Chapter 13 Terms

There are three conditions that affect a Pearson r, what are they?

(1) nonlinearity, (2) outliers, and (3) restriction of range.

What are the 4 assumptions for this test?

1. Random sample 2. Independence of observations 3. Normality 4. Linearity

Since the Pearson r uses interval/and or ratio variables what does this mean for the data?

Because the Pearson r uses interval and/or ratio variables, distances between points can be measured, z scores calculated, and graphs made. The graphs, called scatterplots, can be examined for the degree to which the relationship between the two variables takes the form of a straight line because the Pearson r measures the degree of linear relationship.

Describe how to interpret the strength of a Pearson correlation coefficient:

For a Pearson correlation, r is a value that ranges from -1.00 to +1.00. An r value of zero is less than a weak relationship; it means that there is no relationship between the two variables.As the r value moves further away from zero, in either a negative or positive direction, it represents a stronger relationship between X and Y.

Will using z scores instead of raw scores change the shape of the scatterplot?

NO-The pattern of the dots, the shape, is exactly the same, whether raw scores or z scores are being plotted.

____________ ____________ ____________− a statistical test that measures the degree of linear relationship between two interval/ratio-level variables.

Pearson correlation coefficient

Does correlation= Causation? Why or why not?

Statisticians love to say, "Correlation is not causation." That's because correlation between two variables does not guarantee a cause-and-effect relationship between them. A correlation between two variables only guarantees there is an association between the two variables, not that one causes the other.

What is the Pearson r?

The Pearson r is a specific measure of association.

If variables are correlated what does this mean?

This means that the variables vary together systematically, that a change in one variable is associated with a change in the other.

What are the 4 questions you should ask yourself after calculating the Pearson correlation coefficient?

Was the null hypothesis rejected? How big is the effect? How wide is the confidence interval? Did this test have adequate power?

If two variables correlate, the relationship may be a what?

cause-and-effect relationship, but it doesn't have to be.

_____________ ____ ___________ − formal name for the effect size r 2.

coefficient of determination

Measures of association are statistics that quantify the degree of relationship between two variables. If two variables are related, they are said to be what??

correlated

A ____________ ___________ is a number that summarizes the strength of the linear relationship between two variables.

correlation coefficient

________ __________− a relationship in which high scores on X are associated with high scores on Y. Also called a positive relationship.

direct relationship

_________ __________ − a relationship in which high scores on X are associated with low scores on Y. Also called a negative relationship.

inverse relationship

_________ _____________ − a relationship in which high scores on X are associated with low scores on Y; also called an inverse relationship.

negative relationship

___________ ___________ − the variable that is caused, predicted, or influenced by the explanatory variable; the variable in a relationship test, Y, that is predicted from the other variable, X. Sometimes called the dependent variable.

outcome variable

__________ ______________ − a relationship between two variables in which the value of one can be exactly predicted from the other.

perfect relationship

_______________ ____________ − a relationship in which high scores on X are associated with high scores on Y; also called direct relationship.

positive relationship

____________ ___________ − the variable in a relationship test, X, that is used to predict the other variable, Y; the explanatory variable in a correlation design.

predictor variable

The degree to which two variables vary together determines whether the relationship is _________ or __________.

strong or weak

Correlation just means what?

two variables systematically vary together.

r2 tells the percentage of what?

variability in one variable that is accounted for by the other variable. The amount of variability that can be explained ranges from 0% to 100%. The closer the size of the effect is to 100%, the stronger it is. The closer the size of the effect is to 0%, the weaker it is.

A scatterplot can also be drawn using what?

z scores, not raw scores.