What is the relationship between the coefficient of determination and the correlation coefficient quizlet?

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Terms in this set (32)

Magnitude

An indication of the strength of the relationship between two variables.

Magnitude: +/- .70 - 1.00

Strong relationship

Magnitude: +/- .30 - .69

Moderate relationship

Magnitude: +/- .00 - .29

Weak relationship

Magnitude: +/- .50

Very good in Psychology

Magnitude: -1.00 - +1.00

Rare, not likely to happen in Psychology

Correlation Coefficient

Measures the degree of a relationship on a scale of 0 to 1.00

Squared Correlation is also known as

Coefficient of Determination

Coefficient of Determination (Squared Correlation)

Measures the proportion of variability in the data that is explained by the relationship between X and Y. (this is r-squared)

Positive relationship

An INCREASE in one variable accomapnied by an INCREASE in the other variable - indicated by a positive correlation coefficient.

Negative relationship

An INCREASE in on variable is accompanied by a DECREASE in the other variable - indicated by a negative correlation coefficient.

Assumption of Causality

The assumption that a correlation indicates a causal relationship between the two variables

Directionality

The inference made with respect to the direction of a causal relationship between two variables.

Correlation describes:

A relationship, but DOES NOT demonstrate causation.

Third-Variable Problem

The problem of a correlation between two variables being dependent on another (third) variable.

Third-Variable Problem Example

There may be a correlation between homeless population and crime rate in that both tend to be high or low in the same locations.

Is crime causing homelessness?

Are homeless populations causing crimes?

Third variables:
Drug abuse
Unemployment

Partial Correlation

A correlational technique that involves measuring three variables and then statistically removing the effect of the third variable from the correlation of the remaining two variables.

Restrictive Range

A variable that is truncated and has limited variability.

Curvilinear Relationships

When a correlation coefficient does not adequately indicate the degree of relationship between the variables. (ex. Amount of Anxiety and Performance graph)

Outliers

Produce a disproportionately large impact on the correlation coefficient. (on a scatter plot, point is clearly different from all the other points)

r, in a sample

An estimate of a population coefficient of correlation (ρ-rho)

ρ^2 (rho)

The fraction of the variance in Y due to change in X (as opposed to random variation)

Correlations involve the comparison of two measures to see:

-Whether or not there is a relationship
-The strength of the relationship magnitude
-The direction of the relationship
-Whether you can predict a score (Y) from a score (X)

Spearman's rho (ρ):

A coefficient use when at least one variable is measured on an ordinal scale (rank-order data)

Point-Biserial Correlation

A coefficient is used when one variable is interval/ratio and one variable is dichotomous/nominal

Phi coefficient

A coefficient is used when both variables are dichotomous and nominal.

Y is the ________________ variable

Dependent variable (y-axis)(variable you are trying to predict)

X is the _________________ variable

Independent variable (x-axis) (variable from which you are predicting)

Pearson Correlation (Pearson's r)

Determines the strength of the linear relationship between two variables. (measure the degree and the direction of the linear relationship between two interval/ratio variables)

Perfect linear relationship

-Every change in X has a corresponding change in Y
-Correlation must be between -1.00 or +1.00
-The formula for r is based on the idea of covariance

Covariance

How much do X and Y "vary together"

Steps for calculating r:

1. Make your table
2. Fill in the table
3. Sub the summed values into the equation for r
4. Solve for r

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