# Manuals/calci/KSTESTNORMAL

Jump to navigation
Jump to search

**KSTESTNORMAL (XRange,ObservedFrequency,Confidence,DoMidPointOfIntervals,NewTableFlag)**

- is the array of x values.
- is the frequency of values to test.
- is the mean Value.
- is the standard deviation of the set of values.
- is either TRUE or FALSE.

## Description

- This function gives the test statistic of the K-S test.
- K-S test is indicating the Kolmogorov-Smirnov test.
- It is one of the non parametric test.
- This test is the equality of continuous one dimensional probability distribution.
- It can be used to compare sample with a reference probability distribution or to compare two samples.
- This test statistic measures a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples.
- The two-sample KS test is one of the most useful and general nonparametric methods for comparing two samples.
- It is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples.
- This test can be modified to serve as a goodness of fit test.
- The assumption of the KS test is:
- Null Hypothesis(H0):The sampled population is normally distributed.
- Alternative hypothesis(Ha):The sampled population is not normally distributed.
- The Kolmogorov-Smirnov test to compare a data set to a given theoretical distribution is as follows:
- 1.Data set sorted into increasing order and denoted as , where i=1,...,n.
- 2.Smallest empirical estimate of fraction of points falling below , and computed as for i=1,...,n.
- 3.Largest empirical estimate of fraction of points falling below and computed as for i=1,...,n.
- 4.Theoretical estimate of fraction of points falling below and computed as , where F(x) is the theoretical distribution function being tested.
- 5.Find the absolute value of difference of Smallest and largest empirical value with the theoretical estimation of points.
- This is a measure of "error" for this data point.
- 6.From the largest error, we can compute the test statistic.
- The Kolmogorov-Smirnov test statistic for the cumulative distribution F(x) is:where is the supremum of the set of distances.
- is the empirical distribution function for n,with the observations is defined as:where is the indicator function, equal to 1 if and equal to 0 otherwise.

## Example

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

1 | 15 | 20 |

2 | 17 | 14 |

3 | 19 | 16 |

4 | 21 | 25 |

5 | 23 | 27 |

- =KSTESTNORMAL(A1:A5,B1:B5,19,3.16)

DATA | OBSERVED FREQUENCY | CUMULATIVE OBSERVED FREQUENCY | SN | Z-SCORE | F(X) | DIFFERENCE |
---|---|---|---|---|---|---|

15 | 20 | 20 | 0.19608 | -0.74915 | 0.22688 | 0.03081 |

17 | 14 | 34 | 0.33333 | -0.07293 | 0.47093 | 0.1376 |

19 | 16 | 50 | 0.4902 | 0.6033 | 0.72684 | 0.23665 |

21 | 25 | 75 | 0.73529 | 1.27952 | 0.89964 | 0.16435 |

23 | 27 | 102 | 1 | 1.95574 | 0.97475 | 0.02525 |

ANALYSIS | |
---|---|

MEAN | 17.21569 |

STANDARDDEVIATION | 2.95761 |

COUNT | 5 |

D | 0.23665 |

D-CRITICAL | #ERROR |

**KS TEST**
*TYPE NORMALDIST*

- CONCLUSION - THE DATA IS NOT A GOOD FIT WITH THE DISTRIBUTION.

## Related Videos

## See Also

## References