1. Advanced Higher STATISTICS Spearman’s Rank (Spearman’s rank correlation coefficient) Lesson Objectives 1. Explain why it is used. 2. List the advantages and disadvantages. 3. Understand how to apply the statistical test. 4. Apply it to a relevant context.

2. Soil moisture increases 0 0 Altitude increases Soil moisture 0 Altitude increases 0 0 0 Soil moisture increases Altitude increases Positive correlation r s = +1 No correlation r s = 0 Negative correlation r s = -1 Spearman’s Rank: a relationship?

3. 37 28.5 8 2 15 25 8.5 11 21 31 16 4 Null Hypothesis: there is no significant correlation between percentage of soil moisture and altitude. Alternative Hypothesis: there is a significant correlation between percentage of soil moisture and altitude. 1 2 3 4 5 6 7 8 9 10 11 1224 26 4 0 11 21 9 7 14 5 4 1 2.5 9.5 8 4 5 7 6 2.5 11 1 -2 0.5 0 -0.5 -2 0 -1.5 3 3 -0.5 1 4 0.25 0 1 4 0 2.25 9 9 0.25 ∑ = 0∑ = 31 31186 121728 1716 186 1716 0.108 0.89 CL = 95% Critical Value = 0.591 R s = 0.89, therefore reject Null Hypothesis 12

4. There is a very strong positive correlation. We can reject the null hypothesis and accept the alternative hypothesis. As the altitude increases, the soil moisture also increases. Comparing the statistical result to the critical value shows that the result is 99% significantly confident. There is only a 1% likelihood that the result was due to chance. There is no significant relationship between altitude and soil moisture. Spearman’s Rank: a relationship? State the answer in terms of the null hypothesis. Describe how you might have made the investigation more reliable. Is the relationship statistically significant? What do you reckon? How could you collect better data to make sure the test is reliable? Spearman rank is a widely used technique and is useful for identifying relationships between two variables Spearman rank testing is reasonably quick and easy to calculate Spearman is better if you are unsure that the population used is normally distributed and if the data is measured at the ordinal scale Data is only required to be ordinal (ranked) although other data can be transformed quickly Justify the suitability of using Spearman’s Rank.