# Fisher

Fisher test is a non-parametric test for a difference in proportion between two independent dichotomous samples.

The requirements of the test are:

- Two dichotomous independent samples measured on a nominal or ordinal scale.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout or Table dataset layout containing two nominal or ordinal scale variables. If only a summary of the number of subjects for each combination of the dichotomous groups is available (contingency table) then a 2-way table dataset containing counts can be used.

When entering new data we recommend using New Dataset to create a new **2 variables (categorical)** dataset or **2 x 2 contingency table** ready for data entry.

**Using the test**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Compare Groups**on the**Analyse-it**tab, then click**Fisher** - Click
**Factor A**and**Factor B**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 Groups** then click **Fisher**.

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

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

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

The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. The number of observations of each group in the two samples is shown.

The hypothesis test is shown. The *p*-value is the probability of rejecting the null hypothesis, that the samples have the same proportion in each group, when it is in fact true. A significant p-value implies that the samples have different proportions in each group.

** METHOD ** An exact p-value is calculated using the hypergeometric distribution (see [2]). The 2-tailed p-value is computed as 2 x 1-tailed p
-value.

## Difference of proportions

A point estimate and confidence interval for the difference of proportions between the samples can be shown to evaluate if the difference is practically useful. The point estimate can be expressed as a simple difference of proportions, an odds-ratio, or a relative risk.

To change the point-estimate and confidence interval:

- If the Fisher dialog box is not visible click
**Edit**on the**Analyse-it**tab/toolbar. - Click
**Point estimate**then select**Difference**,**Odds-ratio**or**Relative risk**. - Enter
**Confidence interval**to calculate for the point estimate. The level should be entered as a percentage between 50 and 100, without the % sign. - Click
**OK**.

The point estimate expressed as a simple difference, an odds-ratio, or a relative risk and confidence interval are shown.

** METHOD ** The confidence interval for the point estimate when expressed as a difference is computed using the Normal approximation (see [3]). When expressed as an odds-ratio or relative risk the logit Normal approximation is used (see [3]).

## Further reading & references

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

David J. Sheskin, ISBN 1-58488-440-1 2003; 505. - Practical Non-parametric Statistics (3rd edition)

Conover W.J. ISBN 0-471-16068-7 1999; 209. - Statistics with Confidence (2nd edition)

Gardner M.J., Altman D.G. ISBN 0-7279-1375-1 2000; 45-72.

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