# Manuals/calci/SIGNTEST

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**SIGNTEST(Array,Median,AlternateHypothesis,NewTableFlag)**

- is the set of values to find the statistic value.
- is the median of the array of values.
- is the alternate hypothesis of the array.
- is either TRUE or FALSE.

## Description

- This function gives the test statistic of the Sign test.
- The Sign Test is ued to test the Hypothesis that there is no difference between two continuous distributions X and Y.
- This test is one type of the Non parametric Test.
- The sign test is designed to test a hypothesis about the location of a population distribution.
- The Sign test does not require the assumption that the population is normally distributed.
- The normality of the distribution is doubtable, then Sign test is used to find the statitic instead of one sample T-test.
- The sign test uses the sign of the differences, unlike the paired t test which uses the sign and magnitude of the differences.
- To perform this test, Consider the independent pairs of sample data from the populations .
- From this pair,it must be omitted with no differences .
- The Sign test data are having the following properties:
- 1.The differences of pairs are assumed to be independent.
- 2.Each pairs comes from the same continuous population.
- 3.The values and represent are ordered , so the comparisons "greater than", "less than", and "equal to" are meaningful.
- The test statistic is expected to follow a binomial distribution, the standard binomial test is used to calculate significance.
- The sign test can also be viewed as testing the hypothesis that the median of the differences is zero.
- The sign test Hypothesis is having the following steps:
**Step1**:State Null and Alternative Hypothesis- Two ways to state these: One sample or sample of differences, want to test specific value for the population median M.
- Null: H0:p=1/2is equivalent to M = M0.
- Alternative: Ha:p<1/2 is equivalent to or is equivalent to or Ha:p not equal to 1/2 is equivalent to
**Step2**:Test statistic (no data conditions needed)- S+ = Number of observations greater than or Number of observations with .
- S− = Number of observations less than or Number of observations with .
- Ties are not used, so use n = S+ + S−.
**Step3**: Finding the p-value- Remember, p-value is:
- Probability of observing a test statistic as large as or larger than that observed
- in the direction that supports Ha
- if the null hypothesis is true.

**Step 4**:Use tables of the binomial distribution to find the probability of observing a value of

r or higher assuming p = 1/2 and .

- If the test is one-sided, this is your p-value.
**Step5**: If the test is a two-sided test, double the probability to obtain the p-value.

## Example

A | B | |
---|---|---|

1 | 15 | 10 |

2 | 19 | 17 |

3 | 32 | 35 |

4 | 42 | 38 |

5 | 24 | 16 |

- =SIGNTEST(A1:B5,5,10,true)

X Range | Y Range | Difference |
---|---|---|

15 | 10 | 5 |

19 | 17 | 2 |

32 | 35 | -3 |

42 | 38 | 4 |

24 | 16 | 8 |

P-Value | 0.375 |

## Related Videos

## See Also

## References