CORRELATION & PEARSON Flashcards by CN D

a statistical technique that is used to measure and
describe the relationship between two variables

Correlation

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The corresponding correlation for the entire population is identified
by the Greek letter

rho (ρ)

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the Greek equivalent of the letter r

rho (ρ)

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The sign of the correlation, positive or negative, describes the direction of the relationship

The Direction of the Relationship

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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

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most common use of correlation is to
measure _ relationships

straight-line relationships (The Form of the Relationship)

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in correlation other forms of relationships do exist and there are _ correlations used to measure them.

special correlations (The Form of the Relationship)

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The correlation measures the consistency of the relationship.

The Strength or Consistency of the Relationship

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for a linear relationship the data points could fit perfectly on a _ line

straight line(The Strength or Consistency of the Relationship)

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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)

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The Direction of the Relationship
The Form of the Relationship
The Strength or Consistency of the Relationship

3 characteristics of a relationship

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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

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a perfect negative correlation, have a value of

–1.00

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no linear trend, have a value of

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a strong positive relationship, approximately have a value of

0.9

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a relatively weak negative correlation, approximately have a value of

–0.40

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measures the degree and the direction of the linear relationship between two variables

Pearson correlation

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used to measure the amount of covariability between two variables.

The Sum of Products of Deviations

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Prediction
Validity
Reliability
Theory Verification

Where and Why Correlation Are Used

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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

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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

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One common technique for demonstrating validity is to use a
correlation.

Validity

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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

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One way to evaluate reliability is to use correlations to determine the relationship between two sets of measurements

Reliability

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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