chapter 6 Flashcards
The values of a correlation coefficient
range from:
- 1 to +1
A correlation coefficient provides what
information about the relationship
between the two variables?
Strength (magnitude) and
direction
A relationship between two variables best
described by a straight line is said to be:
Linear
Which test?
Goal: Explore whether an association
exists
X: Ratio
Y: Ratio
Relationship: Linear
Pearson r (Pearson product-
moment correlation)
r2, a measure of the strength of a
relationship, is know as:
The coefficient of
determination
All of the points on the scatterplot fall on
the line. This relationship is said to be:
______________.
Perfect
(Partial credit for
“unlikely!”)
Which test?
Goal: Explore whether an association
exists
X: Interval
Y: Ratio
Relationship: Monotonic
Spearman’s r (Spearman’s
rank-order correlation,
Spearman’s rho, rs)
Restricting the range of a variable (X or Y)
will likely ___________ the correlation
coefficient.
Lower
__________ scores can drastically alter the
magnitude of a correlation.
Extreme
The four explanations of a correlation are:
- Correlation between X and
Y is spurious. - X is the cause of Y
- Y is the cause of X
- A 3rd variable is the cause
of the correlation between
X and Y
Characteristics of relationships:
Direction
negative: x goes up, y goes down
positive: x goes up, y goes up
Characteristics of relationships:
Form
linear is most common
Characteristics of relationships:
Strength
degree of relationship
the shape of a relationship can be determined by a _______
scatterplot
More scatter in correlational data means
less significant the correlation is
less scatter in correlational data means
the data is more linear, so there is more significant correlation
what is the most common correlation coefficient
Pearson r
pearson r can only be measured in what scales
interval or ratio data
a specific measure of correlation is called ____
correlation coefficient
pearson r is always between
-1 and 1
the closer to -1 or 1, the ___ the relationship
stronger
pearson r formula
degree to which X and Y vary together
_______________________________
degree to which X and Y vary separately
Step 1 in solving for Pearson r
Compute SP
∑XY - (∑X)(∑Y)
_________
n
Step 2 in solving for Pearson r
Compute SSₓ
∑X²- (∑X)²
_________
n
Step 3 in solving for Pearson r
Compute SSᵧ
∑Y²- (∑Y)²
_________
n
Step 4 in solving for Pearson r
Compute Pearson r
r = SP
___________
√ SSₓ SSᵧ
What is the most common technique for measuring the strength of a correlation
Coefficient of Determination
What is the equation for Coefficient of Determination)
r² = just square Pearson r
if the correlation coefficient is
r = .10, whats the effect size?
small
if the correlation coefficient is
r = .30, what’s the effect size?
medium
if the correlation coefficient is
r = .50, what’s the effect size?
large
When is Spearman’s Rank Order Correlation used?
When both variables are based on ordinal ranking
What is the formula for Spearman’s Rank?
rₛ = 1 - 6 ∑ Dᵢ²
________
N³ - N
