Chapter 13 STATS TopHat

"post hoc meaning" refers to

"after this therefore because of this"

Visual estimation is also known as

"eyeballing"

_______ correlations vary between ___ and _____ ; and can be positive or negative

0 and +- 1

Correlations are displayed in a concise number between _____ and _____

1 and -1

What are the 3 questions one needs to ask when determining correlation?

1. Does a correlation exist? 2. If a correlation exists, how strong is it? 3. If a correlation exists, what is its pattern or direction?

How to calculate the remaining percentage (the unexplained variation):

100 - r^2

If r^2 = .20 then that means there is a ______% variation

20

Suppose that we calculated a r(8)= .21 (n=15). Do we reject or accept the null hypothesis?

Accept

Correlation is also known as a _________ ________

Correlation Coefficient

________ and ______ are related descriptive statistical techniques that are often used in conjunction with one another

Correlation and Regression

__________ scatterplot is when we have a correlation coefficient of 0.00

Curvilinear Scatterplot

In scatterplots, the DV is located on the ___ axis and the IV on the _____ axis

DV: y axis IV: x axis

_________ _______ indicates that we have gathered observable evidence using our senses

Empirical Support

T/F A correlation coefficient distinguishes between independent and dependent variables.

False

T/F The standard error of the estimate is a summary statistic that expresses our overall degree of error in predicting values of x based upon values of y

False

T/F Perfect correlations are extremely common

False, we rarely ever see a perfect correlation

_________ _______ lies int he mind of the researcher who theorizes that the theory or explanation for some even makes sense

Logical Support

(+-) 0.41 - (+-) 0.60

Moderate

When a set of x and y values increase or decrease together but never increase and subsequently decrease together, we say that they are ___________

Monotonic

________ refers to whether or not one set of scores tends to increase or decrease alongside of another set

Monotonicity

Will correlation alone be sufficient empirical evidence of causation?

No, it will not

Pearson product moment, also known as _________ ___

Pearson's r

_________ ____ is used much more frequently than _______ _____, but the latter is useful for situations in which we cannot use Pearson's r

Pearson's r; Spearman's rho

_______-______ reasoning leads us to neglect alternative explanations for an event

Post-Hoc

Requirements for Spearman's Rho:

Random Sampling Both variables must be at least ordinal The variables must increase monotonically with one another

Some requirements or assumptions for calculating Pearson's r: (5)

Random sampling Continuous interval or ratio level data Normally distributed variables An absence of significant outliers A linear association between the variables

__________ is a logical extension of Pearson's r

Regression

For the same data in the previous question, do we reject or accept the null hypothesis at p<.05?

Reject

____________ (also known as scattergrams, scattergraphs, or dot plots) plot interval or ratio level data onto a graph in a case-by-case manner

Scatterplots

Spearman's rho is also known as ______ _____ ______

Spearman's Rank Correlation

Spearman rank correlation, also known as ________ ____

Spearman's rho

(+-) 0.61 - (+-) 0.80

Strong

An example of a scenario that illustrates a spurious correlation

The more firefighters who arrive at a fire, the greater the fire damage

T/F Correlation and regression are similar to one another in the sense that they both describe relationships between variables

True

T/F -.35 is equally as strong as +.35

True--they only differ in terms of their direction

(+-) 0.81 - (+-) 1.00

Very Strong to Perfect

(+-) 0.00 - (+-) 0.20

Very Weak to None

_______ ________ means examining the scatterplots--also known as "eyeballing"

Visual Estimation

(+-) 0.21 - (+-) 0.40

Weak

Can the line of best fit can more accurately be specified by the linear regression equation?

Yes

Do scatterplots give us approximate ideas of the association's strength and direction?

Yes

Is Spearman's rho a common alternative to Pearson's r

Yes

A type of confusion:

a reversal of cause and effect

The _______ is what constitutes the strength of the correlation

amount

Correlated--means that as one variable changes, another variable _________ (we see a pattern)

changes as well

As values on one variable change, the distribution of the second variable......

changes as well.

