# Caught in a relationship: The case of the Pearson Correlation

Maria T Ping & Willy A Renandya

After teaching for five years, you begin to notice things that happen in your classroom more clearly. For example, you notice that students who read a great deal have a more positive attitude towards language learning, have higher levels of motivation, are more attentive in class and tend to participate more as well. These students also tend to read, speak and write more fluently compared to those who don’t enjoy reading.

In other words, you know that amount of reading is a good indicator of a number of learning variables such as motivation, class participation and improvement in language skills. But you probably don’t know how to capture this relationship (unless you have taken a course in statistics).

One useful statistics that language educators have used to show the relationship between important variables in language learning is Pearson’s Correlation or Pearson r. This statistic can help us understand two things: (1) whether two variables are positively or negatively related (2) the degree or magnitude of the relationship (how big or small is the relationship).

In simple language, when we say that two variables (e.g., amount of reading and vocabulary size) are positively correlated, we are essentially saying that these two variables tend to go together in a certain fashion. And when we say that the correlation is positive and large, we mean to say that the more students read, the larger their vocabulary size. Furthermore, we can also roughly estimate the proportion of variance in the one variable that can be predicted from the other variable by calculating the so-called coefficient of determination (r2).

Procedure

1. Prepare two sets of scores (two variables, namely X and Y). In order to be able to use Pearson’s correlation, make sure that your variables are either interval or ratio scale (you may check it here if you’re unsure about the nature of your variables: https://tinyurl.com/wku6qbh

2. Use Pearson’s r formula to calculate manually. However, as always, you can make use of the online calculators/ programs.

3. Interpret your results and decide whether you have a positive or negative and small, moderate or large correlation. Pearson’s r coefficient value ranges from 0 (this means no correlation, by the way) to -/+1 (perfect correlation).

4. Calculate the coefficient of determination (r2). This coefficient is obtained by calculating the square of correlation coefficient r and then transforming it into percentage (%).

Do note that correlation does not imply causation. When two variables are correlated, r value does not tell us the direction of the relationship. It may be the case that Variable X causes Y to happen, or the other way around.

To investigate a causal relationship between two variable, you will need to design a controlled experiment and use different statistical procedures e.g., the two sample t-test. A worked example of Pearson’s Correlation using Socsstatistics (a free online statistical tool) can be found here.