Dr. Arbuthnot, a Scottish physician, invented the one sample sign nonparametric hypothesis test in 1710, but, what is the one sample sign t test? Sign testing is used to verify the null hypothesis that a distribution’s median equals some hypothesized value. It was invented by Dr. Arbuthnot, a Scottish physician in 1710.

Many hypothesis testing attempt to draw conclusions about continuous data . The problem is that the data are assumed to be from a particular population distribution, which is often a normal distribution. If you want to determine if a single sample of 25 minutes is from a normally distributed population, with a mean time of 25 minutes, then you will use a 1-sample T-test.

Sign test is used for the following:

- To determine which product is preferred
- Perform a test to determine the median value of a single sample (one sign test).
- To test the median of paired differences using data from two dependent samples.

## One Sign Test Sample

The one-sample sign test hypothesis computes a sign test for the median value of a single data set. The nonparametric sign test 1 is a hypothesis test that determines if there is statistically significant variation between the median value of a continuous non-normally distributed data set and a standard. This test is essentially about the median of a continuous populace.

The 1 sample sign test compares the number of observations that are less than or more than the hypothesized value. The one-sample Wilcoxon sign-rank test is similar but less powerful than this 1 sample sign test.

One-sample sign tests are a nonparametric variant of the one-sample t-test. The one sample sign test for a median population can be either one-tailed (right- or left-tailed), or two-tailed based on the hypothesis.

- H
_{0 }:median>= Hypothesized Value k; H_{1 }Median - Right-tailed test – H :median= Hypothesized Value k; H : Median >k
- Two-tailed test – H : median= Hypothesized Value k; H : median value k

## Assumptions about the one-sample sign test

- Data distribution is not normal.
- Random sample of independent measurements taken for a population with an unknown median
- Continuous interest is the variable
- One sample test deals with non-symmetric data sets, which can be skewed to the left or right.

## One sample sign non-parametric hypothesis test

- Describe the claim of the test, and identify the null hypothesis or alternative hypothesis
- Determine the significance level
- Add positive and/or negative signs to the data and determine the sample size (n). n is the sum positive and/or negative signs.
- Get critical value
- Calculate the test statistic
- Use y if n= 25, (approx). Where y is the number of positive or negative signs.

- If the critical value is lower than the test statistic, make a decision.
- The original claim should be interpreted in context.