The Sample Sign is a non-parametric hypothesis test is used to test if the median of a distribution is equal to a specific value.

For run this test it’s important that:

In this case the hypothesis are like in case of two tail test:

• H0: The median is equal to a specific value;
• H1The median is diffferent to the specific value.

In this case the hypothesis are like in case of one tail left test:

• H0: The median is equal to a specific value;
• H1The median is lower than the specific value.

In this case the hypothesis are like in case of one tail right test:

• H0: The median is equal to a specific value;
• H1The median is higher than the specific value.

The way to conduct the hypothesis test is like the one-sample t-tests, but we use another statistics.

For small number of observation (n <= 25) you can compute the statistics in

• Set the specific median value;
• Set for each observation less than the specific median value a sign -, if equal or above a sign +
• Count the number of + and the number of -. You have y= the min number between this.

If you have a big number of observation (n > 25) you need to plug you y value in the formula of image1.