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what is a variable?
measure that can have more than one value
What does a scatter diagram do?
it is plotting one variable against another variable
What is a correlation coefficient?
is a mathematical index that describes the direction and magnitude of a relationship
What is a positive correlation?
the value of one variable goes up while the other rises also
What is negative correlation?
the value of one variable rises while the value of the other falls
What is no correlation?
the pair of variables show no sign of correlation
What does the regression line predict?
predicts the scores on one variable based on what we know about the score on another variable obatined from the regression line.
How is the regression line described?
it is the best straight line through a set of points in a scatter diagram
In stats, what is a sequence or a vector of random variables?
what does the regression line describe?
the best linear relation between the X and Y scores.
What is Covariance?
is a term used to describe the extend to which knowing the value of one variable predicts the value of the other
What is the slope of the regression line?
it is the regression coefficient
regression line- what is the intercept?
- -is the value of Y when X=0
- *this is where the regression line crosses the Y axis
regression line- What is a residual?
the difference between an actual score and the predicted score (predicted by the regression line)
regression line- what is the principle of least squares?
a best fitting line keeps residuals to a minimum
In correlation, what is the intercept always?
HOw is correlation a special case of regression?
bc the scores in correlation of both variables are in standarized form (z units)
What number range does the correlation coefficient range from?
In correlation, what have the scores (x and y) been converted to? and what is their mean?
-converted into Z-scores
-mean is 0
correlation- Bc x and y are both converted into z scores and both of their means is zero, what is the intercept between x and y axes?
it will always be zero
So essentially what is the correlation coefficient?
-is the regression coefficient when both x and y have been converted to z scores
What is the Pearson product moment correlation coeffcient? (2)
- -is a ratio used to determine the degree of variation in one variable that can be estimated from knowledge about variation in the other variable
- *this is the one we use most commonly
What does the null hypothesis state?
that there is no real relationship between teh variables in question
essentially what do we want to do in psych tests to the null hypothesis?
we want to reject it
HOw is the null hypothesis rejected?
if there is a calculated probaility that the association between the 2 variables is significantly differnt from 0 using a t-distribution
INTERPRETING REGRESSION PLOTS- what is criterion validity evidence?
the relationship between a test score and some well defined criterion (job aptitude test and actual job performance)
what is the Pearson product moment correlation commonly used to find?
correlation between 2 continouos variables
What are continuous variables?
variables that can take on any values over a range of values
ex) height, weight, intelligence
What is the Spearmans rho used to find?
asscoation between 2 sets of ranks
What are dichotomous variables?
variables that can have only 2 values
ex) yes-no and correct-incorrect
dichotomous variables- What are true dichotomous?
they naturally form 2 categories
ex) gender: male or female
dichotomous variables- What are artificially dichotomous?
they reflect an underlying continuous scale forced into dichotomy
ex) passing or failing a bar exam bc although there is a range of scores collected, there can only be pass and fail
What is a biserial correlation?
expresses the relationship between a continuous variable and an artificial dichotomous variable
ex) a biserial might try to asses relationship between pasing or failing a bar exam (artificial dichotmous) and GPA in law school (continuous)
What is a point biserial corraltion?
is when one variable is continuous and the other is true dichotomous
ex) this correlation would try to find relationship between gender( true dichot) and GPA (continuous)
HOw is the point biserial correlation expressed?
What is tetrachoric correaltion?
if both variables are artificially dichotomous variables
What is the standard error of estimate?
the SD of the residuals
What is the correlation of determination?
it is the correlation coefficient sqaured
what does the coefficient of determiantion tell us?
how much variation in the scores of Y we know as a fucntion what we know about X
What is coefficient of alienation?
is a measure of the nonassociation between 2 variables
What is shrinkage?
is the amount of decrease observed when a regression equation is craeted for one population then applied to anohter
ex) using an regression eqution for incoming freshmans predicted GPA from their SATs. then using the same equation for next years
What is cross validation?
- using the regression equation derived using one group of subjects to predict performance in a different group of subjects
- *the ddifference between results is standard error of estimate
restrcited range- what if the variability of a variable is extremely restricted?
then significant correlation may be difficult to find even if they may actually be there
ex)trying to find relationship between scores on GRE and performance during 1st year of grad school in math departmanet. no students have been admitted with GRE verbal scores of less than 700. Further most grades in grad school are As. there isnt much variability between students there
What is multivariate analysis?
considers the relationship among combinations of 3 or more variables
What is discriminant analysis?
the linear combination of variables that provides the maximum discrimination between categories
ex) attempts to determine whether a set of measures predicts success or failure on a particular performance evaluation
What does the matrix of a factor analysis show?
correlation between every variable and every other variable
what does factor analysis tell you?
which items clustered with one another
*meaning if we knew how someone asnwered something we can predict with some accuracy how they would asnwer the others in that cluster
the factor analytic mathematical matrix is likley to be...
factor analysis- Why are some clusters or factors negative clusters?
they exsit bc everyone rejects the items
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