PSYC*1010 Chapter 15: Correlation Flashcards
What is correlation?
A statistical technique used to measure and describe the relationship between two variables
How many scores are required from each participant when computing correlation?
Two (one from each variable)
T or F: There is no attempt to manipulate or control variables in a correlation study.
True
What does the sign (+/-) of a correlation indicate?
The direction of the relationship
What is a positive correlation?
A correlation where two variables tend to change in the same direction
What is a negative correlation?
A correlation where two variables tend to change in opposite directions
T of F: The direction of a correlation is related to its strength.
False
What is the most common use of correlation?
To measure straight-line/linear relationships
What does the numerical value of a correlation indicate?
The strength/consistency of a correlational relationship
What is a perfect correlation?
A relationship where the actual data points perfectly fit the specific form being measured
What does a correlation of 1.00 indicate?
A perfect correlation
What does a correlation of 0 indicate?
No consistency between variables
What does the Pearson correlation measure?
The degree and direction of the liner relationship between two variables
What is the notation for the Pearson correlation of a sample?
r
What is the notation for the Pearson correlation of the population?
rho (ρ)
How is the Pearson correlation computed?
By dividing the covariability of X and Y by the variability of X and Y together
What is covariability?
The degree to which two variables vary together
What does the sum of products of deviations measure?
The degree of covariability between two variables
What notation is used to describe the sum of products of deviations
SP
When using a table to calculate SP and the Pearson correlation, what are the headings of each column?
X, Y, (X-M_X), (Y-M_Y), (X-M_X)^2, (Y-M_Y)^2, (X-M_X)(Y-M_Y)
What happens when a constant value is added or subtracted from each X value?
The pattern of data points would shift to the right or left, but correlation stays the same
What happens when a constant value is added or subtracted from each Y value?
The pattern of data points would shift up or down, but correlation stays the same
What happens when each X or Y value is multiplied or divided by a constant positive?
Neither the pattern nor the correlation change
What happens when each X or Y value is multiplied or divided by a constant negative?
A mirror image of the original pattern is produced and the sign of the correlation changes, but the numerical value doesn’t
What is regression?
The process of using relationships to make predictions
What is a common technique for demonstrating validity?
Correlation
T or F: Correlations can’t be used to help measure and describe reliability.
False. They can.
In terms of correlation, what indicates a good level of reliability?
A strong positive correlation
In terms of correlation, what indicates poor reliability?
A weak correlation
If a measurement procedure produces stable and constant measurements, what is it considered to be?
Reliable
T or F: The prediction of a theory could be tested by determining the correlation between two variables.
True
What are four considerations to bear in mind when encountering a correlation?
- Correlation is not proof of a cause-and-effect relationship
- The value of a correlation can be greatly affected by the range of scores in the data
- One or two outliers can have a dramatic effect on the value of a correlation
- Correlation shouldn’t be interpreted as a proportion
What is the most common error in interpreting correlations?
Assuming that a correlation necessarily implies a cause-and-effect relationship
What is needed to establish a cause-and-effect relationship?
A true experiment being conducted
T or F: The correlation within a restricted range could be completely different from the correlation obtained from a full range.
True
What is an outlier?
An individual with X and/or Y values that are substantially different from the values obtained for the other individuals in the data set
What is the correlation of determination?
The effect size of a correlation
What does the correlation of determination measure?
How much of the variance in one variable can be determined from its relationship with the other variable
What is the notation for the correlation of determination?
r^2
What does an r^2 value of 0.01 to 0.08 indicate?
A small effect
What does an r^2 value of 0.09-0.24 indicate?
A medium effect
What does an r^2 value of 0.25 or greater indicate?
A large effect size
What does “regression toward the mean” refer to?
The fact that when there is a less-than-perfect correlation between two variables, extreme scores (high or low) for one variable tend to be paired with less extreme scores (closer to mean) on the second variable
What are the null and alternate hypotheses for a two-tailed correlation test?
H0: ρ = 0 (no population correlation)
H1: ρ ≠ 0 (population correlation present)
What are the null and alternate hypotheses for a one-tailed correlation test predicting a positive relationship?
H0: ρ ≤ 0 (population correlation not positive)
H1: ρ > 0 (population correlation positive)
What are the null and alternate hypotheses for a one-tailed correlation test predicting a negative relationship?
H0: ρ ≥ 0 (population correlation not negative)
H1: ρ < 0 (population correlation negative)
When a nonzero correlation is obtained from a sample, what are the two interpretations the hypothesis must decide between?
- There is no correlation in the population and the sample value is the result of sampling error (H0)
- The nonzero sample correlation accurately represents the nonzero correlation in the population (H1)
How are degrees of freedom calculated for correlations?
df= n-2
