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# Analysis and Interpretation of Correlation

Take two random things, such as the number of phone calls taken, and the amount of water drank although they are random, what if they're not? Can we figure out if these are related? The answer is correlational analysis. Through analysis and interpretation of correlation, we can identify if two random concepts are related/ associated with one another.

• We will start by exploring correlational analysis in research and then examine some types of correlation analysis.
• Next, we will cover correlation coefficients: appropriate use and interpretation.
• Then we will look at correlation analysis examples and how they are visually presented on scattergrams. We will see how informal interpretations can be inferred from such graphs.
• To finish off, we will look at the strengths and weaknesses of correlations.

## Correlation Analysis in Research

Correlations measure the association between two variables (co-variables) that exist naturally, meaning researchers do not manipulate the variables. Thus, correlations are non-experimental research methods.

Correlations are used when conducting:

• 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 manipulate the variables.

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

Suppose you have developed a new scale and want to test its reliability.

You could investigate it with the test-retest method. When using this method, researchers get some participants to complete the scale and then ask the same participants to complete the scale again later.

The researchers then run a correlational analysis to see if the scores from the first time correlated with the second time. If they do, it suggests that the scale has high reliability.

A correlation exists when the scores on one variable covary or are associated with another variable's values.

Correlation analysis is widely used in psychological and real-world research.

For example, you may have come across studies that look at the relationship between gender and emotional intelligence. Although it seems like this study would perform correlation analysis, it is investigating differences between the two groups, males and females, and this is not what correlational analyses do.

It is important to keep in mind that a correlation can only be performed when the two variables of the study present continuous data. If one of the variables is categorical, like the example above, a correlation cannot be performed because the variable is discrete.

A discrete variable is a variable that includes nominal or ordinal data, e.g. gender or order of finishing a race. Conversely, a continuous variable is a variable that provides interval data, e.g. intelligence scores or weight.

## Types of Correlation Analysis

There are three types of correlation:

• Positive correlation: From these, researchers can infer when one variable increases, the other variable also increases.

• Negative correlation: It can be inferred that as one variable increases, the other variable decreases, or vice versa.

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

## Correlation Coefficients: Appropriate Use and Interpretation

Correlation coefficients (r) indicate the strength between two variables in numerical terms. And these can range from -1 to +1. The number 0 means there is no correlation. Negative numbers indicate negative correlations, and positive numbers indicate positive correlations.

Researchers are not only interested in the type of correlation but also check the magnitude of correlations; this refers to how strong the relationship between the variables is.

Researchers look at the correlation coefficient (R-value) to establish the magnitude of the correlation.

The interpretation is the following:

 An R-value... ... indicates Smaller than 0.19 there is almost no correlation of 0.2 to 0.39 there is a low/small correlation of 0.4 to 0.69 there is a moderate/substantial correlation of 0.7 to 0.89 there is a high/strong correlation of 0.9 to 1.00 the is a very high/strong correlation

When conducting scientific work, researchers usually do not only present correlations in a written manner but also express them visually through scatterplots. Let's take a look at these graphs.

## Visual presentation of Correlations in Research: Scattergrams

To create a scattergram, researchers plot one variable against the other on a graph and inspect them to determine the relationship between the variables.

Normally when plotting a graph, it is important to determine which axis variables should go on. However, this is not the case in correlational scattergrams.

The purpose of why researchers visually present correlational findings on scattergrams is to allow others to understand and interpret the relationship between the two variables easily.

Let's look at what the graph would generally look like for positive, negative, and zero/no correlation.

## Correlation Analysis Example: Positive, Negative and No Correlations

A positive correlation indicates that the other will also increase as one variable increases in value.

In scattergrams with near-perfect correlations with a ‘line of best fit’ plotted, the data points are expected to be extremely close and follow the line closely.

The line of best fit is the line that best describes the relationship between points on a scattergram.

Fig 1 - Scatter plot of a perfect positive correlation.

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

Fig. 2 - Scatter plot depicting a positive correlation where the data points are spread out from the line of best fit.

Let’s look at a positive correlation depicted in the image. Note the points are spread out from the line of best fit.

In negative correlations, the researchers can assume that as one variable increases, the other decreases.

For instance, as stress levels increase, how much sleep we get reduces. Experimental research should be conducted to establish if stress causes poor sleep hygiene. As from correlational study, we cannot establish cause and effects; instead, only relationships can be established.

Fig. 3 - Scatterplot illustrating a negative correlation.

When two variables are not correlated or show a zero correlation, the data points are spread randomly on the scattergram, making it difficult to see any pattern between the variables.

### Informal Interpretations of Correlation

From scattergrams, we can make informal interpretations of correlations. Informal interpretations are essentially when the researcher or reader attempts to understand the relationship between variables by interpreting scattergrams rather than based on statistical findings.

However, researchers should refrain from mentioning informal interpretations of correlation in psychological publications. Instead, they should only include correlational analyses from statistical findings. The scattergrams are usually included so the reader can understand and visualise the findings.

## Evaluation of the Strengths and Weaknesses of Correlations

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

These are some of the strengths of correlations:

• One of the main strengths of using correlations is that they are a fairly simple and easy-to-carry statistical test.
• Correlations are informative and allow researchers to test for general associations in the real work and test the validity and reliability of their experiments and developed tools, such as questionnaires.
• Correlations can be done on data collected in laboratory settings and in natural settings, and so have extensive practicality.
• The research method does not require any manipulation from the researchers; this, in turn, makes the study of certain topics possible. It wouldn't be ethical to encourage people to become obese so that researchers can study the relationship between obesity and rates of heart disease. The strength is that correlation can test for naturally occurring events.

These are some of the weaknesses of correlations:

• One of the main limitations of correlations is that these types of analyses do not indicate causation. Although there may be a correlation between cheese consumption and car accidents, one cannot establish that consuming cheese causes car accidents.
• Given the lack of cause-and-effect correlations establish, there is always the chance that a third variable may influence the relationship. As the research is only exploring two variables, what if others are causing the changes; these are called confounding variables.

## Analysis and Interpretation of Correlation - Key takeaways

• Correlations measure the association between two variables (co-variables).
• Researchers might decide to use correlations are a form of non-experimental research.
• There are three types of correlations: positive correlation, negative correlation, and zero/no correlation, which indicate the direction of the co-variables relationship.
• Correlation coefficients (r) indicate the strength between two variables 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.

#### Flashcards in Analysis and Interpretation of Correlation 9

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How do you analyse correlation?

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

What is correlation analysis and its types?

Correlation analysis identifies and measures correlations. The different types of correlations are:

• Positive correlations.
• Negative correlations.
• No correlations.

Where is correlation analysis used?

In psychology, non-experimental studies typically use correlations to identify and measure the associations between variables. For example, it may be used to test the reliability of scales, tests and questionnaires.

What is correlation analysis? What is an example?

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

What is the relationship between analysis and correlation?

A correlational analysis is a statistical test used to identify and measure the relationship between co-variables.

## Test your knowledge with multiple choice flashcards

Correlation coefficients range from -1 to +1.

What correlation is weaker, 0.2 or 0.8?

What correlation is stronger, -0.7 or -0.4?

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