This method is an alternative to a one-sample t-test when the data cannot be assumed to be normally distributed. This method is based on the ranks of observations rather than on their actual values

- To determine if the median/location of the population from which your data is drawn statistically significantly different from the specified median
- To know the basic descriptive statistics about your data
- To know the descriptive statistics plot such as box-plot, distribution histogram, and density distribution plot about your data

- Your data contain only 1 group of values (or 1 numeric vector)
- Your data are meaningful to measure the distance from the specified median
- The values are independent observations
- No assumption on the distributional shape of your data, which means your data may be not normally distributed

- The band inside the box is the median
- The box measures the difference between 75th and 25th percentiles
- Outliers will be in red, if existing

- Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
- Density Plot: to estimate the probability density function of the data

**Histogram**

When the number of bins is 0, plot will use the default number of bins

**Density plot**

**Results of the Wilcoxon Signed-Rank Test**

- P Value < 0.05, then the population median is significantly different from the specified median. (Accept the alternative hypothesis)
- P Value >= 0.05, then the population median is NOT significantly different from the specified median. (Accept the null hypothesis)

*From the default settings, we concluded that the scales were significantly greater than 1 (P = 0.006), which indicated the patients were suffering from Depression.*

This method is an alternative to two-sample t-test when the data cannot be assumed to be normally distributed

- To determine if the medians of two population from which your 2 groups data drawn are statistically significantly different from each other
- To determine if the distributions of 2 groups of data differ in locations
- To know the basic descriptive statistics about your data
- To know the descriptive statistics plot such as box-plot, distribution histogram, and density distribution plot about your data

- Your data contain only 2 groups of values (or 2 numeric vectors)
- Your data are meaningful to measure the distance between 2 groups values
- The values are independent observations
- No assumption on the distributional shape of your data
- Your data may be not normally distributed

Notes:

- The band inside the box is the median
- The box measures the difference between 75th and 25th percentiles
- Outliers will be in red, if existing

- Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
- Density Plot: to estimate the probability density function of the data

**Histogram**

When the number of bins is 0, plot will use the default number of bins

**Density plot**

- P Value < 0.05, then the population medians of 2 groups are significantly different. (Accept alternative hypothesis)
- P Value >= 0.05, no significant differences between the medians of 2 groups. (Accept null hypothesis)

*From the default settings, we concluded that there was no significant differences in 2 groups Rating scale (P=0.44).*

This method is an alternative to paired-sample t-test when the data cannot be assumed to be normally distributed.

- To determine if the difference of paired data is statistically significantly different from 0
- To know the basic descriptive statistics about your data
- To know the descriptive statistics plot such as box-plot, distribution histogram, and density distribution plot about your data

- Your data contain 2 groups of values (or 2 numeric vectors)
- Your data are meaningful to measure the distance from the specified median
- The values are paired or matched observations
- No assumption on the distributional shape of your data
- Your data may be not normally distributed

- One person's pre-test and post-test scores
- When two samples have been matched or paired

Notes:

- The band inside the box is the median
- The box measures the difference between 75th and 25th percentiles
- Outliers will be in red, if existing

- Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
- Density Plot: to estimate the probability density function of the data

**Histogram**

When the number of bins is 0, plot will use the default number of bins

**Density plot**

- P Value < 0.05, then the Before and After are significantly different. (Accept the alternative hypothesis)
- P Value >= 0.05, then the Before and After are NOT significantly different. (Accept the null hypothesis)

*From the default settings, we concluded that there was no significant difference after the treatment. (P=0.46)*