Transcript Correlation etc.

Psychology Practical (Year 2) PS2001
Correlation and other topics
Correlation
A brief review
• It is a level of analysis between description and
explanation
– It can allow prediction
• Examination of relationships between two variables (for
same individual)
• If a relationship (association) exists then this should
allow us to predict the behaviour on one variable from the
measure of behaviour on another variable (regression)
• A measure of consistency of relationship
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Correlation
Key points
• No manipulation or control –not an experiment
– Can control when and where measured and sample,
but no 'direct' control exercised
• Variables measured 'in situ'
• Statistically you may find a relationship is indicated
between two variables, but you cannot determine ‘cause
and effect’ –
– There may be a number of other, unmeasured
variables that could be interrelated and responsible
for the relationship found
– There may be an effect, but a correlation will not
prove this - need an experimental design
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Techniques
• For interval data:
– Pearson's Product-Moment Correlation – this is the
best known correlation and the most used.
• For categorical data:
– Spearman's Rank Correlation Coefficient
– Kendall's tau statistics
• In general:
– Correlation examines the degree to which the two
variables change together: covary
• Partial correlation:
– Uses Pearson’s
– Allow examination of a relationship between two
variables while at the same time controlling for
another variable
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Characteristics of a Relationship
• Direction
– Positive (+) or negative (-)
• Form
– Linear or non-linear
• Degree
– How well data fit the form (consistency or
strength)
– From 0 (no fit) to 1 (perfect fit)
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Visual Characteristics: an example
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•
•
•
•
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2 variables - X & Y
X on horizontal axis
Y on vertical axis
Look for a 'form' made by
the points representing the
scores
• Rising to right is +
• Falling left to right is -
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6
4
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0
0
2
4
6
8
10
Language Score
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Positive linear
correlations –
these are based
on 1000 pairs of
numbers. Each
square with a
number
corresponds to its
mirror graphical
representation.
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Strength of a correlation
Cohen (1988) suggested the following interpretations of correlations:
Interpretation
correlation
Small
0.10 – 0.29
Medium
0.30 – 0.49
Large
0.50 – 1.00
But this depends on context. If this is in the context of a very highly
controlled physics experiment one would expect high correlations,
but not in the context of testing a general population’s attitudes. So
judgements about the extent or strength of a correlation should if
possible be made in the context of similar studies.
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Why Use Correlations?
• Prediction
– A relationship allows predictions to be made of one
behaviour from another
• Validity
– To demonstrate a test scale is valid by showing a
significant relationship between it and another
accepted scale for a related construct
• Reliability
– To show consistency of measurement on two
occasions (indirectly for internal consistency)
• Theory verification
– Use to support hypotheses that predict
relationships between variables
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Spearman's Correlation rS
• A non-parametric version of Pearson's correlation
coefficient
• Uses ordinal data that is given a ranking to create
numerical values
• Same general comments apply to this form of
correlation as to Pearson's
• Can be used for ordinal data as can identify non-linear
relationships - a measure of consistency independent
of its specific form
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Correlation Matrix
• SPSS produces a matrix to present correlation coefficients between
variables, if you are reporting a number of correlations, you should
use a table in the form of a matrix
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Partial Correlation
• Similar to Pearson’s
• Allows control of an additional variable
• Usually one thought to influence the two other variables
of interest
• Removal of this confounding variable permits better
examination of relationship between two variables of
interest
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Two Correlation Coefficients
• Separate for two groups
– Use Split File procedure
• Comparing
– Use separate coefficients (and n) to determine if two r values
differ significantly
– Convert r values to z values (table)
– Calculate Zobs from formula
– Is Zobs value equal to or greater than 1.96 - at either end of the
distribution?
– If yes then two coefficients differ significantly
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Cronbach's Coefficient Alpha
• Measures internal consistency
• Estimate of reliability of a scale
• How well the items measure the same underlying
construct
• Examines average correlation between all items in
the scale
• Value from 0 to 1 (highest reliability)
• Expect a minimum value of .70 for a moderate to
large scale
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SPSS Output - Alpha Value
Reliability Statistics
Cronbach's
Alpha
.571
Cronbach's
Alpha Based
on
Standardized
Items
.595
N of Items
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SPSS Output - Item Total Statistics
Item-Total Statistics
Computer Q1
Computer Q2
Computer Q3
Computer Q4
Computer Q5
Computer Q6
Computer Q7
Computer Q8
Computer Q9
Computer Q10
Computer Q11
Computer Q12
Computer Q13
Computer Q14
Computer Q15
Computer Q16
Computer Q17
Computer Q18
Computer Q19
Computer Q20
Scale Mean if
Item Deleted
58.02
57.66
57.31
57.47
58.06
58.29
57.87
57.56
57.75
58.10
57.46
56.85
57.50
57.32
56.58
56.53
57.24
58.15
58.11
57.80
Scale
Variance if
Item Deleted
49.700
56.260
69.132
62.409
59.082
61.779
50.407
57.050
52.608
49.312
53.911
61.169
55.438
60.603
58.527
58.318
54.987
51.282
48.085
56.407
Corrected
Item-Total
Correlation
.526
.287
-.418
-.149
.040
-.113
.464
.207
.481
.598
.261
-.093
.238
-.054
.125
.134
.245
.469
.571
.343
Squared
Multiple
Correlation
.517
.316
.591
.488
.258
.194
.538
.351
.539
.656
.601
.687
.504
.274
.381
.280
.594
.551
.805
.490
Cronbach's
Alpha if Item
Deleted
.498
.547
.662
.612
.579
.599
.508
.556
.517
.489
.545
.605
.550
.594
.566
.565
.549
.512
.485
.544
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SPSS Output - Item Total Statistics
• Corrected item-total correlation
– Correlation of item to overall scale score
– Low or ‘opposite direction’ item correlations suggest
ambiguous statement, statement that poorly reflects
construct, or possibly failure to correctly score item
• Alpha if item deleted
– Overall alpha value of scale if that item is deleted
– Items that if omitted would improve alpha should be
examined - will be same items indicated by previous
column output
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