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Why do we convert raw scores to Z scores when figuring a correlation coefficient?
It gives us a standardized value in which low scores are negative numbers, & high scores are positive numbers
How would you describe the following correlation coefficients: -.87, 0, .90, .06?
-.87: strong negative linear correlation
0: no linear correlation
-.90: strong positive linear correlation
.06: weak positive linear correlation
What does the null hypothesis state when testing the significance of a correlation coefficient?
The true correlation in the population is zero.
What is the formula for degrees of freedom when conducting a t test for the correlation coefficient? If we had a study with 35 individuals, what would be the degrees of freedom?
df= N- 2
df= 33
If there is a strong linear correlation between health & income, what is the direction of causality?
can't say; health could cause income (greater / less earning potential); income could cause health; a third variable could be impacting both health & income
What is an outlier?
a score that has an extreme value in relation to other scores in a distribution
If a professor wants to predict test grades from the hours a student studied, what is the procedure called? What is the predictor variable? What is the criterion variable?
procedure: bivariate prediction
criterion variable: test scores
predictor variable: hours studied
What is a regression coefficient?
(b) in the linear prediction equation: indicates how many units of change is predicted in the criterion variable for each unit of change in the predictor variable
What is the regression constant?
(a) in the linear prediction equation; the Y intercept; predicted score on the criterion variable when the score on the predictor variable is 0; the number you always start with when calculating regression/ prediction line
1. An I/O psychologist studying adjustment to the job of new employees found that employees' amount of education (in number of years) predicts ratings by job supervisors two months later. If:
Regression Constant = 0.5
Regression Coefficient = 0.4
Individual has 10 years of education
-What is the predictor variable?
years of education
1. An I/O psychologist studying adjustment to the job of new employees found that employees' amount of education (in number of years) predicts ratings by job supervisors two months later. If:
Regression Constant = 0.5
Regression Coefficient = 0.4
Individual has 10 years of education
- What is the criterion variable?
job's supervisor's rating
1. An I/O psychologist studying adjustment to the job of new employees found that employees' amount of education (in number of years) predicts ratings by job supervisors two months later. If:
Regression Constant = 0.5
Regression Coefficient = 0.4
Individual has 10 years of education
- What is the linear prediction rule for this example?
y = 0.5 + (0.4) (10)
1. An I/O psychologist studying adjustment to the job of new employees found that employees' amount of education (in number of years) predicts ratings by job supervisors two months later. If:
Regression Constant = 0.5
Regression Coefficient = 0.4
Individual has 10 years of education
-What is the predicted job rating for the employee in this example?
y = 4.5
What is a scattergram and how do you interpret it?
-a graph that shows the relation of 2 variables through dots representing data points
-no correlation: dots are randomly selected with no clear line/ relationship
-curvilinear: dots arranged in a curve going up or down
-positive correlation: dots in line going up from left to right
-negative correlation: dots in line going down from left to right
How do you describe the pattern of the data in a positive correlation? In a negative correlation? In a curvilinear correlation?
-positive: high scores go with high scores, low with low
-negative: high scores go with low scores, low with high
-curvilinear: data points appear arched
What are the possible results of multiplying two Z scores when observing the correlation between variables?
-high scores (+) x high scores (+) = positive z scores
-low scores (-) x low scores (-) = positive z scores
-high scores (+) x low scores (-) = negative z scores
How is the proportionate reduction in error figured in order to compare correlations?
by squaring each correlation coefficient
Describe a correlation matrix.
In a correlation matrix, variables are listed on top and left side, and the relationship between the variables are listed in each cell
What is a regression line?
Shows the relationship between predictor & criterion variable
How do you calculate error in regression?
score on the criterion variable - predicted score
What is the null hypothesis when conducting a bivariate linear prediction?
-null: predicted amount of change of the criterion variable is 0 when predictor variable increases by one standard deviation (B)(standardized regression coefficient=0)
What is the statistical procedure for predicting a criterion variable from more than one predictor variable?
multiple regression
Explain the chi-square test:
1. What kind of variables do you have?
Nominal
Explain a chi-square test:
2. What is the main idea of the test?
examine if pattern is observed frequencies fits the expected pattern of frequencies
Explain a chi-square test:
3. What calculation is necessary for the statistic?
take difference between observed & expected frequencies; square & sum the differences divide by expected frequency of each cell
Explain the chi-square test:
4. What type of table is used?
contingency table; distribution of 2 nominal variables listed so that you have frequencies for each cell & combination / totals
Explain a chi-square test:
5. How would you describe the distribution?
chi-square distributions of 2 nominal variables listed so that you have frequencies for each cell & combinations/ totals
Explain a chi-square test:
6. What is the primary debate regarding chi-square tests?
small expected frequencies
What is the difference between the chi-square test for goodness of fit and the chi-square test for independence?
-goodness of fit is limited to 1 variable, and independence test is not
-the independence test looks for a relationship between multiple nominal variables
-independence means no relationship between the variables
For the chi-square test for goodness of fit, what is the df? What is the null hypothesis?
df= number of categories minus 1
-the null for goodness of fit is that proportion of people over categories breaks down the same for the 2 populations
What is the minimum number of predicted points on a graph required for drawing a regression line?
A minimum of 2 data points is required to draw a regression line
Why are regression errors squared?
We square regression errors because summing the positive and negative errors will cancel out
What is the name for adding these squares together? (error in regression)
The sum of squared errors
How do the correlation coefficient & regression coefficient relate in hypothesis test for a linear prediction rule?
Linear prediction, if the correlation coefficient is significant, the regression coefficient will be significant
What is the formula if there are 2 predictor variables?
-y = a + b1 (x1) + b2 (x2)