Psyc 300A midterm 2

Bivariate data

involves two variables (X & Y), often two data points form the same thing (eg. person) but can be two things related by something (such as date)

Correlation

method to describe the relationship between two variables (varies from -1 to 1)

Regression

predicting the values of one variable from another variable (includes a slope and an intercept)

Sum of products

describes how each score deviates from each mean

Covariance (cov)

like variance, but for the products, measure of covariablity, not in any meaningful units

Pearson r

degree to which two variables covary, standardized measure of correlation

Sampling error

discrepancy between sample statistics and population parameter (each sample has inherent variability from the population, so central tendency and variability may differ across samples) each sample may increase or decrease r by chance

unmeasured third variable

two things can be related because of some other factor that we didn't track in our study (eg. crime and ice cream because of summer weather) (mediation and moderation tests can be used to test for third variable influences)

Heterogenous sample

when your sample includes multiple sub-samples, can decrease r if sub-samples behave differently, can increase r by chance if sub-samples line up into a correlation

truncated range

when data are collected form a restricted range of the full scale, the resulting scores may provide incomplete or misleading across the entire range (most often reduces r, but can sometimes increase r by chance)

non-linear relationship

correlations may not be linear, treating a non-linear relationship as linear can decrease r, treating a linear relationship as non-linear can also decrease r

Heteroscedasticity

variability changes across our range (affects standard deviation in Pearson correlation equation, increase in variability will decrease r), can be cause by a skew in one or both of our variables

sample size assumption

larger sample size does not mean larger correlation, will have an impact on whether we decide the correlation is significant

Spearman rho note

if there is heteroscedasticity or skew in data, transform into ordinal/ranked before using Pearson r

Regression line

a mathematically defined line that best represents the bivariate relationship

Slope

how much one variable changes when another variable increases by one

Y-intercept

how much of one variable do you have in the absence of the other

error in regression

variability in our data makes it unlikely that we will find a perfect prediction

explained variability

how close our predictions are from the actual value (how well have we predicted one variable from the other)

unexplained variability

how far our predictions are from the actual value (how poorly we predicted one variable from the other)

Ay

y-intercept, a constant in the equation that shifts the regression up or down

By

slope, a coefficient in the equation that changes the steepness of the relationship

Ax

X-intercept, a constant in the equation that shifts the regression left or right

regression lines convergence

regression lines converge where the mean of X and Y lines meet

what happens when r = 0 (slopes also 0)

regression line is equal to the means of Y and X

what happens when r = 1

the two regression lines converge and become the same

residuals

the deviation each score is from the predicted value of the regression line

explained variability in regression

how much error is reduced because we are taking into account the correlation (asking if regression is better than the mean), better if the scores are closer to regression line than to the mean

r

standardized measure of association between X and Y

r2

proportion (or percent) of variability accounted for in Y by variability in X