Correlational Designs

Correlational Designs

Correlational Designs
–Used to measure relationships between two or more variables (r)
• Explanation
• Prediction
–No conclusions about cause and effect may be drawn

More and more researchers are making causal conclusions inappropriately.
They are making causal conclusions from correlational data, which you can NOT do.

Analyzing Data
• Correlation Coefficients
– “r”can range from -1 to +1
– Negative correlation = as one variable decreases, other increases
The negative doesn't mean the correlation is any less strong, it simply goes in the other direction.
ex. Typing skill and typing errors
– Positive correlation = as one variable increases, other also increases
ex. Standardized test scores and GPA
– Zero correlation = no relationship between the two variables

Plotting Correlational Data --Scatterplots
The more scattered the dots are on the graph, the closer the correlation coefficient gets to zero

Interpreting Correlations
• Correlation coefficient “r”
–Ranges from -1 to 1
–Indicates whether relationship is positive or negative
–Statistical significance (p-value) depends on size of relationship and size of sample

Magnitude of r Interpretation
Look at the absolute value of r to determine the magnitude of r
So what does r mean, anyway?
.00 to .40 weak relationship
.41 to .60 moderate relationship
.61 to .80 strong relationship
.81 or above very strong relationship.

More on CorrelationalDesigns
• Predicting from Multiple Variables
–Can compute several individual correlation coefficients to produce a correlation matrix (a table showing how the different variables correlate)
• Or can conduct a Multiple Regression Analysis - puts all the variables together for one coefficient (R)
–Yields coefficient R, which can be interpreted similarly to the simple correlation, r
–Also yields R2(coefficient of determination)
Coefficient of determination = Effect size estimate for correlational studies = how much of the result we can explain by the effect of all the other variables
ex. Reading Comprehension has many variables. R2 = How much of the reading comprehension can we explain through these other factors?

Imagine trying to dissect the concept “Reading Comprehension.” It is made up of several related factors, such as:
•Fluency
•Intrinsic Motivation
•Verbal IQ
•Working Memory Capacity
•Background Knowledge
If we sum up the portion of those components that uniquely overlaps with reading comprehension, we can explain a big part of reading comprehension. That is essentially what R2 in a multiple regression does.
So R2tells you, given all of the factors we’ve entered into the equation, how much of Reading Comprehension can be explained by those factors.

Other Uses of Correlational Data
• Structural Equation Modeling (aka. SEM, Path Analysis, Hierarchical, Stepwise) –maps out relationships among several variables
–Instead of lumping everything into a multiple regression, we can put them into a structural equation model; Allows researchers to see the “big picture”as well as relationships among individual variables
• Factor Analysis –how do individual variables or items in a measure combine to create “mega-
variables”
–E.g. Several items on a questionnaire might relate to your interest in a topic. Instead of treating each item as an individual variable, we combine them as one “factor”
•Path Modeling - shows how all of the factors correlated together AND how they work together to predict supportive computer use (looks like boxes with arrows going every which way showing correlational values between each combination)