Chapter 15 - 2220
when working with a population what do we use
"p" - hypothesis testing will be talking about p
when working with a sample what do we use
"r"
null hypothesis for p
H0: ρ = 0
alternative hypothesis for p
H1: ρ ≠ 0
convergent validity
look for correlations between your measure and other, similar measures
criterion validity
look for correlations between your measure and real-world outcomes
SPSS output for correlations
- displays correlation (r = -.851) - displays sample size (N = 10) - displays a p value (p = .002)
small correlation coefficient
.10
medium correlation coefficient
.30
large correlation coefficient
.50
Mallory found a large (strong) correlation between the amount of time people spent studying and the grades they received on a test. In her sample, people who studied less performed worse on the test. The correlation coefficient in this study was most likely ___________. a. +1.50 b. +.25 c. -.80 d. +.75
.75 because the two variables are going in the same direction
7 assumptions when using r
1. data are randomly selected from the population 2. the underlying population distributions for our variables are approximately normal 3. homoscedasticity: Each variable should vary equally across all levels of the other variable. (For example, we should not have more variability in grades at high levels of absenteeism vs. low levels of absenteeism). 4. we have scale variables (interval or ratio) when computing r 5. we are looking at a linear relationship 6. outliers can have a STRONG impact on the value of r (especially with smaller sample sizes) 7. we have pairs of scores
3 properties of correlation coefficient
1. the correlation coefficient can be positive or negative (denotes the type of relationship, not the strength) 2. the correlation always has a value that is between (or equal to) -1.00 or +1.00 3. the magnitude of the coefficient indicates how strong the correlation is not the sign of the coefficient (coefficients of +.80 and -.80 both indicate equally strong correlations)
what are the 3 ways for variables to be correlated?
1. variable A might cause variable B 2. variable B might cause variable A 3. a third variable (variable C) might cause both variables A and B
non-linear relationship
A relationship that graphs as a curved line - a relationship is clearly present though
teeter-totter analogy for negative correlations
A teeter-totter provides a nice analogy for a negative correlation. As one side of the teeter-totter rises (e.g., as variable 1 increases), the other side drops (e.g., variable 2 decreases).
thermometer analogy for positive correlations
A thermometer provides a nice analogy for a positive correlation. As the temperature increases, the mercury level rises (higher temperatures are paired with higher mercury levels).
CORRELATION IS NOT THE SAME AS CAUSATION
Just because Variable A is correlated with Variable B, it does not necessarily mean that Variable A causes Variable B (or vice versa).
coefficient alpha
a commonly used estimate of internal reliability. can be thought of as an average of all possible split-half correlations - also known as Krohn Bachs alpha - when we are talking about alpha in this way, we are not talking about a type 1 error rate
Pearson correlation coefficient (r)
a statistic that quantifies the linear relationship between two SCALE variables - very useful and common measure of correlation - also called the Pearson product moment correlation coefficient
correlation coefficient
a statistic that quantifies the relationship between two variables - typically a linear relationship
negative correlation
an association between two variables in which participants with high scores on one variable tend to have low scores on the other variable - high scores tend to be paired with low scores and low scores tend to be paired with high scores
positive correlation
an association between two variables such that participants with high scores on one variable tend to have high scores on the other variable as well, and those with low scores on one variable tend to have low scores on the other variable - high scores tend to be paired with high scores and low scores tend to be paired with low scores - ex. high attendance rates --> higher exam grade
internal reliability (consistency)
consistency between items in the same scale. the extend to which multiple measures or items are answered in the same manner by the same set of people - are all items in a scale measuring the same idea? - split-half reliability - coefficient alpha
split-half reliability
correlate scores from one half of the scale with scores from the other half (e.g. correlate even and odd items)
partial correlation
degree of association between two variables that remains after accounting for (statistically removing) the association of a third variable with those two variables - allows for a researcher to "control for" the presence of a third variable
as a coefficient becomes more ___ from 0.00 it indicates a stronger correlation
distant
perfect linear correlations
every point on a scatter plot will fall upon the line of best fit - this could occur for a positive or a negative relationship - as points get closer to the line of best fit (on average) the correlation becomes stronger (closer to +1.00 or -1.00) - if every data point falls perfectly on the line of best fit, the correlation will be equal to 1.00 or -1.00
when is the Pearson correlation coefficient not appropriate to use?
for describing non-linear relationships - we need a relationship that can be described by a straight line - we will have to graph!
if we are comparing scatterplots, how can we tell which one has a stronger correlation?
if we drew a line of best fit through the data, the scatterplot with more dots on the line would have a stronger correlation
we need to have good ___ to distinguish between the possibilities variables are correlated
internal validity - conduct an experiment
discriminant validity
look for a lack of correlation between your measure and dissimilar measures
direction of a negative correlation
one variable increases, while the other decreases
when we calculate correlations, scores are ____
paired together
test-retest reliability
refers to whether the scale being used provides consistent information every time the test is taken - provide the scale to the same people on two different occasions - large, positive correlation = good consistency across time
linear relationships
relationships that can be described by a straight line (rather than a non-linear function, such as a curve)
covariance
represents the degree to which two variables vary together - When high scores on one variable are paired with high scores on the other, the covariance will be positive and large. - When high scores on one variable are paired with low scores on the other, the covariance will be negative and large. - covariance on its own is not very interpretable we need to know more about the data score
r is a ____ version of covariance
standardized - Covariance divided by the product of the standard deviations of x and y. - This scaling restricts the values of r such that it must be between -1 and +1 (inclusive). Again, the coefficient r represents the strength of a linear relationship between two scale variables.
as one variable changes, the other variable would be expected to ____
systematically increase or decrease (to some degree) - there is a predictable relationship between the 2 variables - ex. as people attend class more often, they tend to earn higher grades on exams
saying that there is a correlation between two variables indicates ___
that there is a systematic relationship between those variables
T/F: that this does not require one variable to cause a change in the value of the other variable (though that may be the case).
true
just because a measure is reliable does not mean that it is also valid
true - reliability is a prerequisite for validity - but if something is reliable, this does NOT mean it is valid
direction of a positive correlation
variables increase or decrease together
