PSC 041 Chapter 8: Bivariate Correlational Research

bivariate correlation

an association that involves exactly two variables

how to describe associations between two quantitative variables

scatterplots and correlation coefficient r

reading correlation coefficient

+/- association

strength or "how much"; strong = close to 1 or -1

mean

the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores

graphic when one variable is categorical

use a bar graph, not a line graph

bar graph vs. line graph

Line graph represents each person

Bar graphs show the mean of each group and the difference btw the means is the association

correlation/association data

-two variables

-always measured

-supported by study design, not a specific statistic

Association most important validities

construct and statistical and statistical

Construct Validity for Association Data

-for each variable

-operational definitions--how well does it measure the construct?

Statistical Validity

-how well does data support the conclusion?

-strength and precision of measurement, replications, outliers, range restrictions, and if a zero association may be curvilinear

Questions for Statistical Validity

-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

effect size

the magnitude, or strength, of a relationship between two or more variables

-indicates the importance of the relationship (though you need context)

-larger = more important & vise versa

small effect sizes can compound over many observations

true

especially over time or may people

Benchmarks for Effect Size

r= 0.2 is typical for psych

rare for r= 0.4

be skeptical for larger associations

small sizes may not have precise estimates

Effect Size Range

0.05 very small or very weak

0.1 small or weak

0.2 moderate

0.3 fairly powerful effect

0.4 usually large in psych--either very powerful or possibly too good to be true (based on small sample size)

A correlation coefficient is a

point estimate of the true correlation in a population

What do you use to find the preciseness of correlation coefficients

95% confidence interval

Sample Size and Precision

-small samples have wider (less precise) CIs

-large samples have narrower (more precise) CIs

can be used to predict for future studies; more stable

CIs that don't contain zero

are statistically significant

statistically significant

the conclusion assigned when p < 0.05, when it is unlikely the result came from the null hypothesis population; when the 95% CI does not contain zero & the true relationship is unlikely to be zero

CIs that do contain zero

can't rule out that the true association is zero

not statistically significant

replication

the process of conducting a study again to test whether the result is consistent

outlier

a score that stands out as either much higher or much lower than most of the other scores in a sample

-exerts disproportionate influence

-have the most influence when the sample size is small

when are outliers most problematic for bivariate correlations?

when they involve extreme scores on both 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

-use the statistical technique correlation for restriction of range to estimate the missing values

-usually makes correlations look smaller

-can apply when one variable has very little variance

curvilinear association

an association between two variables which is not a straight line; instead, as one variable increases, the level of the other variable increases and then decreases (or vice versa)

-r only measures the slope of a straight best fitting line

casual criteria

covariance, temporal precedence, internal validity

directionality problem

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

-temporal precedence

third variable problem

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

-internal validity

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.

-not necessary for association claims

-a third variable will not always impact the correlation

-internal validity

external validity

-sampling techniques

-add studies to get generalizability

-moderators

moderator

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

-relationship differs when there is a moderator

hypothesis

-An idea that you can test

-Framed as a statement not a question

-A prediction about the relationship between the variables of interest. Be sure to name the two variables (and their levels, if appropriate)

Correlation relationships vs Causational relationships

correlational:

-The experimenter is not in control of either variable

-variables are measured

causational:

-Experiment must be in control (manipulates) the "cause" variable

-Describe how changes in one variable brings about (or causes) the change in the other variable

null hypothesis

-no difference in the outcome variable as a function on the predictor variable

-generally means there are no differences between groups or the one group of interest is not different from "zero" or "chance".

non-directional hypothesis

there is a relationship between the two variables; does not specify the direction of the relationship

Directional hypothesis

there is a relationship between the variables and describes the relationship

What differs between correlational and causational relationships?

format/study design/methodology

Are graphs from correlational and causation studies fundamentally different?

No, you can't tell from a graph which kind it is.

What matters is the methodology (where you got the data)

There's no causation without....

manipulation

Are casual relationships are correlations, but not all correlations have causal relationships

true

3 criteria for causation

1. Covariance (correlation; true for correlation & causal studies)

2. Temporal precedence (directionality problem)

3. Internal validity (third-variable problem)

-not as important for correlational studies, but needed to understand the results

Ways to get correlational data

-Naturalistic observation

-Archival research

-Survey

Correlations are not always visualized as a scatter plot

true

If one variable is categorical, the data may be plotted using bar graphs

correlation coefficient

-Statistic used to describe the relationship between two variables

-Used when both variables are on a continuous** scale (usually)

-Research can be correlational or experimental

Correlation Coefficient Review

-Possible values range from -1 to +1

-Absolute value = strength of the relationship

-Sign = the direction of the relationship (+/-)

-A larger r -value indicates higher confidence in the prediction between the two variables (i.e., if you know the x value, you will have a good estimate of the y value).

The best fit line/regression is the same line across all correlations but the strength of the r is determined by the spread of the points around the line (closeness to the line)

true

Statistical Validity: What Does a Small Effect Size Mean?

-Small correlations accumulate over time and people (snowball)

-Static or long term

-Statistical significant and practical significance

Sample Size and Outliers

-No matter the sample size, the trend/distribution/spread should still stay the same

-Frequency not true of real data

-Outliers in a small sample size can skew the trend & the interpretation of data

-Not corrected for by the other points

-Large sample size protects you for a skewed interpretation of the data from extreme values

Reasons for Outliers

-Measurement Error: Inaccurate data collection methods or instruments

-Extreme Values: Naturally occurring extreme values in the population, such as exceptionally high or low scores

-Sampling Bias: Non-representative samples can include individuals who differ significantly from the rest of the population

-Unusual Conditions: Unique circumstances affecting certain participants, such as stress or illness

-Human Error: Errors made by researchers or participants

-Variability in Human Behavior: Psychological data often involves complex human behaviors that can vary widely

reasons for correlations

-Causal: A change in X causes a change in Y

-Direct: X is related to Y and Y is related to X in a direct relationship

-Spurious: Both X and Y are related to some other variable and are only related to each other in a spurious relationship

-Coincidence: Perhaps it is coincidence