to genes (all of it is due to
environmental differences). h 1.00 All of
variance is due to genes.
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Heritability

• does not measure how much of a given persons
  intelligence (say) is due to genes
• This is impossible to quantify
• Heritability measures how much variability in a
  trait is explained by variability in genes
• appears not to account for group differences in
  intelligence

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Examples Of Heritability Coefficients

• Piebald Holstein Cow
• h2 .95 (color)
• h2 .3 (milk production)
• Pigs
• h2 .55 (body fat)
• h2 .15 (litter size)

h2 is specific to the environment and population
studied.
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Heritably estimates are specific to populations
and environments in which they are measured!
Example 1 Heritability of skin color in Norway
and the United States. Its higher in the
United States. Why? Because, in Norway the
environment contributes more to phenotypic
variation than family background. In the United
States family background contributes more to
variation in skin color then the environment.
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Example 2 Heritability of Tuberculosis.
Decreased during the 20th century because of
changes in the environment. Up to and during the
19th century, everyone who was exposed to germ
got sick if they were susceptible. Improved
hygiene made it less likely that genetically
disposed individuals will get TB. Thus,
heritability of TB decreased as environmental
diversity increased.
Heritably estimates are specific to populations
and environments in which they are measured!
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How to Reduce h21. Interbreed - this reduces
?2g2. Increase ?2e.
How to Increase h21. outcrossing - new genes2.
mutation - new genes3. select for rare
characteristics4. reduce ?2e.