Psychology Practical (Year 2) PS2001

Correlation and other topics

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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

• 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 -

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:

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.

Interpretation correlation

Small 0.10 – 0.29

Medium 0.30 – 0.49

Large 0.50 – 1.00

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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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Reliability Statistics

.571 .595 20

Cronbach'sAlpha

Cronbach'sAlpha Based

onStandardized

Items N of Items

SPSS Output - Alpha Value

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SPSS Output - Item Total StatisticsItem-Total Statistics

58.02 49.700 .526 .517 .498

57.66 56.260 .287 .316 .547

57.31 69.132 -.418 .591 .662

57.47 62.409 -.149 .488 .612

58.06 59.082 .040 .258 .579

58.29 61.779 -.113 .194 .599

57.87 50.407 .464 .538 .508

57.56 57.050 .207 .351 .556

57.75 52.608 .481 .539 .517

58.10 49.312 .598 .656 .489

57.46 53.911 .261 .601 .545

56.85 61.169 -.093 .687 .605

57.50 55.438 .238 .504 .550

57.32 60.603 -.054 .274 .594

56.58 58.527 .125 .381 .566

56.53 58.318 .134 .280 .565

57.24 54.987 .245 .594 .549

58.15 51.282 .469 .551 .512

58.11 48.085 .571 .805 .485

57.80 56.407 .343 .490 .544

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Scale Mean ifItem Deleted

ScaleVariance if

Item Deleted

CorrectedItem-TotalCorrelation

SquaredMultiple

Correlation

Cronbach'sAlpha if Item

Deleted

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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