### Specification

- List B from Topic B (Cognitive), focusing on the Spearman rank test.

#### Spearman´s Rank

Spearman’s rank correlation coefficient, also known as the Spearman’s rho, is a statistical measure used to determine the strength and direction of a relationship between two variables that are measured on an ordinal or continuous scale. It is a non-parametric method, which means that it does not assume a specific distribution of the data. To conduct a Spearman’s rank correlation analysis, you would follow these steps:

**Collect the data:**Gather the data for the two variables of interest, making sure that both variables are measured on an ordinal or continuous scale.**Rank the data:**For each variable, assign a rank to each value based on its position in the data set. For example, if there are 10 data points, the lowest value would be ranked as 1, the next lowest as 2, and so on, up to the highest value, which would be ranked as 10.**Calculate the difference between the ranks:**For each pair of data points, calculate the difference between the ranks of the two variables.**Square the differences:**Square each of the differences obtained in step 3.**Sum the squared differences:**Sum all the squared differences obtained in step 4.**Calculate the correlation coefficient:**Use the formula rho = 1 – (6 * sum of squared differences) / (n^3 – n)

where n is the number of data points, and rho is the correlation coefficient.

- Interpret the results: The correlation coefficient will range from -1 to 1. A coefficient of -1 indicates a perfect negative correlation, a coefficient of 1 indicates a perfect positive correlation, and a coefficient of 0 indicates no correlation. The correlation coefficient can be used to determine the strength and direction of the relationship between the two variables.
- Test the significance: Compare the correlation coefficient to a critical value in a table to determine whether it is statistically significant.

It is important to note that spearman correlation assumes a monotonic relationship between the variables, meaning that when one variable increases, the other variable also increases or decreases in a consistent direction. Additionally, it does not assume normality on the data, which is useful when the data is non-normal.

#### Past Paper questions

- Give two reasons why Tau used a Spearman’s rank test on his data. (2)
*October 2018* - Serenity used the Spearman’s rank test to see if her results were significant. Give two reasons why Serenity used the Spearman’s rank test for her data. (2)
*January 2022* - Tau used p≤0.01 as his level of significance for a one-tailed test. Tau had twenty participants. Identify the critical value for a Spearman’s rank test for Tau’s data. The critical values can be found in the formulae and statistical tables at the front of the paper. (1)
*October 2018* - Tau made a type II error when deciding whether his results were significant or not. Explain why Tau made a type II error. (2)
*October 2018* - Arrissa carried out a Spearman’s rank test for a one-tailed test and found a calculated value of –0.58. Explain whether Arissa’s results were significant at p≤0.05. (2)
*June 2017* - Complete Table 1 and calculate Spearman’s Rank test between the average number of hours sleep in a night and the number of aggressive acts in a week. The formula can be found in the formulae and statistical tables at the front of the paper. You must express your answer to two decimal places. (4)
*October 2017* - State two reasons why the researchers used a Spearman’s rank test. (2)
*January 2017* - Complete Table 1 and calculate Spearman’s Rank correlation coefficient for Hassan’s study. (4)
*June 2019* - Interpret you Spearman’s Rank correlation coefficient from (a)(1) in terms of strength
**and**direction. (2)*June 2019*