Wilcoxon Signed-Rank test

Paired sample rank test

Expected difference between two populations' median

tails:
One Way ANOVA tutorial

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 Independent samples
Normal Distribution Normal distribution of the analyzed population
equal standard deviation Equal standard deviation, σ12=...=σk

Required Sample Data

average 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

Test statistic

Z statistic

Normal Distribution

Normal distribution two tailed Normal distribution two tailed Normal distribution two tailed
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: This test is robust for outliers. It is not recommended to exclude outliers unless you know the reasons
method When n<=40 uses the exact value from table, otherwise z approximation
distribution: 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

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: example from excel


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


Results

 
validation message
tresults