6 Correlation

In previous activities, you learned how to enter data into Jamovi and produce descriptive statistics to help summarise and explore a dataset. In this activity, you will move on to one of the most commonly used inferential statistical techniques in the social sciences: correlation.

In research, inferential statistical tests are often used to test hypotheses. A hypothesis is a prediction about what researchers expect to find in their data based on theory, previous evidence, or observation. For example, a researcher may predict that higher stress levels will be associated with poorer sleep quality; that increased age may be related to poorer memory; or that increased exercise will be linked to higher wellbeing.

Correlation analyses are used when researchers want to investigate whether two variables are related to one another. They examine whether changes in one variable are associated with changes in another. Relationships may be positive (both variables increase together) or negative (as one variable increases, the other decreases).

Activity 5: Correlation

Timing: Allow 20 minutes

The video uses a fictional research example investigating the relationship between mood and serotonin levels. In the example, participants complete a standardised questionnaire measuring depression, while serotonin levels are assessed using blood samples. The aim is to investigate whether lower serotonin levels are associated with higher levels of depressed mood. Specifically, the hypothesis predicts that ‘there is a negative correlation between serotonin and depression score’.

As you work through the activity, you will learn how to:

• run a correlation analysis in Jamovi
• select variables for analysis
• interpret the direction and strength of a correlation
• understand statistical significance within the correlation output
• report and interpret correlation results appropriately.

The video will guide you through the process of carrying out a Pearson correlation using the Correlation Matrix option in Jamovi, as well as explaining how to interpret the output produced by the software.

Download this video clip.Video player: Video 4: Correlation

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Transcript: Video 4: Correlation

SPEAKER

Correlation-- in the following tutorial, you will be shown how to carry out a simple correlation analysis. Correlations tell us about the relationship between pairs of variables-- for example, height and weight or age and memory performance.

We're going to do a worked example. This example is based on a fictional study investigating the relationship between mood and serotonin levels. As some drugs that are given to people to treat depression work by stimulating serotonin pathways, we might expect to see a relationship between depression scores and serotonin levels in the blood. Specifically, we might predict that people with lower levels of serotonin have higher levels of depression.

To test the relationship between mood and serotonin levels, we first need a way of measuring these two things. We could give participants a standardized test to reliably measure their depression levels. In this example, we could use the Beck Depression Inventory, which involves filling out a short questionnaire about their feelings and depressive symptoms. This is then numerically scored. Serotonin level could be measured by taking blood from each participant and assessing the level of the neurotransmitter detected in the samples.

This is what the data looks like in jamovi, and this can be found in the file below. The different columns display the following data. Part_ID refers to the ID number assigned to the participant. We use these numbers as identifiers instead of participant names, as this allows us to collect data while keeping the participants anonymous. This is good practice in psychology, especially when collecting potentially sensitive data, such as that about mental health. Age is usually recorded to allow the researcher to rule out age as a possible confounding variable.

BDI_Score is our first variable of interest, depression score. This is measured by the Beck Depression Inventory and is scored between 0 and 63. Higher scores indicate higher levels of depressed mood.

Serotonin is our second variable of interest. In this case, levels of the neurotransmitter in participants' blood samples were measured in nanograms per mil.

Running the correlation-- to start the analysis, click on Analyses. Select Regression, and click Correlation Matrix. This brings up the Correlation Matrix dialog box. Here, we can see all our variables from the data file displayed in the box on the left.

To tell jamovi what we want to analyze, we need to move our variables to the box on the right. First, select BDI_Score in the left-hand box, and click on the arrow to move it to the right-hand box. Then select Serotonin in the left-hand box, and click on the arrow to move it to the right-hand box, the same box that BDI_Score has moved to. Now you will see both variables in the right-hand box, as shown.

We next want to make sure that we have ticked certain things in the boxes below, to make sure they are included in our output. Under correlation coefficients, we need to make sure Pearson is selected. Normally, jamovi selects Pearson as the default. As you can see, we have the option to select Spearman or Kendall's tau-b. For the purposes of the example, we want to use Pearson.

Under Additional Options, we want to select Report significance, Flag significant correlations, N sample size. What we select under hypothesis depends on our predictions about the outcome. If we were unsure whether the relationship between our variables is likely to be positive-- that is, as one variable increases, so does the other-- or negative-- as one variable increases, the other decreases-- we would choose correlated. If we had good scientific reason to expect the relationship to be positive-- as one variable increases, so does the other-- we would select correlated positively. If we had good scientific reasons to expect the relationship to be negative-- as one variable increases, the other decreases-- we would select correlated negatively.

