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# Analysis and Interpretation of Correlation

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Two different variables may have a link between them. They may have a statistical relationship that we can analyse. Scientists have found important pieces of data when two factors have been linked through the analysis of this type of data (for instance, smoking and lung cancer rates.) Without this form of data analysis, we would undoubtedly miss valuable links between variables that could have massive implications.

## What is correlation?

Correlations measure the association between two variables (co-variables).

Remember: correlation does not indicate causation.

Correlations may be used for :

• Non-experimental studies on two variables (there is no defined dependent or independent variable, just two variables measured together).

• Studies where there may be a causal relationship (dependent and independent variable), but it isn’t ethical or practical to investigate that relationship.

• To test the reliability of scales, tests, and questionnaires.

Suppose you have come up with a new scale and want to test its reliability. You could investigate it with the test-retest method. You could get some participants to complete the scale, then ask the same participants to complete the scale again at a later date. Then you can run a correlation to see if the scores have a high correlation. If they do, it suggests your scale has high reliability.

There are three types of correlation:

• Positive correlation: when one variable increases, the other variable also increases.

• Negative correlation: when one variable increases, the other variable decreases, or vice versa.

• Zero/no correlation: there is no correlation between the variables.

There are two ways to check the correlation between co-variables:

• Plotting the co-variables into a scattergram.

• Analysing them statistically which then generates correlation coefficients.

Let’s study these two methods.

### Scattergram

To create a scattergram researchers plot pairs of data on a graph and inspect them to determine the relationship between the variables. Let's take a look at what the graph would generally look like for positive, negative, and zero/no correlation.

#### Positive correlation

In this example graph, the points are pretty much in a perfect correlation. If you put a ‘line of best fit’ onto the points, they would be extremely close and follow the line perfectly.

Example of positive correlation, Erika Hae - StudySmarter Originals.

Line of best fit: a line that best describes the relationship between points on a scattergram.

Remember: the more spread out the points are from a line of best fit, the weaker the correlation is.

Let’s have a look at a weak positive correlation, note the points are spread out from the line of best fit:

Example of weak positive correlation, Erika Hae - StudySmarter Originals.

#### Negative correlation

Here is an example of a negative correlation. As one variable increases, the other one decreases.

Example of negative correlation, Erika Hae - StudySmarter Originals.

#### Zero/no correlation

Finally, here’s an example of zero/no correlation. Here, the data points are scattered (no pun intended), and there’s no clear link or correlation between the two.

Example of zero/no correlation, Erika Hae - StudySmarter Originals.

### Correlation coefficients

Correlation coefficients (r) indicate the strength between two variables in numerical terms.

Correlation coefficients can range from -1 (perfect negative) to +1 (perfect positive). The number 0 means there is no correlation.

Negative numbers indicate negative correlations and positive numbers indicate positive correlations. A correlation is stronger the closer it is to 1 or -1. So a correlation of 0.7 is stronger than 0.3. Similarly, a correlation of -0.7 is stronger than -0.3.

So, if we were to apply this to our graphs above:

• Graph 1 would have a correlation coefficient of roughly 1, as it is a clear positive correlation.

• Graph 2 would have a correlation coefficient of roughly 0.75 (closer to +1), as it is a weaker but still a positive correlation.

• Graph 3 would have a correlation coefficient of roughly -1, as there is a clear negative correlation.

• Graph 4 would have a correlation coefficient of roughly 0, as there is zero/no correlation.

## Evaluation of the strengths and weaknesses of correlations

Let’s discuss some strengths and weaknesses of using correlations in scientific studies.

### Strengths

These are some of the strengths of correlations:
• Correlations can determine if a relationship between two variables exists and it can be explored further in an experimental study. We described one of the uses of correlation for non-experimental studies on two variables. If a correlation is determined, a researcher may decide to conduct an experiment on these variables.
• Correlations are quick and easy to carry out, no need for a controlled environment like in an experiment, no IV or DV.
• Correlation coefficients are a very clear and easy way to describe the relationship between variables as they are an exact number and therefore simple to understand. Correlation has the potential to provide a test for reliability and validity, as the test-retest method can be used to see if correlations exist between variables multiple times.
• Ethically, we can establish correlation records without manipulating variables. So, we can study the correlation between variables we otherwise wouldn’t be able to experiment with due to ethical reasons. An example is obesity and rates of heart disease. It wouldn't be ethical to encourage people to eat more to become overweight and then obese to simply study if they develop any diseases. However, we can see if there is a correlation between the two based on medical data.

### Weaknesses

These are some of the weaknesses of correlations:

• A correlation can only describe the relationship between two variables. Correlation does not indicate causation.
• Due to this previous fact, there is no cause and effect relationship between the co-variables. There is always a chance there is a third influencing variable.
• Correlations are often misquoted to describe a phenomenon as fact (causation) when they only describe a relationship.
• We need to make sure that we also use a significance test to ensure the correlation isn’t purely due to chance.

## Analysis and Interpretation of Correlation - Key takeaways

• Correlations measure the association between two variables (co-variables).
• Researchers might decide to use correlations for non-experimental studies on two variables. They can use correlations in studies where there may be a causal relationship but it is not ethical or practical to investigate it or to test the reliability of scales, tests, and questionnaires.
• There are three types of correlations: positive correlation, negative correlation, and zero/no correlation.
• Correlations can be checked using a scattergram or statistically with correlation coefficients.
• Correlation coefficients (r) indicate the strength between two variables in numerical terms and can range from -1 (perfect negative), to 0 (zero/no correlation) to +1 (perfect positive). A correlation is stronger the closer it is to 1 or -1.

You can determine correlations by plotting the data points on a scattergram and then inspecting the graph to see if a correlation exists. You can also analyse correlations statistically with correlation coefficients.

Correlation analysis checks if there is a relationship between two variables and the strength of the relationship. There are different types of analysis used depending on the data. The types normally used are the Pearson correlation, Kendall rank correlation, Spearman correlation, and the Point-Biserial correlation.

In psychology, correlations are typically used for non-experimental studies on two variables in studies where there may be a causal relationship (dependent and independent variable) but it is not ethical or practical to investigate it. They are also used to test the reliability of scales, tests, and questionnaires.

Correlations measure the association between two variables. For example, amount of caffeine drunk and hours of sleep.

## Final Analysis and Interpretation of Correlation Quiz

Question

What do correlations measure?

The association between two variables (co-variables).

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Question

What are the three types of correlations?

Positive correlation, negative correlation, zero/no correlation.

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Question

What are the two ways to check if there is a correlation between co-variables?

Scattergram and correlation coefficients.

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Question

What is a line of best fit?

A line that best describes the relationship between points on a scattergram.

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Question

In a perfect correlation, where would the points be in relation to the line?

The points would be extremely close and follow the line perfectly.

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Question

What does it indicate if points are spread out far from the line?

The correlation is weak.

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Question

Correlation coefficients range from -1 to +1.

True

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Question

For a correlation coefficient, what does the number 0 mean?

There is no correlation.

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Question

What correlation is weaker, 0.2 or 0.8?

0.2

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Question

What correlation is stronger, -0.7 or -0.4?

-0.7

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