# Wilcoxon Signed-Rank test

## Paired sample rank test

Expected difference between two populations' median

Target: To check if the diffrence between the average (mean) of two or more groups (populations) is significant, using sample data
ANOVA is usually used when there are at least three groups, since for two groups you can use t tests.

Example1: A farmer use four differnt fertilizers in four fields. The farmer compare sample average of apples' weight from each field to decide if the difference between the fertilizers is significant.

## Assumptions

 Independent samples Normal distribution of the analyzed population Equal standard deviation, σ1=σ2=...=σk

## Required Sample Data

 Sample data from all compared groups

## Parameters

k - Number of groups.
ni - Sample side of group i.
n - Overall sample side, includes all the groups (Σni, i=1 to k).
xi - Average of group i.
x - Overall average (Σxi,j / n, i=1 to k, j=1 to ni).
Si - Standard deviation of group i.

## Hypotheses

H0: var1 ≥ var2 H0: var1 = var2 H0: var1 ≤ var2
H1: var1 < var2 H1: var1 ≠ var2 H1: var1 > var2

## Normal Distribution

c - continuity correction, when U > μ: c = -0.5, when U < μ: c = 0.5

## Test calculation

The tool uses the critical value tables when n ≤ 25 and a normal approximation for a larger sample size

### Statistic Data

 α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error) μ0: Expected difference, usually zero outliers: included excluded This test is robust for outliers. It is not recommended to exclude outliers unless you know the reasons method automatic z approximation When n<=40 uses the exact value from table, otherwise z approximation distribution: continuouses discrete Continuity correction for discrete distribution (relevent only for normal approximation)

Enter raw data directly
Enter raw data from excel

## Enter sample data directly

Header: You may change groups' name to the real names.
Data: When entering data, press Enter after each value.
Difference = Right - Left

 Groups Before After data

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

## Enter sample data from excel

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of consecutive columns includes the header, and paste below. . click to see example:

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

### Results

 sample average sample average sample size n sample SD median skewness symmetrical normality outliers outliers count W+ W-
validation message
tresults