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# Wilcoxon–Mann–Whitney-test

## 1 sample Wilcoxon test

If Diff median is selected and one of the comparing column contains 1 value the 1 sample Wilcoxon test is calculated. To calculate the if there is a significant difference in Median between a dataset and a Hypothesized value. This non parametric test is for not normally distributed data but before using this test try to find out why the data is not normally distributed see "What to do with not normally distributed data".

### Interpretation

• The smaller the p value is the more likely there is a significant difference between the dataset and the hypothesized value.
• Develve uses the commonly accepted value of p < 0.05 for significance.
• Because Develve uses normal approximation sample size must be bigger than 20
• For a good power (0.8 in Develve) the sample size data sets must be bigger than the minimum sample size calculated.
• If the datasets is normally distributed use the 1 sample t-test

#### For a good result the data must

• The data is paired.
• Data is randomly and independent

### Colors of the cells

• Green
No significant difference
• Yellow
Significant difference
• Orange
Sample size to small

### Formula #### With tie correction

Ties are data point with the same value. With the z value the p value can be found in the normal table.

#### Legend = smallest sum of ranks = Amount of samples minus values that are the same as comparing value = amount of ties of the absolute rank

### Sample size

Sample size calculation is the same as with the 1 sample t-test but with 15% more samples.
The result is the minimum sample size of the dataset.

#### not equal #### bigger smaller ### Example

To use the 1 sample Wilcoxon test first select "non normal distributed" when the box is unselected the one sample t-test is calculated. Then select Diff median. In this example E is significantly different from the median of A and D not. For both test the sample size is to low but for the comparison D to A it is maybe worth to invest to do more measurements. Data file

# 2 sample Mann whitney test

If Diff median is selected and the comparing column and this column contains more than 1 value, the Mann–Whitney-test is calculated between this column and the comparing column. This to calculate if there is a significant difference of the Median of the two datasets. This non parametric test is for not normally distributed data but before using this test try to find out why the data is not normally distributed see "What to do with not normally distributed data"

### Interpretation

• The smaller the p value is the more likely there is a significant difference between the 2 datasets.
• Develve uses the commonly accepted value of p < 0.05 for significance.
• Because Develve uses normal approximation sample size must be bigger than 20
• For a good power (0.8 in Develve) the sample size for both data sets must be bigger than the minimum sample size calculated.
• If both datasets are normally distributed use the 2 sample t-test

#### For a good result the data must

• Data is randomly and independent.
• The data is continuous.
• The shape of the distribution of both datasets is the same.

### Colors of the cells

• Green
No significant difference
• Yellow
Significant difference
• Orange
Sample size to small

### Formula

Both datasets are sorted and ranked in order. The sum of the ranks of each dataset is calculated ( and )  With the smallest U value the z score is calculated. #### With tie correction

Ties are data point with the same value. With the z value the p value can be found in the normal table.

#### Legend and = Sum of ranks (the ranking is the absolute value of the difference) and = Amount of samples = amount of ties of a rank

### Sample size

Sample size calculation is the same as with the 2 sample t-test but with 15% more samples. is the biggest one of the two comparing data sets. The result is the minimum sample size for both data sets.

#### not equal #### bigger smaller ### Example

To use the 2 sample Mann Whitney test first select "non normal distributed" when the box is unselected the 2 sample t-test is calculated. Then select Diff median. In this example C is significantly different from the median of A and B not. The minimum sample size for the comparison A and B is to low but the difference in not significant so it is not worth to invest in more measurements. Data file