How do you interpret a Wilcoxon Signed Ranks Test

Question

I need to understand what the meaning of a negative z value is. I carried out a study on chatbot personality using Likert type items and found that the z-value for the paired test of prosocial-friendly was -3.021. Can anyone tell me what this means?

Answer 1

Hi Brinda,

Z values are taken from standard normal table. In life it just so happens that a lot of data is normally distributed. I few notable features of the normal distribution are:

1. It is a symmetric distribution

2. The mean = median is the center of the distribution

3. It is a bell shape curve

Here is a link to a picture of the standard normal curve.

https://towardsdatascience.com/understanding-the-68-95-99-7-rule-for-a-normal-distribution-b7b7cbf760c2

While a lot of data follows the normal distribution the standard deviation and mean (for each data set) can be very different so we use the standard normal distribution to transform any normal distribution to a distribution with a mean of 0 and a standard deviation of 1.

A negative z value means that the random variable (or value) you are looking for is a certain number of standard deviations to the left of the mean of the standard normal distribution (while a positive z value means that the random variable (or value) you are looking for is a certain number of standard deviations to the right of the mean of the standard normal distribution).

You can use the Standard Normal Table to find the probability of finding a z value less than a certain z value (for ex. Pr(Z < 1.645) = .95 ) . The Empirical Rule states that for a normal distribution approximately:

- 68% of your data is within 1 standard deviation from the mean

- 95% of your data is within 2 standard deviations from the mean

- 99.7% of your data is within 3 standard deviations from your mean

So it can be interpreted that it will be very unlikely to find a z value of -3.021. You can surmise from the empirical rule the chance of getting a z value less than -3.02 is less than .05% or looking up the value on the z distribution table the Pr(Z < z = -3.012) = 0.001298

I hope that is helpful Brenda.