Analyze – Descriptive Statistics – Crosstabs|Mathematics – Statistics
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 is used to explore the relationship between two ordinal variables. It can also be used to measure association between one dichotomous nominal and one ordinal variable (Babbie et al., 2014, p. 227). 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 interval/ratio variables. This measure is similar to Gamma in how it can be understood and establish direction of association.
Value of Measures of Association 0.00 + or – .01 to .09 + or – .10 to .29 + or – .30 to .99
Strength of Association None- no assocation at all Weak- uninteresting association Moderate- worth making note of Evidence of a strong association- extremely interesting Perfect- strongest association possible 1.00
Measures of Association in SPSS
Analyze – Descriptive Statistics – Crosstabs
Place your dependent variable in the Row and your independent variable in the Column. Click “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 one ordinal and one dichotomous nominal), or Pearson’s r for interval/ratio variables.
Measures 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 by 4% if we know that 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 subjective class identification and opinion on government welfare spending is shown above. Gamma is used because both variables are ordinal. The value of .071 means that knowing a person’s subjective class status improves our estimate of his/her opinion on government welfare spending by 7%. Based on the chart above, this relationship is weak. It is also not statistically significant since .144>.05. Notice both IV and DV’s codings are consistent (all from low to high), thus the positive sign of .071 indicates IV and DV are positively associated, though not statistically significant.
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:
