# Sign

Sign test is a non-parametric test for a difference in central location (median) between two paired samples.

The requirements of the test are:

- Two paired samples measured on an ordinal or continuous scale.
- Samples need not be normal and need not have similar shape distributions.

## 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 the test**

**Using the test**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Compare Pairs**on the**Analyse-it**tab, then click**Sign**. - Click
**Variable X**and**Variable Y**and select the variables to compare. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - 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 **Compare Pairs** then click **Sign**.

X ≠ Y to test if the median(X) is not equal to median(Y). |

X > Y to test if the median(X) is greater than median (Y). |

X < Y to test if the median(X) is less than median (Y). |

The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. Since the test uses the sign of the difference between paired observations, the number of positive, negative and zero differences are shown.

The Sign statistic and hypothesis test are shown. The *p*-value is the probability of rejecting the null hypothesis, that the samples have the same median, when it is in fact true. A significant p-value implies that the two samples have different medians.

**METHOD ** An exact p-value is calculated using the Binomial distribution (see [1] or [2]).

## Median difference point estimate

If both samples are continuous the median difference and confidence interval can be calculated to quantify the difference between the samples in terms that can be practically evaluated.

To calculate a confidence interval:

- If the Sign test dialog box is not visible click
**Edit**on the**Analyse-it**tab/toolbar. - Enter
**Confidence interval**to calculate for the difference in medians. The level should be entered as a percentage between 50 and 100, without the % sign. - Click
**OK**.

The median of the differences and confidence interval are shown.

** METHOD ** The median difference and confidence interval are calculated using the Hodges-Lehman method (see [2]).

## References to further reading

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

David J. Sheskin, ISBN 1-58488-440-1 2003; 621. - Practical Non-parametric Statistics (3rd edition)

Conover W.J. ISBN 0-471-16068-7 1999; 157-164.

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