chap 8

bivariate correlation

is an association that involves exactly two variables.

effect size

a quantitative measure of the magnitude of a difference between groups or the strength of a relationship between variables. While a p-value tells you if a result is likely due to chance, effect size tells you if the result is practically meaningful or impactful in the real world.

cohen-d:These measure the absolute difference between group averages, typically expressed in standard deviation units

r:These measure the absolute difference between group averages, typically expressed in standard deviation units

how r works

• Strength = how far the number is from 0

• Direction = whether the number is positive or negative

r = +0.26

• Direction: positive

• Strength: weak (because 0.26 is close to 0)

r = -0.80

• Direction: negative

• Strength: strong (because 0.80 is far from 0)

construct validity

How Well Was Each Variable Measured?

-Does the measure have good reliability? Is it measuring what it’s intended to measure? What is the evidence for its face validity, its concurrent validity, its discriminant and convergent validity? For example, you could ask whether the 4-item measure of marital satisfaction used in the Cacioppo study had good internal reliability and whether it had convergent validity. Does it correlate with other measures of marital happiness?

statistical validity

-factors that might have affected the scatterplot, correlation coefficient r, bar graph, or difference score that led to your association claim. You need to consider the strength and precision of your estimate, if it has been replicated, any outliers that might have affected the overall findings, restriction of range, and whether a seemingly zero association might actually be curvilinear.

confidence interval

the range of values that are plausible for the true population correlation.

• Higher confidence → wider interval

• Lower confidence → narrower interval

• Statistically significant CI: does not cross 0
  → e.g. [.04, .45] or [-.50, -.10]

• Not statistically significant CI: does include 0
  → e.g. [-.05, .30]

what true population being zero means

When the true population correlation (ρ) = 0, it means:

In the entire population, there is no linear relationship between the two variables.

summary

r=The relationship you actually calculate from your data.

true population correlation= The real relationship in the entire population.

CI= A range of plausible values for the true population correlation (ρ)

p=How surprising your result is if there is actually NO relationship in the population (ρ = 0)

restriction of range

In a bivariate correlation, the absence of a full range of possible scores on one of the variables, so the relationship from the sample underestimates the true correlation.

curvilinear association

An association between two variables that is not a straight line; instead, as one variable increases, the level of the other variable increases and then decreases (or vice versa). See also negative association, positive association, zero association.

moderator

A variable that, depending on its level, changes the relationship between two other variables.

spurious association

A bivariate association that is attributable only to systematic mean differences on subgroups within the sample; the original association is not present within the subgroups.

cross-lag correlations

shows whether the earlier measure of one variable is associated with the later measure of the other variable. Cross-lag correlations thus address the directionality problem and help establish temporal precedence.

autocorrelational

In a longitudinal design, the correlation of one variable with itself, measured at two different times

criterion variable

another name for a dependent or outcome variable in statistics. It is the "effect" or "outcome" being studied in relationship to the predictors.