We use linear regression to find relationships
between two or more variables and to create a model that attempts to describe
the relationship.
A scatterplot is a 2-dimensional graph that displays
pairs of data (i.e. observations).
A correlation coefficient is a number that tells
strength and direction of a relationship.
·
0 means no linear relationship exists
(could be there is a curved relationship)
·
+1 or -1 means the points fall on a perfect
straight line
·
The closer the number is to +1 or -1,
the stronger the relationship.
·
Rule of thumb is that +0.7 or -0.7 (or more) is a strong relationship; +0.5 or
-0.5 indicates a moderate relationship.
Kinds of correlation coefficient – the one used
depends on the kind of data:
·
Pearson r – used for data measured at
least on an interval level (such my as data for TL, SL, and SV scales)
·
Spearman rho – used for linear
relationships when data is measured on an ordinal scale (such as a ranking)
·
Phi – used for linear relationships for
data measured dichotomously (e.g. yes/no, pass/fail)
·
also Point Biserial and Eta....don’t
care about these for now
For a null hypothesis, the expected correlation is 0. The key question is whether the variance from
what we expect can be attributed to a relationship that really exists, or is
the variance found only because of a sampling error.
A one-tailed hypothesis assumes the relationship is
positive or negative.
A two-tailed hypothesis makes no assumption about
the relationship.
For a correlational study, degrees of freedom =
N-2. One degree of freedom is lost for
every variable in the model. Degrees of
Freedom represents how many numbers are free to vary in a calculation sequence
(Steinberg, 2008).
References
Rumsey, D. (2009). Statistics II for Dummies.
Hoboken, NJ: Wiley Publishing, Inc.
Steinberg, W. J. (2008). Statistics Alive! Thousand Oaks, CA: Sage Publications.
