Topic 6 - Correlational Research

what is a bivariate correlation

an association that involves exactly two variables

how do you describe associations between two quantitative variables

using scatterplots and the correlation coefficient r

how do you graph associations when one variable is categorical

a bar graph - shows the mean at the top of the bar

this shows the difference between group averages to see if there is an association (not rlly CC r)

statistical validity of an association claim asks about…

• factors that may have affected the scatterplot 

• correlation coefficient r 

• bar graph

• difference score that led to your association claim

• strength/precision of estimate 

• has it been replicated 

• any outliers 

• is there a restriction of range

• is the association curvilinear

______ effect sizes are more important

larger

____ effect sizes can ______ over many observations

"small”, compound

an r of 0.05 might initially be described as

very small/weak

an r of 0.10 might initially be described as

small or weak

an r of 0.20 might initially be described as

moderate

an r of 0.30 might initially be described as

fairly powerful

an r of 0.40 might initially be described as

unusually large in psych - very powerful or too good (based on a small sample)

a sample statistic will NEVER match…

the population it came from (sampling error) 

other random samples (sampling variability) 

standard error quantifies…

the typical amount we expect a particular sample statistic to vary from the true population parameter

central limits theorem

as long as a sample is large enough (often considered n≥30n), the distribution of its sample means will be approximately a normal distribution, regardless of the shape of the original population's distribution

in simple terms, what is a confidence interval

a single samples best guess about the population’s true value

what is a confidence interval made up of?

a point estimate (the SINGLE best guess within the confidence interval)

upper limit

lower limit

error bars connecting the upper and lower limit

in better terms, what is a confidence interval

a range of plausible values for the population parameter based on our sample data 

what is the BEST definition of a confidence interval

if we were to repeat the sample many times, about 95% of the resulting confidence intervals would contain the true population parameter 

correlational research designs are NOT…

investigating causal claims

experimental

how do i talk about the relationship between two group means

effect size (cohens d)

statistical significance (t-test)

cohen’s d 

the distance between means in standard deviation units

what is a moderator variable

a variable that adds nuance to association claims but does not affect internal validity

which two variables are the most important to establish for an association claim

statistical and construct validity

effect size 

describes the strength of a relationship between two or more variables 

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 which is not a straight line

as one variable increases, the level of the other variable increases and then decreases etc

can look like a bowl lwk

directionality problem

(in a correlational study) the occurrence of both variables being measured around the same time - making it unclear which variable came first

third-variable problem 

(in a correlational study) the existence of a plausible alternative explanation for the association between two variables 

spurious association

a bivariate association that is attributable only to a systematic mean differences on subgroups within the sample

the original association is not present within the subgroups

if both variables are quantitative in a bivariate correlational study, what graph is used

scatterplot

if one variable is quantitative and the other categorical in a bivariate correlational study, what graph is used

bar graph

what is used to describe the relationship in a scatterplot 

the correlation coefficient r 

what is used to describe the relationship in a bar graph

the difference between the two group means