CORRELATION & PEARSON Flashcards
a statistical technique that is used to measure and
describe the relationship between two variables
Correlation
The corresponding correlation for the entire population is identified
by the Greek letter
rho (ρ)
the Greek equivalent of the letter r
rho (ρ)
The sign of the correlation, positive or negative, describes the direction of the relationship
The Direction of the Relationship
Some relationships tend to have a linear form; the points in the scatter plot tend to cluster around a straight line.
The Form of the Relationship
most common use of correlation is to
measure _ relationships
straight-line relationships (The Form of the Relationship)
in correlation other forms of relationships do exist and there are _ correlations used to measure them.
special correlations (The Form of the Relationship)
The correlation measures the consistency of the relationship.
The Strength or Consistency of the Relationship
for a linear relationship the data points could fit perfectly on a _ line
straight line(The Strength or Consistency of the Relationship)
Every time X increases by one point, the value of Y also changes by a _ and predictable amount.
consistent (The Strength or Consistency of the Relationship)
- The Direction of the Relationship
- The Form of the Relationship
- The Strength or Consistency of the Relationship
3 characteristics of a relationship
- perfect negative correlation, –1.00,
- no linear trend, 0.00,
- a strong positive relationship, approximately +.90
- a relatively weak negative correlation,
approximately –0.40
different values for linear
correlations
a perfect negative correlation, have a value of
–1.00
no linear trend, have a value of
0
a strong positive relationship, approximately have a value of
0.9
a relatively weak negative correlation, approximately have a value of
–0.40
measures the degree and the direction of the linear relationship between two variables
Pearson correlation
used to measure the amount of covariability between two variables.
The Sum of Products of Deviations
- Prediction
- Validity
- Reliability
- Theory Verification
Where and Why Correlation Are Used
If two variables are known to be related in some systematic way, it is possible to use one of the variables to make accurate predictions about the other.
Prediction
If two _ are known to be related in some systematic way, it is
possible to use one of the variables to make accurate predictions
about the other.
variables
One common technique for demonstrating validity is to use a
correlation.
Validity
If a test actually measures intelligence, then the scores on the test should be related to other measures of intelligence—for example, standardized IQ tests, performance on learning tasks, problem-solving ability
Validity
One way to evaluate reliability is to use correlations to determine the relationship between two sets of measurements
Reliability
When reliability is high, the correlation between two measurements
should be strong and positive
Reliability
One way to evaluate reliability is to use _ to determine the relationship between two sets of measurements
correlations
When reliability is _, the correlation between two measurements
should be strong and positive
high
The prediction of the theory could be tested by determining the correlation between the two variables.
* Well-being and positivity
* Rumination and depression
Theory Verification
The prediction of the _ could be tested by determining the
correlation between the two variables
Theory
• Well-being and positivity
• Rumination and depression
Theory Verification
simply describes a relationship
between two variables
correlations
It does not explain
why the two variables are related.
Correlation
should not and cannot be interpreted as proof of a cause- and-effect relationship between the two variables.
Correlation
the value of a correlation can be greatly by the _ of scores represented in the data.
range of scores
the correlation within a restricted range could be completely _ from the correlation that would be obtained from a full range of scores
different
_ , can have a dramatic effect/influence on the value of a correlation.
outliers
One or two extreme data points
outliers
When judging how “good” a relationship is, it is tempting to focus on the numerical value of the correlation. However, a _ should NOT be interpreted as a proportion.
correlation
A correlation that have numerical value of .5 DOES NOT MEAN that you can make predictions with 50% _
accuracy
To describe how accurately one variable predicts the other, you
must _ the correlation.
square (r²)
a correlation of r = .5 means that one variable partially predicts the other, but the predictable portion is only _ % of the total variability.
.25 or 25%
a correlation of r = .5 means that one variable _ predicts the other, but the predictable portion is only r² = 0.25 (or 25%) of the total variability.
partially
the predictable portion of the total variability
the value r²
The value r² is called
coefficient of determination
it measures the proportion of variability in one variable that can be determined from the relationship with the other variable.
the value r²
A correlation of r = 0.80 (or –0.80) means that r² = 0.64
or 64% of the _ in the Y scores can be predicted from the
relationship with X.
variability
high or low scores are?
extreme scores
score that are more toward the mean are what scores?
less extreme scores
When there is a less-than-perfect correlation between two variables, extreme scores (high or low) for one variable tend to be paired with the less extreme scores (more toward the mean) on the second variable.
Regression toward the Mean
less-than-perfect correlation between two variables, extreme scores (high or low) for one variable tend to be paired with the less extreme scores (more toward the mean) on the second variable
are _ for any situation
TRUE
if you get a extreme high/low score most likely the next time you’ll get a _ extreme scores
less extreme scores
statistical hypothesis, no direction is specified, two tailed test
Non-directional Hypotheses
statistical hypothesis, either an increase or decrease in population mean score (located in the critical region), one tailed test
Directional Hypotheses
Non-directional Hypotheses
Ho : ρ = 0
There is no population correlation
Non-directional Hypotheses
H1 : ρ ≠ 0
There is a real correlation
Directional Hypotheses
Ho : ρ ≤ 0
The population correlation is not positive.
Directional Hypotheses
H1 : ρ > 0
The population correlation is positive
The hypothesis test evaluating the significance of a correlation can be conducted using either a _ or an _ (Regression)
t statistic or an F-ratio
An alternative method for measuring effect size is to determine how much of the variability in the scores is explained by the _ effect
treatment effect
the concept behind this measure is that the treatment causes the scores to increase (or decrease), which means that the treatment is causing the scores to vary
Measuring the Percentage of Variance Explained, r²
in correlation the _ causes the scores to increase (or decrease), which means that the treatment is causing the scores to vary
treatment
how much of the variability is explained by the treatment
percentage of variance accounted for by the
treatment and is identified as r²
we can measure how much of the variability is explained by the
treatment, we will obtain a measure of the size of the treatment
_
the size of the treatment effect
_ (1988) also proposed criteria for evaluating the size of a
treatment effect that is measured by r²
Cohen
r² = 0.01
small effect
r² = 0.25
large effect
r² = 0.09
medium effect
r (degrees of freedom, n-2) = calculated value for the correlation, probability level, and the type of test used (one- or two-tailed)
APA standart format of pearson correlation
A correlation for the data revealed a significant relationship between amount of education and annual income, r (28)= +.65, p <.01, two tailed.
r (degrees of freedom, n-2) = calculated value for the correlation, probability level, and the type of test used (one- or two-tailed)
In a study with several variables, correlations between all possible variable _ are computed.
all possible variable pairings
a study measured people’s annual income, amount of education, age, and intelligence, how many possible pairing are theres?
6 possible pairings leading to 6 different correlations
number of possible pairings = number of different correlations
a study with several/multiple variables
results from multiple correlations are most easily reported in a table called a correlation _, using footnotes to indicate which correlations are significant.
correlation matrix
The analysis examined the relationships among
income, amount of education, age, and intelligence
for n = 30 participants. The correlations between
pairs of variables are reported in Table 1. Significant
correlations are noted in the table.
sample report in correlation matrix
