Study for SPSS Test Flashcards
Correlation
measure of the degree of association between two variables (x and
y) initially assumed to be numerical
Pearson’s correlation
Investigates the linear relationship between x and y (scatterplot of x and y)
Pearson’s correlation assumptions
Assumes both x and y to be numerical and that at least one is
normally distributed.
Pearsons correlation H0
: There is no linear association in the
population between the two variables X and Y
(ρ=0).
Spearmans rank correlation
Investigates any monotonic* relationship between x and y
Spearmans rank correlation assumptions
At least one variable should be continuous (the other could be ordinal) –
they do not have to be normal (ranks)
Spearmans H0
There is no association in the population
between the two variables X and Y (ρs=0)
Myotonic
As one increases so does other but maybe not at constant rate
Linear regression
e investigation of the relationship between two independent continuous
variables, X and Y (X’s for multiple linear regression). It can be used to predict Y
(dependent/response variable) from the X(s) (independent /predictive variable(s))
Simple linear regression equation
Y= β0 + β1X1 + e
Simple linear regression assumptions
Linear relationship between X(s) and Y – Check by Correlation, scatterplot of
X and Y, OR scatter plot of the Normalised Predicted values vs Dependent
values
* Normal distribution of RESIDUALS – Check by a Histogram of Residuals, or
by inspection of the P-P plots
* Constant variance – Check by a Scatterplot of Residuals vs Normalised
Predicted (sausage shaped, random scatter)
* Independent observations – Check by Scatterplot of Normalised Residuals
and Predicted - AGAIN (no organisation)
Simple linear regression fit of mode
The coefficient of variation, R2, indicates how much of the variation in Y
is explained by the proposed model
Simple linear regression what does ANOVA do
This divides the overall variation into the
variation explained by the regression model and the residual (left over or not
explained) variation and compares them.
SLR ANOVA H0
The relationship between X and Y in the population is not informative. The
regression coefficients are zero i.e. Ho: β0 = β1 = 0
SLR tests of individual coefficents H0
H0β0: The intercept is zero i.e. β0 = 0
H0β1: The effect of Xi is constant β1 = 0 i.e. the coefficient is flat