Transcript h 2

Four Basic Types Of
Measurement:
• Categorizing
– Nominal
• Ranking
– Ordinal
• Determination of the size interval
– Interval
• Determination of the size of ratios
– Ratio
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?
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)
Varying amounts of information





Nominal scales:
Name of category does not imply rank,
even if it is a number.
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?
Frequency Distributions
(Nominally Scaled Data)
• Bar graph - histogram
• Mode - summary statistic
y
mode
ordinate
(frequency)
x
abscissa
• Ordinal scales:
- Numbers convey relative magnitude.
– rank of one usually assigned to highest
magnitude
– can’t add or subtract ranks, e. g., ranks
of weight
Rank:
1
2
3
4
5
Weight (lbs.)
200
20
3
2
.5
Ordinal Scales
Summary Statistics:
• Central Tendency: Median (as many
observations above median as below
it)
• Variability: Range (difference
between the smallest and highest
values)
• Interval scales:
– Size of difference is known
– Units are of equal size
• Ratio scales:
– True zero point exists
– Multiplication or division possible
Magnitude of Psychological Judgments
as a Function of Physical Intensity
CALCULATING THE MEAN
Given the raw data: 2, 4, 6, 8, 10
Mean = X
X
•
=
N
2 + 4 + 6 + 8 + 10
=
5
30
=
=6
5
i
Arithmetic Mean = Center of Gravity
Symmetrical Distributions
Asymmetrical Distributions
Symmetrical Distributions
Skewed (Asymmetrical)
Distrubutions
Measures of Central Tendency in
a Positively Skewed Distribution
Binomial Distributions
CALCULATING DEVIATIONS
FROM THE MEAN
Given the raw data: 2, 4, 6, 8, 10
Mean Deviation
=
Mean Absolute Deviation =
Variance

Standard Deviation

2
=
äã X X i ëí
0
N
4 2 0 2 4 0
 0
5
5
äã X X i ëí
N
4 2 0 2 4 12
 2 . 4
5
5
äã X X i ëí
N
2
äã X X i ëí
2
 
N
2
=
40 5  8 2 . 82
MEASURING WITH THE
STANDARD DEVIATION: ZSCORES
Given the raw data: 2, 4, 6, 8, 10
if X 6 and  8
2 6 4
Z 2 

1 . 42
8
8
8 6 2

. 709
8 
8
8
Z
4 6 2
Z 4 

. 709
8
8
10 6 4
Z 10 

1 . 42
8
8
CORRELATION
z x  r xy C z y
i
r xy (
i
x y  x y
y
i
)
Normal Distribution
r+1.0
= +1.0
r = -1.0
Zy
Zy
Zy
ZxZx
or
Zx
Example of Positive Correlation
Examples of Positive, Negative
and Minimal Correlation
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.
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
measures what it purports to measure?
• Validity and reliability are measured as
correlation coefficients.
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.
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?
• Hertiability is calculated by determining
phenotypic variance and the magnitudes
of its two components (genetic and
environmental variance)
Calculation of Heritability
Heritability: The proportion of variance of a
phenotype that is attributable to genetic
variance.
2p = 2g + 2e
2
2
G E
2
P
Heritability =
+
=
2
P
h2
=
1
2G
2P
(h2 > 0 < 1)
Which Contributes More to Area?
Width or Length
Heritability
HERITABILITY DOES NOT
APPLY TO INDIVIDUALS!
Example: h2 of IQ = 0.6. This does not
mean that 60% of an individual’s IQ is
genetic and 40% is environmental.
Heritability
Heritability is Specific to the
Population in which it’s Measured
Minimum & maximum values of
2G

h (coefficient of heritability):
__
h
2
=
2
P
(h2 > 0 < 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.
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.
HERITABILITY ESTIMATES ARE
SPECIFIC TO POPULATIONS AND
ENVIRONMENTS IN WHICH THEY ARE
MEASURED!
Example 1: Heritability of skin color in
Norway and the United States. It’s 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.
HERITABILITY ESTIMATES ARE SPECIFIC
TO POPULATIONS AND ENVIRONMENTS
IN WHICH THEY ARE MEASURED!
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.
How to Reduce h2
1.
2.
Interbreed - this reduces 2g
Increase 2e.
How to Increase h2
1.
2.
3.
4.
outcrossing - new genes
mutation - new genes
select for rare characteristics
reduce 2e.