statistics for the Social Sciences forum

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Measures and Strengths of Association

Remember that while we may find two variables to be involved in a relationship, we also want to

know the strength of the association. Each type of variable has its own measure to determine

this though. Three measures will be discussed in this paper, Lambda, Gamma, and Pearson’s r.

Lambda

Lambda is a measure of association which should be used when both variables are nominal.

Essentially this means that knowing a person’s attribute on one variable will help you guess their

attribute on the other (Babbie et al., 2014).

Gamma

Gamma can be used for two ordinal variables or one nominal and an ordinal. Unlike lambda,

gamma indicates a strength of an association and a direction. The closer to -1.00 or +1.00, the

stronger the relationship, whereas the closer to 0 the weaker the relationship. You can

determine the direction of a relationship the following way:

A negative association is indicated by a negative sign. This means that as one variable increases

the other decreases- the variables are moving away from each other. For example, as social

class increases, prejudice decreases. On the other hand, a positive association, indicated by a

plus or positive sign, means that both variables change in the same direction, either increase or

decrease. For example, as social class increases, so too does prejudice or as social class

decreases, so too does prejudice.

Correlation Coefficient- Pearson’s r

Pearson’s r, also known as the correlation coefficient, is the test measure used to determine the

association between variables that measure at the interval-ration level. This measure is similar

to Gamma in how it can be understood and establish direction.

Strength of Association

Value of Measures of Association

None 0.00

Weak- uninteresting association + or - .01 to .09

Moderate- worth making note of + or - .10 to .29

Evidence of a strong association- extremely interesting + or - .30 to .99

Perfect- strongest association possible 1.00

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Measure of Association in SPSS

Analyze – Descriptive Statistics – Crosstabs

Place your dependent variable in the Row and

your independent variable in the Column.

Select Statistics to choose which test you will

run for the measure/strength of association.

You will select Lambda for nominal variables,

Gamma for ordinal variables, or correlations

for the Pearson’s r for Interval Ratio variables.

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Measure of Association in SPSS- Understanding Output

Lambda

The test above is looking at the relationship between one’s political affiliation and their race. We

look at the value .036, which is the measure when political party is the DV (see in table). This

means that we can improve our guessing of political affiliation 4% is we know the person’s race.

Based on our notes above, this is a pretty weak relationship and an uninteresting association

overall. Would we still continue? Yes, maybe. It is important to note that this is one element of

the larger picture we are searching for.

Gamma

The relationship between one’s race and their support for affirmative action policies is shown

above. Gamma is used because support for affirmative action policies is an ordinal variable even

though race is nominal. The value of -.377 means that knowing a person’s race would improve

our estimate of his or her preference to affirmative action by 37%. Based on the chart above,

this relationship is strong and extremely interesting. The negative sign would be significant and

considered if the IV were ordinal and able to ‘move’ in any direction. However, a person can not

‘move’ among race categories.

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Pearson’s r

For this test we are looking at the correlation between a person’s age and the number of hours

they spend watching television. Keep in mind that the survey only questioned adults over the

age of 18. So, if you are interested in seeing number of hours for children, this is not a good data

set for that. We want to square the correlation here (.130 x .130) to determine the coefficient of

determination. This new measure = .0169. We interpret this as approximately 2% of the

variation in time watching television is determined by a person’s age.

Fast-forward Thinking

This data, coupled with the statistic from the test of significance (ex. Chi-square, t Test, or

ANOVA), will help you to interpret your findings:

Strength of Association

Statistical Significance

Interpretation

Comment

Strong Significant Knowledge of the IV improves prediction of DV, AND the relationship can be generalized from the sample to the population.

Look what I have discovered.

Strong Nonsignificant Although knowledge of the IV improves prediction of the DV in the sample, the relationship cannot be generalized to the population.

Close, but no luck…

Weak Significant Knowledge of the IV is of little help in predicting the DV but may be generalized to the population.

That’s no big deal.

Weak Nonsignificant Knowledge of the IV provides little help in the prediction of the DV in the sample and cannot be generalized to the population.

Back to the drawing board completely.

Copied from Babbie, E. et al. (2013). Adventures in Social Research. (8th ed.). Thousand Oaks:

SAGE.