Chapter 8: Bivariate Correlational Research

Question 1

Bivariate correlation

Answer 1

An association that involves exactly two variables. AKA bivariate association.

Question 2

Categorical variables

Answer 2

Values fall into categories (qualitative/nominal).

Question 3

Quantitative variables

Answer 3

Range of values (ordinal, interval, ratio).

Question 4

Scatterplot

Answer 4

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”.

Question 5

Bar graph

Answer 5

Best way to represent the correlation/association between two categorical variables. Bars represent group averages that allow you to examine the difference between groups.

Question 6

Correlation/association

Answer 6

The study involves measuring both variables.

Question 7

Examine relationship between categorical and quantitative variables

Answer 7

Can be examined using a t-test or ANOVA, depending on the # of categories.

Question 8

Tip for reading correlation statistics

Answer 8

Go down the diagonal and pick either the upper righthand corner or bottom lefthand corner - the data is duplicated.

Question 9

Examine relationship between two categorical variables

Answer 9

Use Chi-square. Will yield cross-tabulation and Chi-square tests in SPSS.

Question 10

Conclusion basis

Answer 10

Study design, not statistical analysis!!

Question 11

Primary validities for association claims

Answer 11

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?

Question 12

Construct validity questions

Answer 12

1. Operationalization: How was it measured?
2. Reliability questions: Test-retest reliability, internal reliability, inter-rater reliability.
3. Measurement validity questions: Face validity/content validity, predictive/concurrent validity, convergent validity, discriminant validity.

Question 13

Statistical validity questions

Answer 13

1. How strong is the relationship?
2. How precise is the estimate?
3. Has it been replicated?
4. Could outliers be affecting the association?
5. Is there restriction of range?
6. Is the association curvilinear?

Question 14

Examining relationship strength

Answer 14

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.

Question 15

Effect size

Answer 15

The strength of a relationship between two or more variables.

Question 16

How strong is the relationship?

Answer 16

1. All else being equal, large effect sizes are more important.
2. Small effect sizes can compound over many observations.
3. Effect sizes also allow you to compare associations to each other with benchmarks.

Question 17

How precise is the estimate?

Answer 17

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).

Question 18

95% CI does not contain zero

Answer 18

Statistically significant - the correlation is unlikely to have come from a population in which the association is zero.

Question 19

95% CI that does contain zero

Answer 19

Not statistically significant - we can’t rule out that the true association is zero.

Question 20

Replication

Answer 20

The process of conducting a study again to test whether the result is consistent. Assists in supporting a study’s statistical validity.

Question 21

Outlier

Answer 21

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).

Question 22

Restriction of range

Answer 22

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.

Question 23

Curvilinear association

Answer 23

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

Question 24

Internal validity

Answer 24

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.

Question 25

When is the 3rd variable a problem?

Answer 25

In a correlational study, the existence of a plausible alternative for the association between two variables. The 3rd variable makes it look like there is a bivariate relationship between two variables because of its presence in the data. Look at the pattern of data to determine if the relationship still exists for each group separately!

Question 26

External Validity

Answer 26

How did they get their sample? Matters less than construct and statistical validity. It’s not about the size of the sample: It’s how the sample was recruited and collected. Moderator variables address external validity.

Question 27

How important is external validity?

Answer 27

If a bivariate correlational study fails to use random sampling, it should not lead us to automatically reject the findings.
Many associations generalize to samples that are very different from the original sample. For example, older adults (Os) might score lower on both variables than college students (Ys), but the same association might still exist within each age group. So a study including young people will yield the same finding as a study using older people ie generalize to other populations.

Question 28

Moderation

Answer 28

The relationship between two variables changes depending on the level of another variable.

Question 29

Difference between moderators and third variables

Answer 29

When there is a moderator, the relationship between A and B is simply different at the levels of the new variable (e.g., the relationship between attendance and wins differs depending on residential mobility).
When there is a third variable problem, the relationship between A and B is only there because both A and B are related to a third variable (both well-being and substantive conversations are related to education). It’s a spurious relationship.

Question 30

Directionality problem

Answer 30

In a correlational study, the occurrence of both variables being measured around the same time, making it unclear which variable in the association came first. (issue of temporal precedence)

Question 31

Spurious relationship

Answer 31

A bivariate association where the original association is not present within the subgroups. (third variable problem)