four basic types of measurement: categorizing –nominal ranking –ordinal determination of the...

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 guessesTwo words - one guessFour words - two guessesEight 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)

x

y

abscissa

ordinate

(frequency)

mode

• Bar graph - histogram• Mode - summary statistic

•Ordinal scales: - Numbers convey relative

magnitude.– rank of one usually assigned to

highest magnitude– can’t add or subtract ranks, e. g.,

ranks of weightRank: Weight (lbs.)1 2002 203 34 25 .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 i

N

= 2 + 4 + 6 + 8 + 10

5

= 305

= 6

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

MEANGiven the raw data: 2, 4, 6, 8, 10

Mean Deviation =

Mean Absolute Deviation =

Variance =

Standard Deviation =

Σ ä ã X − X i ë í

N = 0

4 + 2 + 0 − 2 − 4 5 = 0 5 = 0

Σ ä ã X − X i ë í

N 4 + 2 + 0 + 2 + 4

5 = 125 = 2 . 4

Σ ä ã X − X i ë í 2

N

σ 2 = σ = Σ ä ã X − X i ë í

2

N

40 / 5 = 8 = 2 . 82

σ 2

σ

MEASURING WITH THE STANDARD

DEVIATION: Z-SCORES

Given the raw data: 2, 4, 6, 8, 10

if X = 6 andσ = 8

Z 4 = 4 − 6 8

= − 2 8 = − . 709 Z10 =

10 − 6 8

= 4 8 = 1 . 42

Z 2 = 2 − 6 8

= − 4 8 = − 1 . 42 Z8 =

8 − 6 8

= 2 8 = . 709

CORRELATION

z x i = rxy C zy i

= r xy( x y − xy i

σ y

)

Normal Distribution

Z y

Z x

+1.0

or

r = +1.0 r = -1.0

Zy

Zx

Zy

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)

σ2

σ2σ2

σ2G

P

E

P

+ = 1

σ2

σ2G

P

=h2

(h2 > 0 < 1)Heritability =

Calculation of Heritability

σ2p = σ2

g + σ2e

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

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 h (coefficient of heritability):

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.

σ2

σ2

G

P

=h2

(h2 > 0 < 1)__

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. Interbreed - this reduces σ2g

2. Increase σ2e.

How to Increase h2

1. outcrossing - new genes2. mutation - new genes3. select for rare characteristics4. reduce σ2

e.