The unexplained variation is also known as the ______ ____ _______

coefficient of alienation (the un-shared variation)

The _______ ___ ________ (r^2) refers to the amount of variation in one variable that is explained or accounted for by the variation in another variable

coefficient of determination

A __________ _______ is something that lurks in the background

confounding variable

The use of ________ ________ helped solidify the argument

control variables

A _________ _______ is a number that quantifies the strength and direction of an association between two variables

correlation coefficient

When two random variables are associated, we say that they are ______

covary

Vertical Axis (y axis) is where the _______ variable is found (the criterion)

dependent

Positive Correlation, meaning both arrows go in the same direction, depicts a ________ ________

direct correlation

The best fit line indicated not just linearity, but also ________

direction

The way that two variables covary (the _______ of a correlation)

direction

What should one do every time they try to interpret a correlation?

draw arrows that represent their variables

r^2 is also known as a measure of ______ _______ (or shared variation)

explained variation

The ______ the absolute value, the _________ the relationship

greater; stronger

Horizontal axis (x axis) is where the _______ variable is found (the predictor)

independent

If no pattern exists, then one could say that two variables are statistically _________ of one another

independent

No correlation =

independent

Negative Correlation, meaning that the arrows go in opposite directions, depicts an ________ _______

indirect correlation

The _______(a) is the point at which the regression line crosses the y-axis when X = 0

intercept

Negative relationship is also known as ________

inverse

The _____ depicts the form of the relationship, in the sense that a straight line indicated whether or not the association is linear

line

One can increase the interpretability of our scatterplots by adding a _____ ____ ______ _____

line of best fit

Scatterplots also indicate whether or not the association is ________--which refers to the ability to draw a straight line through the data points

linear

Independent:

means the values on one variable do not tend to have any corresponding values on the other variable

There is a variety of types of correlation coefficients, also known as the _______ ___ ________

measures of association

The stronger the association, the _______ likely its casual

more likely

When two variables tend to vary in opposite directions, as one increases the other decreases, the relationship is a ________ one

negative

To go apart -

negative correlation

If a straight line can NOT be drawn through the data points, there may be ______ relationship at all

no

If a straight line can NOT be drawn through the data points, there may be ____ _______ at all

no relationship

When the dots are scattered randomly or even start forming a circle, there is _______ relationship

no relationship

Correlation coefficients are also sensitive to ________ as is the case with means and standard deviations

outliers

In a ________ _______, two variables occur in lockstep with one another, whereby each variable increases or decreases at a consistent rate with respect to the increases or decreases of the other variable

perfect correlation

having an r or rs that equals 1.00 means it is a _______ correlation

perfect correlation

When two variables tend to increase or decrease together, their association has a ________ direction

positive

Go together =

positive correlation

One of the requirements for Pearson's r is that a _________ sampling method should be used

random

The lone of best fit is also known as the _________ line

regression

To control these various other factors, researchers often use a technique called _________

regression

This (best fit line) line depicts the form of the __________, in the sense that a straight line indicated whether or not the association is linear

relationship

Before actually calculating correlation coefficients, we produce a ________ in order to get an initial sense of what the association, if any, looks like

scatterplot

The _______ (b) is the steepness of the best fit line; it represents the amount of change in Y for every unit of change in X

slope

A ___________ correlation is one in which the association is caused by a third variable that affects both of the association's two variables simultaneously

spurious

The extent to which two variables covary (the ______ of a correlation)

strength

The more close the dots hug the imaginary line, the _________ the relationship

stronger

In the linear regression equation, (a) stands for:

the intercept

In the linear regression equation, (b) stands for:

the slope of the regression line or its steepness

What can we determine using correlation and regression?

the strength and direction of an association between variables

In the linear regression equation, X stands for:

the value of the predictor variable

The word negative means ____ ____ ______

to go apart

Non-monotonic

when scores increase AND decrease together