Chapter 8: Bivariate Correlational Research Flashcards
Bivariate correlation
An association that involves exactly two variables. AKA bivariate association.
Categorical variables
Values fall into categories (qualitative/nominal).
Quantitative variables
Range of values (ordinal, interval, ratio).
Scatterplot
Best way to represent the correlation/association between two quantitative variables. Indicates the strength and direction (+/- or 0) of the relationship, represented by correlation coefficient “r”.
Bar graph
Best way to represent the correlation/association between two categorical variables. Bars represent group averages that allow you to examine the difference between groups.
Correlation/association
The study involves measuring both variables.
Examine relationship between categorical and quantitative variables
Can be examined using a t-test or ANOVA, depending on the # of categories.
Tip for reading correlation statistics
Go down the diagonal and pick either the upper righthand corner or bottom lefthand corner - the data is duplicated.
Examine relationship between two categorical variables
Use Chi-square. Will yield cross-tabulation and Chi-square tests in SPSS.
Conclusion basis
Study design, not statistical analysis!!
Primary validities for association claims
Construct validity: How well was each variable measured?
Statistical validity: How well do the data support the conclusions?
Also, might ask about external validity: Who do the results apply to?
Construct validity questions
- Operationalization: How was it measured?
- Reliability questions: Test-retest reliability, internal reliability, inter-rater reliability.
- Measurement validity questions: Face validity/content validity, predictive/concurrent validity, convergent validity, discriminant validity.
Statistical validity questions
- How strong is the relationship?
- How precise is the estimate?
- Has it been replicated?
- Could outliers be affecting the association?
- Is there restriction of range?
- Is the association curvilinear?
Examining relationship strength
Use Cohen’s guidelines for r.
2 associations may be statistically significant, but may differ in the strength of the relationship.
r = .12, p = .04 - SMALL
r = .35, p = .03 - MEDIUM
r = .67, p =.01 - LARGE
Larger effect sizes, if everything else is equal, are usually more important. But it depends on the context.
Effect size
The strength of a relationship between two or more variables.
How strong is the relationship?
- All else being equal, large effect sizes are more important.
- Small effect sizes can compound over many observations.
- Effect sizes also allow you to compare associations to each other with benchmarks.
How precise is the estimate?
A correlation coefficient is a point estimate of the true correlation in the population.
We use confidence intervals and p values to communicate precision.
p: Likelihood of getting a correlation of that size just by chance, assuming there is no correlation in the real world.
A larger effect size is more likely to be statistically significant (but doesn’t guarantee it).
A small sample is more easily affected by chance events.
A small correlation (r= .08) in a large sample (n = 1,000), may be statistically significant (p=.04).
A large correlation (r = . 80) in a small sample (n = 10), may be statistically non-significant (p = .36).
95% CI does not contain zero
Statistically significant - the correlation is unlikely to have come from a population in which the association is zero.
95% CI that does contain zero
Not statistically significant - we can’t rule out that the true association is zero.
Replication
The process of conducting a study again to test whether the result is consistent. Assists in supporting a study’s statistical validity.
Outlier
An extreme score that can have a very strong impact on correlation coefficients. Particularly problematic in small samples.
Look at scatterplot to identify outlier(s).
Restriction of range
Lack a full range of scores. Makes correlation appear smaller by underestimating the true correlation (decreases statistical validity). Can apply when a variable has very little variance.
Curvilinear association
The relationship between two variables is not a straight line; it might be positive up to a point and then become negative (or vice versa). Sometimes when the results suggest there is no relationship, there is in fact a curvilinear relationship.
Example: r = .01
Internal validity
This type of validity is less relevant for association claims. However, it is still good to check this out to make sure you don’t wrongly assume there is a causal relationship.
