# Discussion Correlation Coefficient

March 8, 2022
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## Discussion Correlation Coefficient

Discussion Correlation Coefficient

Description
Is the Measure of Consistency a State of Mind?
In your unit readings from the Psychological Testing and Assessmenttext, you read about three sources of error variance that occur in testing and assessment. These include test construction, test administration, and test scoring and interpretation. Additionally, other sources of error may be suspect. You were also introduced to reliability coefficients, which provide information about these sources of error variance on a test (see Table 5-4).

The following reliability coefficients were obtained from studies on a new test, THING, purporting to measure a new construct (that is, Something). Alternate forms of the test were also developed and examined in subsequent studies published in the peer-reviewed journals. The alternate test forms were titled THING 1 and THING 2. (Remember to refer back to your Psychological Testing and Assessment text for information about using and interpreting a coefficient of reliability.)

Internal consistency reliability coefficient = .92
Alternate forms reliability coefficient = .82
Test-retest reliability coefficient = .50

Describe what these scores mean.
Interpret these results individually in terms of the information they provide on sources of error variance.
Explain whether these data are acceptable.
Explain under what conditions they may not be acceptable and under what conditions, if any, they may be appropriate.
RESPONSE GUIDELINES
Respond to the posts of at least two other learners.

LEARNING COMPONENTS

Define test reliability.
Explain statistical knowledge needed to use and interpret tests.
Analyze peer-reviewed literature on reliability.
Apply writing and citations skills appropriate for doctoral-level learners.

RESOURCES
Discussion Participation Scoring Guide.

Correlation Coefficient Formula: Definition
Correlation coefficient formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where:

1 indicates a strong positive relationship.
-1 indicates a strong negative relationship.
A result of zero indicates no relationship at all.

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Meaning
A correlation coefficient of 1 means that for every positive increase in one variable, there is a positive increase of a fixed proportion in the other. For example, shoe sizes go up in (almost) perfect correlation with foot length.
A correlation coefficient of -1 means that for every positive increase in one variable, there is a negative decrease of a fixed proportion in the other. For example, the amount of gas in a tank decreases in (almost) perfect correlation with speed.
Zero means that for every increase, there isn’t a positive or negative increase. The two just aren’t related.
The absolute value of the correlation coefficient gives us the relationship strength. The larger the number, the stronger the relationship. For example, |-.75| = .75, which has a stronger relationship than .65.

What is Pearson Correlation?
Correlation between sets of data is a measure of how well they are related. The most common measure of correlation in stats is the Pearson Correlation. The full name is the Pearson Product Moment Correlation (PPMC). It shows the linear relationship between two sets of data. In simple terms, it answers the question, Can I draw a line graph to represent the data? Two letters are used to represent the Pearson correlation: Greek letter rho (ρ) for a population and the letter “r” for a sample.

Potential problems with Pearson correlation.
The PPMC is not able to tell the difference between dependent variables and independent variables. For example, if you are trying to find the correlation between a high calorie diet and diabetes, you might find a high correlation of .8. However, you could also get the same result with the variables switched around. In other words, you could say that diabetes causes a high calorie diet. That obviously makes no sense. Therefore, as a researcher you have to be aware of the data you are plugging in. In addition, the PPMC will not give you any information about the slope of the line; it only tells you whether there is a relationship.

Real Life Example

Pearson correlation is used in thousands of real life situations. For example, scientists in China wanted to know if there was a relationship between how weedy rice populations are different genetically. The goal was to find out the evolutionary potential of the rice. Pearson’s correlation between the two groups was analyzed. It showed a positive Pearson Product Moment correlation of between 0.783 and 0.895 for weedy rice populations. This figure is quite high, which suggested a fairly strong relationship.

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