What is a correlation?
Statistical technique that is used to measure and describe the relationship between two variables
- the variables are simply observed as they exist naturally in the environment
What are the three characteristics of a relationship?
1. Direction of the relationship
- the sign of the correlation, positive or negative, describes the direction of the relationship
2. The form of the relationship
- points on the scatter plot tend to cluster around a straight line that helps show the relat
The sign (+ and -) and the strength of the correlation are ______.
independent (e.g. a correlation that is either -1.00 or 1.00 still indicates a strong relationship)
Define the Pearson correlation?
Measures the degree and direction of the linear relationship between two variables
What does the numerator and denominator measure?
Numerator: the covariablility of X and Y
Denominator: variability of X and Y separately
What is shown when there is a perfect linear relationship?
every change in the X variable is accompanied by a corresponding change in the Y variable
-e.g. every time the value of X increases, there is a perfectly predictable decrease in the value of Y
- covariability is greater, and so the correlation = 0
What would be the overall correlation value when there is no linear relationship?
0 because there is no covariability
What is the sum of products (SP)?
- similar to SS
- measure the amount of covariability between two variables ( X and Y )
- SS uses squares and SP uses products
What is the relationship between the Pearson correlation and z-scores?
- z-scores identify the exact location of each individual scores
- each X value can be transformed into a z-score, Zx, using the mean and standard deviation for the set of Xs
- each Y value can be Zy
Can the SP have a 0 value?
Yes. SP can be positive, negative, or zero depending on the relationship between X and Y
Where and why correlations are used?
1. Prediction
- If two variables are known to be related in a systematic way, then it is possible to use one of the variables to make accurate predictions about the other
- e.g. SAT can predict chances of success in College (although not the only predicto
What are the four considerations when interpreting correlations?
1. Correlations simply describe the relationship between two variables. It does not explain why the two variables are related. A correlation should not and cannot be interpreted as proof of a cause-and-effect relationship between two variables
2. The valu
Does a correlation equal causation?
Hell nah.
- Although there may be a causal relationship, the simple existence of a correlation does not prove it
- e.g. although here is a strong correlation between the amount of churches and the amount of crime, the true causal variable is the size of t
What is a restricted range? Why should you be cautious of interpreting a correlation with a restricted range?
Whenever a correlation is computed from scores that do not represent the full range of possible values, you should be cautious in interpreting the correlation.
- e.g. you are interested in looking at creativity and IQ, although your sample only consists o
What are outliers? How do they affect the correlation?
An outlier is an individual with X and/or Y values that are substantially different from the values obtained for the other individuals in the data set
e.g. a set of scores are near a 0 correlation (r = -0.08). In the addition of an outlier at points (14,1
What is the coefficient of determination?
The value r squared measures the proportion of variability in one variable that can be determined from the relationship with the other variable
- e.g. correlation r = 0.80 means that r squared = 64% of the variability in the Y scores can be predicted from
A researcher finds a correlation of r 0.60 between salary and the number of years of education for a group of 40-year-old men. How much of the variance in salary is explained by the years of education?
r2 = 0.36, or 36%
What is the null and alternative hypotheses for a correlation?
H0: p = 0 (There is no population correlation.)
H1: p does not equal to 0 (There is a real correlation.)
What is the null and alternative hypotheses for a directional?
H0: p less than or equal to 0 (The population correlation is not positive.)
H1: p > 0 (The population correlation is positive.)
What is a sampling error that can occur in a correlation?
1. There is no correlation in the population (p = 0), and the sample value is the result of sampling error. Remember, a sample is not expected to be identical to the population. There always is some error between a sample statistic and the corresponding p
What is the degrees of freedom?
df = n - 2