Methods and Measurement in Psychology

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Methods and Measurement in Psychology
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Statistics

• THE DESCRIPTION, ORGANIZATION
• AND INTERPRATATION OF DATA

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DESCRIBING DATA
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SCALING

• The method by
• which one puts
• numbers to variables.

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1. NOMINAL

• The most Primitive of all scales and is included
  by definition in all other scales.

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Criteria

• 1. NAMING OR POINTATABLE VARIABLE

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Criteria
2. NO NUMERICAL ANALYSIS POSSIBLE
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EXAMPLES

• Drivers License

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Examp.

• Social Security Number

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Examp.

• Numbers On The Backs of Football Players

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Scale 2

• ORDINAL

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• The objects of a variable set can be rank ordered
  on some operationally defined characteristic.

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Ordinal Scale

• Rank order in terms of the magnitude of the
  variables i.e.

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• More of, or less of, one variable with respect to
  another variable.

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• Requires the use of the nominal scale.

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Examples

• Positions in a race 1st, 2nd etc.

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The Scale You Are Most Familiar With

• GRADES
• A gt B gt C gt D gt F

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Problems With Ordinal Scales

• 1. No Zero point

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• 2. What is the magnitude of the distance between
  units of the scale

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Example

• Grades
• A gt B gt C gt D gt F
• What is the last upper number
• What is the last lower number
• How much less is a B from an A.
• How much less is a C from a B etc.

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High Ordered Metric Scale

• Tries to measure the distance between two ordinal
  variables

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Ideally, grades are equal distance from one
another
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A gt B gt C gt D gt F

• You can take the test and get one of two grades,
  A or C.

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• You dont have to take the test and get a B.

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If One Takes The Test

• The subjective gain of getting a B is so small
  relative to getting a C that one would gamble for
  the A.

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Subjective loss less than the subjective gain
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If One Takes the Assured B

• The subjective loss of the B by taking the test
  is too large relative to the gain of getting an
  A. One would not gamble for the A.
• The distance AB is shorter than the distance BC .

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Choose B for sure
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One Can Make The Same Comparisons Between Grades
BC and CD.
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• When One Makes All Of The Possible Choices, One
  Sees That The Distances Do Not Rank Order
  Themselves In Terms Of Magnitude.

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Scale 3

• INTERVAL SCALE

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• 1. Possesses all of the characteristics of the
  Nominal and Ordinal scale especially rank-order

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• 2. Numerically equal distance on the an interval
  scale means equal distance on the property being
  measured

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• There Must Be An Arbitrary Zero.

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Examples

• Centigrade and Fahrenheit temperature scale.
  Both based on the Freezing And boiling point of
  water.

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The underling concept is mean molecular motion.

• Centigrade scale starts at zero and has 100 equal
  intervals.
• Fahrenheit scale starts at 32 and ends at 212
  with 180 equal appearing intervals

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The Distances Between Rank Orders Is Equal

• The distance from 20 degrees to 30 degrees is the
  same as the distance between 75 degrees and 85
  degrees, or
• -75 degrees and -85 degrees.
• There Are Ten Degrees Of Difference

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One Can Use Most Of The Mathematical Operations
With Interval Scales

• ADD, Subtract, Multiply, Divide, Square, and Take
  Square Root.
• Will be used in most of the statistical methods
  covered below.

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Ratio Scale

• The most powerful of the scale.
• An Absolute Zero.
• Includes Nominal, Ordinal and Interval Scales
• Equal Intervals.
• The Ratio Between Intervals Are Equal

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Example

• Kelvin or Absolute Zero Temperature scale.
  Defined as that point where all molecular motion
  (Brownian movement) stops.
• There is no true Ratio scale in Psychology

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ORGANIZING DATA
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DATA ORGANIZATION

• Frequency Distribution
• A distribution that counts the number of
  individuals obtaining a given score and arranges
  those counts in a rank order from high to low or
  low to high (ordinal scale).

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Histogram
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Histogram of a set of scores
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Frequency Polygon of the same set of scores
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Frequency polygon plus histogram
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Measures of Central Tendency

• How common are you?

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MODE

• Common Use Pie Ala Mode, the hump of ice cream
  on the pie!
• Mode The most frequently measured score!
• Distribution of scores can have more than one
  hump!

