# Estimating Correlation

## Practise the skill of estimating the correlation of data on a scatter graph in this self marking exercise.

##### Level 1Level 2Real LifeExam-StyleDescriptionHelpMore Statistics

This is level 2: Estimating Pearson's Correlation Coefficient. You will be awarded a trophy if you get at least 9 correct and you do this activity online.

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This is Estimating Correlation level 2. You can also try:
Level 1 Real Life

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## Description of Levels

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Level 1 - Estimating the type of correlation in words

Level 2 - Estimating Pearson's Correlation Coefficient

Real Life - Arrange the given statements in groups to show the type of correlation they have.

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## Example

The video above is from the excellent Corbett Maths.

Phrases like "strong", "moderate" or "weak" are used to describe the strength of the correlation, and it's usually subjective, there is no definitive agreement on how to match the phrases to the Pearson Product-Moment Correlation Coefficient

The thresholds for labelling a correlation as "very weak", "weak", "moderate", "strong", or "very strong" are somewhat arbitrary and can vary depending on the field of study or the preferences of a researcher.

For instance, in some social sciences, correlations are often lower, so a researcher might consider a correlation of 0.4 as "strong". In contrast, in some natural sciences where relationships might be more deterministic, a "strong" correlation might require a higher threshold.

Here's one of the common scales:

• 0.0 - 0.2 or 0.0 to -0.2: Very weak or no correlation
• 0.2 - 0.4 or -0.2 to -0.4: Weak correlation
• 0.4 - 0.6 or -0.4 to -0.6: Moderate correlation
• 0.6 - 0.8 or -0.6 to -0.8: Strong correlation
• 0.8 - 1.0 or -0.8 to -1.0: Very strong correlation

However, others might use a different scale like:

• 0.0 - 0.1 or 0.0 to -0.1: Negligible correlation
• 0.1 - 0.3 or -0.1 to -0.3: Weak correlation
• 0.3 - 0.5 or -0.3 to -0.5: Moderate correlation
• 0.5 - 0.7 or -0.5 to -0.7: Strong correlation
• 0.7 - 1.0 or -0.7 to -1.0: Very strong correlation

It's also important to remember that Pearson's r only measures linear relationships. Therefore, even if Pearson's r is close to 0, there might still be a strong non-linear relationship between the variables.

In practice, it's often good to not just rely on the value of Pearson's r, but also visually inspect the data through scatter plots and consider the context of the data being analysed. The terminology one uses to describe the strength of a correlation should be carefully chosen based on the standards of the field and the nature of the data.

In order to complete this exercise, because there are nine different examples, you could order the diagrams then order the phrases or coefficients in order to make a ranking match.

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