A-Level Biology - Spearman's rank correlation coefficient

Summary

In this video, David explains the Spearman rank correlation coefficient, which measures monotonic relationships between variables, unlike Pearson's correlation that focuses on linear relationships. He illustrates how to calculate the Spearman coefficient using an example involving two plant species, Daisy and Poppy. The process includes ranking the data, calculating the differences in ranks, and determining the significance of the correlation. Despite a negative correlation value, the statistical test confirms no significant correlation exists between the percentage covers of the two species. The video emphasizes the importance of understanding these statistical methods in biology.

Takeaways

• 📊 The Spearman rank correlation coefficient measures the strength and direction of the monotonic relationship between two variables.
• 🔄 Values of the Spearman rank correlation range from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation.
• 📈 Unlike Pearson's correlation, Spearman's correlation is used for non-linear relationships.
• 🧑‍🔬 Spearman rank correlation is useful for assessing independent samples, such as the percentage cover of different plant species.
• 📋 To use Spearman's correlation, start by stating the null hypothesis, which assumes no correlation between the variables.
• 🔢 Data should be ranked ordinally from lowest to highest before performing the correlation calculation.
• 💡 In case of tied ranks, assign the average rank to the tied values.
• ⚖️ After ranking, calculate the difference in ranks for each pair, square those differences, and sum them.
• 🔍 The significance of the Spearman rank correlation is determined by comparing the calculated value to critical values from a table at a chosen confidence level.
• ✔️ If the calculated Spearman value is smaller than the critical value, the null hypothesis is accepted, indicating no correlation.

Q & A

What is the range of values for the Spearman rank correlation coefficient?

The Spearman rank correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

How does Spearman rank correlation differ from Pearson's correlation?

Spearman rank correlation measures monotonic relationships that are not necessarily linear, while Pearson's correlation is used specifically for assessing linear relationships.

Can Spearman rank correlation handle tied ranks? If so, how?

Yes, Spearman rank correlation can handle tied ranks by assigning each tied value the average rank of the positions they occupy.

What is the null hypothesis in the context of the Spearman rank correlation?

The null hypothesis states that there is no correlation between the two variables being studied.

In the example given, what two plant species were assessed for correlation?

The example assessed the correlation between the percentage cover of Daisies and Poppies.

What method is used to rank the data in Spearman rank correlation?

Data is ranked from lowest to highest for each variable, using ordinal data or rank values instead of raw data.

What does the calculated RS value of -0.445 indicate in the example?

The calculated RS value of -0.445 indicates a negative correlation between the percentage cover of Daisies and Poppies.

What significance level is commonly used when testing Spearman rank correlation?

A common significance level used in biostatistical tests for Spearman rank correlation is 95%, corresponding to a p-value of 0.05.

How do you determine whether to accept or reject the null hypothesis?

You compare the calculated RS value to the critical RS value from the table of critical values. If the calculated value is smaller than the critical value, the null hypothesis is accepted; otherwise, it is rejected.

What conclusion was drawn from the analysis of the correlation between Daisies and Poppies?

The conclusion was that there is no significant correlation between the percentage cover of Daisies and Poppies, despite the negative RS value.