# Spearman correlation

This procedure is available in both the Analyse-it Standard and the Analyse-it Method Evaluation edition

Spearman correlation is a non-parametric test to determine the degree of correlation (association) between two variables.

The requirements of the test are:

- Two variables measured on an ordinal or continuous scale.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain two ordinal or continuous scale variables.

When entering new data we recommend using New Dataset to create a new **2 variables** dataset ready for data entry.

**Using t**he test

**Using t**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Correlation**on the**Analyse-it**tab, then click**Spearman**. - Click
**Variable X**and**Variable Y**and select the variables. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - Enter
**Confidence interval**to compute around the Spearman*rs*. The level should be entered as a percentage between 50 and 100, without the % sign.**statistic** - Click
**OK**to run the test.

Excel 97, 2000, 2002 & 2003:

Select any cell in the range containing the dataset to analyse, then click **Analyse **on the **Analyse-it **toolbar, click **Correlation** then click **Spearman**.

rs ≠ 0 to test if the variables are correlated. |

rs > 0 to test if the samples are positively correlated, where observations of the variables tend to increase together. |

rs < 0 to test if the samples are negatively correlated, where observations of one variable tend to increase as observations in the other variable decrease. |

The report shows the number of observations analysed, and, if applicable, how many missing cases were pairwise deleted.

The Spearman *rs* correlation statistic and confidence interval are shown.

** METHOD ** The confidence interval is calculated using the Fisher's Normal transformation (see [1] or [2]).

The hypothesis test is shown. The *p*-value is the probability of rejecting the null hypothesis, that the variables are independent, when it is in fact true. A significant p-value implies that the two variables are correlated.

** METHOD ** The p-value is calculated using the *t-* approximation (see [1]). For small sample sizes ≤ 30 exact tables should be used (see [2]), or use the Kendall correlation which calculates exact *p*-values for small samples.** **

When both variables are continuous scale the scatter plot (see below) shows a visual assessment of the strength of association.

## Further reading & references

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 1016. - Practical Non-parametric Statistics (3rd edition)

Conover W.J. ISBN 0-471-16068-7 1999; 314.

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