We stated above that we expect serotonin levels to fall as depression increases, i.e. a negative correlation. So we should select correlated negatively. Once you've done this, your Correlation Matrix dialog box should mirror the image shown. The output will then update on the right-hand side based on our selection.

The output-- so what does the output show you? The correlation table only has two variables in it, so it's not too hard to read in this example, but sometimes you might be investigating the relationship between several variables all at once. If that were the case, you would have multiple variables in your table. Regardless of the number of variables you have in this table, the way you read it is always the same.

In our example, you can see we have variables displayed on the left-hand side of the table and across the top. The part of the table that contains numbers is the section that we want to focus on. This is highlighted in the red box in the image shown.

These correlation statistics tell us three things. Firstly, the direction of the correlation between the variables, Pearson's r. Secondly, the strength of the correlation between the variables is Pearson's r. And finally, whether this correlation is significant or not from the p-value.

The Pearson's r is used to determine the strength and the direction of the correlation. We can tell the direction of the relationship between the variables from the Pearson correlation line. If the Pearson's coefficient r is positive, this means that as the value of one variable goes up, the value of the other variable also increases. In contrast, if the relationship is negative, this means that as the value of one variable goes up, the value of the other variable goes down. As you can see, our Pearson's r is minus 0.97. This indicates a negative relationship between our two variables.

The strength can also be read from the Pearson correlation line. Ignoring the direction of this value-- that is, whether it's positive or negative-- the Pearson's coefficient, or r, tells you the strength of the relationship. 0.8 or above is very strong. 0.5 or above is strong. 0.3 or above is medium. Less than 0.3 is weak. Looking at our Pearson's r, which is minus 0.97, we can see that there is a very strong negative relationship between our two variables, as Pearson's r is larger than 0.8.

The p-value tells us whether or not this relationship is significant. In psychology, we tend to accept values of less than p equals 0.05 as significant. As you can see, our p-value is less than 0.001, indicating that the negative correlation between depression score and serotonin level is significant. As such, we can confirm that our hypothesis, which predicted that there will be a negative correlation between depression scores and serotonin level, is supported and correct.

You will also notice at the bottom of the table, jamovi has noted that a hypothesis is one tailed. This means that we have tested a directional prediction. That is that the relationship between BDI score and serotonin will be negative, and the p-value reflects that.

Quick quiz-- question one, what does the correlation table show? Is it A, there is no significant correlation between depression score and serotonin level; B, that depression score and serotonin level are highly positively correlated; C, that depression score and serotonin level are highly negatively correlated; or D, the correlation between depression score and serotonin level is an example of a perfect correlation?

The answer is C. There is a correlation between depression score and serotonin level, which you can tell by looking at the Pearson's r, or the Pearson correlation coefficient. So A is incorrect. Looking at the value of the coefficient, it is neither positive-- so B is incorrect-- nor a perfect correlation, which is either 1.0 or minus 1.0 So D is incorrect. The two variables are highly negatively correlated.

Question two, do the results in the table support the hypothesis that there will be a significant negative correlation between depression score and serotonin level? Answer A, yes; B, no; or C, they neither support nor refute this claim?

Null-hypothesis significance testing uses a rule to decide whether you should accept or reject the null hypothesis, H0, in favor of the research hypothesis, H1. To determine this, the p-value needs to be less than 0.05. As this is the case here, as p is less than 0.001, the answer is A. The negative correlation between depression score and serotonin level is significant, so you can reject the null hypothesis, that there is no relationship between the variables, in favor of your research hypothesis.

Writing up the results-- when writing up your results, you need to report the strength, direction, and significance of the correlation, along with the correct statistics, and give a meaningful interpretation of your findings. A Pearson's correlation is reported using the small letter r, followed by the degrees of freedom, df, in parentheses. So in this case, we may say something like, the results showed a very strong significant negative relationship between depression score and serotonin level. r bracket 18, close bracket, equals minus 0.97. p is less than 0.001, one-tailed test. As serotonin scores increased, the participants' depression scores decreased.

This brings us to the end of the tutorial. Why not download the data set used in this tutorial and see if you can produce the same output on your own? You could also try adding age into the correlational analysis to see what you find.

End transcript: Video 4: Correlation

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Now you have seen how to carry out a correlation analysis in Jamovi, you can practise these skills yourself using the example dataset activity which you can download below and open using the File menu in Jamovi. Try reproducing the same analysis and explore what happens when you include additional variables in the correlation matrix. You can download a PDF version of this tutorial, and the dataset used in it below:

File: Correlation tutorial

File: Correlation dataset

Practising these techniques yourself will help you become more confident both in using Jamovi and in understanding how correlations can be used to investigate relationships between variables in research.