PSYC20009 Lecture Notes - Lecture 2: Pearson Product-Moment Correlation Coefficient, Null Hypothesis, Scatter Plot
Lecture 2 - Monday 31 July 2017
PSYC20009 - PERSONALITY & SOCIAL PSYCHOLOGY
LECTURE 2
CORRELATION
TODAY
•1. Overview of correlation
•2. Characteristics
•Direction; Form; Degree Some features of correlations
•Causality; extreme points; regression to the mean
•3. Pearson correlation coefficient
•4. Features of correlation
•5. Null hypothesis testing
•Hypothesis testing for correlation
•6. Spearman correlation coefficient
•7. Examples using SPSS
•8. Moving towards regression
1. CORRELATION
•The bottom line of this chapter:
•Correlation deals with the association between two variables and is one of the most important
data analytic techniques in psychology.
•Whether or not we can truly believe in the measures.
•If, for instance, we find that IQ or personality trait measure isn’t associated with any
measurable behaviours then there is no use even testing for it.
IN A NUTSHELL..
•Bivariate analyses are analyses concerned with relationship
between two variables.
•Bi = two, variate = variables. 2 variables.
•Correlation is the standardised metric quantifying degree
and direction of linear relationship between two numeric
variables (i.e., X and Y)
ASSOCIATION BETWEEN VARIABLES
•A possible psychological research question: Is there an
association
between
ANXIETY and
JOB
SATISFACTION?
•Almost never have
perfectly
correlated data.
SCATTERPLOTS
•Plots pairs of X-Y
scores.
•The same set of n
= 6 pairs of scores
(X and Y values) is shown in a table and in
a scatterplot. Notice that the scatterplot
allows you to see the relationship between
X and Y.
Lecture 2 - Monday 31 July 2017
PSYC20009 - PERSONALITY & SOCIAL PSYCHOLOGY
WHY IS CORRELATION IMPORTANT?
•One of the most frequently used statistics.
•Important to be able to interpret it correctly.
•Fundamental to theory building in psychology – and outside of psychology as well!
•Building block for more sophisticated methods you will encounter in future years.
•Eg., Multiple Regression, Factor Analysis, Structural Equation Modelling, partial correlations.
2. CHARACTERISTICS OF CORRELATIONS
•The bottom line:
•A correlation coefficient can be positive or negative.
•You need to understand the difference between positive and negative correlations.
•An association between two variables can be linear or non-
linear.
•A correlation coefficient ranges from -1 to +1 where +1 or
-1 indicates a perfect positive or negative correlation.
•A correlation of 0 indicates no association between the
two variables.
•Characteristics of a relationship between two variables
include direction, form and degree.
DIRECTION
•Positive correlation: 2
variables tend to go in same
direction.
•Negative correlation: 2
variables tend to go in
opposite directions.
•Examples of positive and
negative relationships. (a) Beer
sales are positively related to
temperature. (b) Coffee sales are
negatively related to temperature.
FORM
•Correlation measures the linear relationship
between two variables.
If there is a nonlinear relationship, the correlation value may be deceptive.
If the two variables are independent of one another, the correlation will be approximately zero.
Lecture 2 - Monday 31 July 2017
PSYC20009 - PERSONALITY & SOCIAL PSYCHOLOGY
DEGREE
•Perfect linear relation: every change in the X variable is
accompanied by a corresponding equal change in the Y
variable.
•Correlations range from -1 to +1. The r value basically.
•Rough rules of thumb on how big/small correlations are include:
•Small effect: .1 <r < .3 or -.3 > r> -.1
•Medium effect: .3 < r < .5 or -.3 > r > -.5
•Large effect: .5 < r < .7 or -.5 > r > -.7
•Note that these are not formal! Context matters!
•With some research questions, correlations of .05 can be large
•With others, correlations as high as .6 or .
8 can be low
•R-squared
•Percentage of variance accounted for (more
on this in regression)
•Examples of different values for linear
correlations:
•(a) shows a strong positive relationship,
approximately +0.90;
•(b) shows a relatively weak negative
correlation, approximately –0.40;
•(c) shows a perfect negative correlation, –
1.00;
•(d) shows no linear trend, 0.00.
3. PEARSON’S CORRELATION
COEFFICIENT
•The bottom line:
•The Pearson correlation coefficient (r) is
most commonly used in psychology and measures the linear
association between two continuous
variables.
•It compares how much the two
variables vary together to how!
Document Summary
Characteristics: direction; form; degree some features of correlations, causality; extreme points; regression to the mean, 3. In a nutshell. : bivariate analyses are analyses concerned with relationship between two variables, bi = two, variate = variables. 2 variables: correlation is the standardised metric quantifying degree and direction of linear relationship between two numeric variables (i. e. , x and y) Association between variables: a possible psychological research question: is there an association between. Scatterplots: plots pairs of x-y scores, the same set of n. = 6 pairs of scores (x and y values) is shown in a table and in a scatterplot. Notice that the scatterplot allows you to see the relationship between. 1 indicates a perfect positive or negative correlation: a correlation of 0 indicates no association between the two variables, characteristics of a relationship between two variables include direction, form and degree. Form: correlation measures the linear relationship between two variables.