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Median
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Where is the word Median Used in Common Parlance?
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• Keep Off The Median used in Highway Driving

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Mean

• Average

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Positively Skewed Distribution
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Positively Skewed Distribution

• Note how the positive numbers pull the mean to
  the right.

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Measures of Variability

• How unique are you------How scores differ one
  from another.

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• Range
• Lowest to highest

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Deviation

• The difference between a score and some constant
  measure

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• The constant can be any measure, but that which
  makes most sense is one of the measures of
  central tendency

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Deviation score

• X - MEAN DEVIATION

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• S sum of

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SUM OF MEANS

• S (X MEAN) 0

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How do I get rid of negative deviation scores

• SQUARE THE DEVIATION SCORES

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• S (X MEAN)2 0

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VARIANCE

• S (X MEAN)2
• N

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• Is there a way to compare the same individual on
  two different tests?

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Standard Scores

• z scores are called Standard Scores

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• COMPARE THE DEVIATION SCORE OF EACH TEST TO ITS
  STANDARD DEVIATION

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• z (X MEAN)
• S.D.

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Characteristics of a z distribution

• z DISTRIBUTIONS ARE CHARACTERIZED BY THE
  PARAMETERS OF A NOTRMAL CURVE

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• THE S.D. OF A z DISTRIBUTION 1

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• THE MEAN OF A z DISTRIBUTION 0

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A NORMAL CURVES OF IQ
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Normal Curves
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How the mean, median and mode are effected by
skewness
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Three types of normal curvesdepends on range of
x values
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DESCRIBING THE RELATION BETWEEN TWO VARIABLES
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Correlation

• Correlation allows one to compare two different
  groups using parameters of a normal distribution.

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Correlation Coefficient

• Correlation coefficient r has a range from -1
  to 1

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Calculation formula

• r S(zxzy) /N

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Assume the following data
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Use of correlation

• Correlation coefficient allows one to account for
  the variation of trait 1 to the variation of
  trait 2.

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Caveat (warning) of correlation data

• Does not allow for inferring causation

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INTERPRETING THE DATA
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Existing Data

• One has existing data that shows high blood
  pressure is a consistent problem within class X
  people.

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• With in the class of X people, high blood
  pressure has a mean of 50 points higher than
  normal and a S.D. of 5 points.

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Causal Interpretation of Data

• Assert a hypothesis concerning the variable of
  interest.

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Hypothesis0 (null)

• Drug A does not causes a significant drop in
  blood pressure for those people who have chronic
  high blood pressure

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Hypothesis1 (experimental hypothesis)

• Drug A does causes a significant drop in blood
  pressure for those people who have chronic high
  blood pressure.

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Draw a sample of X people with high blood pressure

• Note here, one already has for their disposition
  the Mean and S.D. of higher blood pressure for
  the Population of X people.

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Random Sample of 25 people from population X
given Drug A

• Measure the drop in blood pressure of those 25
  selected people.

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Results

• Mean drop in blood pressure after being given
  Drug A is 10 points with a S.D. 2.5.

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Question is Drug A effective?

• Test the mean difference between that for the
  population from that of the sample.

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Calculate a z score

• Since one has sampled the population of X, one
  wants to assure oneself that one has an unbiased
  estimate of the population that is represented by
  the sample.

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What calculating the z score does

• The calculation of the z score forces the
  assumption that the mean of the blood drop is 0
  and a S.D. of 1.

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One gains the unbiased estimate by correcting the
S.D

• SE (standard error)
• S.D./(N-1)-1/2

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Critical ratio

• Critical ratio obtained mean
• SE

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Numerically our example

• SE SD/(N-1)-1/2
• SE 2.5/(24)-1/2 2.5/4.9 0.51

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Sample Population mean divided by SE

• 10 0/SE 10/0.51 19.61
• From a z distribution if the ratio is larger than
  1.96 one calls that change significant.

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Go back to the two Hypotheses

• Reject Hypothesis0
• Accept Hypothesis1

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Confidence interval

• A confidence interval is saying that within 2 SE
  of the mean difference 95 of the time one would
  find the mean of the sample.