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
