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Methods and Measurement in
Psychology
Statistics
• THE DESCRIPTION, ORGANIZATION
AND INTERPRATATION OF DATA
DESCRIBING DATA
SCALING
The method by
which one puts
numbers to variables.
1. NOMINAL
• The most Primitive of all scales and is
included by definition in all other scales.
Criteria
• 1. NAMING OR
POINTATABLE VARIABLE
Criteria
2. NO NUMERICAL
ANALYSIS POSSIBLE
EXAMPLES:
• Drivers License
Examp.
• Social Security Number
Examp.
• Numbers On The Backs of
Football Players
Scale 2
• ORDINAL
• The objects of a variable set
can be rank ordered on some
operationally defined
characteristic.
Ordinal Scale
• Rank order in terms of the
magnitude of the variables i.e.
• More of, or less of, one
variable with respect to
another variable.
Requires the use of the nominal scale.
Examples
• Positions in a race; 1st, 2nd etc.
The Scale You Are Most Familiar
With
• GRADES
•A>B>C>D>F
Problems With Ordinal Scales
• 1. No Zero point
• 2. What is the magnitude of
the distance between units of
the scale
Example
•
•
•
•
•
•
Grades
A>B>C>D>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.
High Ordered Metric Scale
• Tries to measure the distance
between two ordinal variables
Ideally, grades are equal distance
from one another
A>B>C>D>F
• You can take the test and get
one of two grades, A or C.
• You don‘t have to take the test
and get a B.
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.
Subjective loss less than the
subjective gain
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 .
Choose B for sure
One Can Make The Same
Comparisons Between Grades BC
and CD.
• When One Makes All Of The
Possible Choices, One Sees
That The Distances Do Not
Rank Order Themselves In
Terms Of Magnitude.
Scale 3
• INTERVAL SCALE
• 1. Possesses all of the
characteristics of the Nominal
and Ordinal scale especially
rank-order
• 2. Numerically equal distance
on the an interval scale means
equal distance on the property
being measured
• There Must Be An Arbitrary
Zero.
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
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
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.
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
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
ORGANIZING DATA
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).
Histogram
Histogram of a set of scores
Frequency Polygon of the same set
scores
of
Frequency polygon plus
histogram
Measures of Central Tendency
• How common are you?
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!
Median
Where is the word Median Used in
Common Parlance?
• Keep Off The Median – used in Highway
Driving
Mean
• Average
Positively Skewed Distribution
Positively Skewed Distribution
• Note how the positive numbers pull the
mean to the right.
Measures of Variability
• How unique are you------How scores differ
one from another.
• Range
• Lowest to highest
Deviation
• The difference between a score and some
constant measure
• The constant can be any
measure, but that which
makes most sense is one of
the measures of central
tendency
Deviation score
• X - MEAN = DEVIATION
• Σ = sum of
SUM OF MEANS
• Σ (X – MEAN) = 0
How do I get rid of negative
deviation scores
• SQUARE THE DEVIATION
SCORES
•
Σ (X – MEAN)2 = 0
VARIANCE
• Σ (X –
N
•
2
MEAN)
• Is there a way to compare the
same individual on two
different tests?
Standard Scores
• z scores are called Standard
Scores
• COMPARE THE DEVIATION SCORE OF
EACH TEST TO ITS STANDARD
DEVIATION
• z = (X – MEAN)
S.D.
Characteristics of a z distribution
“z” DISTRIBUTIONS ARE
CHARACTERIZED BY THE
PARAMETERS OF A NOTRMAL CURVE
• THE S.D. OF A z DISTRIBUTION = 1
• THE MEAN OF A “z” DISTRIBUTION = 0
A NORMAL CURVES OF IQ
Normal Curves
How the mean, median and mode
are effected by skewness
Three types of normal curves
depends on range of x values
DESCRIBING THE RELATION
BETWEEN TWO VARIABLES
Correlation
• Correlation allows one to compare two
different groups using parameters of a
normal distribution.
Correlation
Coefficient
• Correlation coefficient “r” has a range from
-1 to + 1
Calculation formula
• r = Σ(zxzy) /N
Assume the following data
Use of correlation
• Correlation coefficient allows one to
account for the variation of trait 1 to the
variation of trait 2.
Caveat (warning) of correlation
data
• Does not allow for inferring
causation
INTERPRETING THE DATA
Existing Data
• One has existing data that
shows high blood pressure is a
consistent problem within
class X people.
• 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.
Causal Interpretation of Data
• Assert a hypothesis
concerning the variable of
interest.
Hypothesis0 (null)
• Drug A does not causes a
significant drop in blood
pressure for those people who
have chronic high blood
pressure
Hypothesis1 (experimental
hypothesis)
• Drug A does causes a
significant drop in blood
pressure for those people who
have chronic high blood
pressure.
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.
Random Sample of 25 people from
population X given Drug A
• Measure the drop in blood
pressure of those 25 selected
people.
Results
• Mean drop in blood pressure
after being given Drug A is 10
points with a S.D. 2.5.
Question is Drug A effective?
• Test the mean difference
between that for the population
from that of the sample.
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.
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.
One gains the unbiased estimate
by correcting the S.D
• SE (standard error) =
•
S.D./(N-1)-1/2
Critical ratio
• Critical ratio = obtained mean
•
SE
Numerically our example
• SE = SD/(N-1)-1/2
• SE = 2.5/(24)-1/2 = 2.5/4.9 = 0.51
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.
Go back to the two Hypotheses
• Reject Hypothesis0
• Accept Hypothesis1
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.