Difference between revisions of "Manuals/calci/KSTESTNORMAL"
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− | <div style="font-size:25px">'''KSTESTNORMAL(XRange,ObservedFrequency, | + | <div style="font-size:25px">'''KSTESTNORMAL (XRange,ObservedFrequency,Confidence,DoMidPointOfIntervals,NewTableFlag)'''</div><br/> |
− | *<math> | + | *<math>XRange</math> is the array of x values. |
*<math>ObservedFrequency</math> is the frequency of values to test. | *<math>ObservedFrequency</math> is the frequency of values to test. | ||
− | *<math> | + | *<math>Confidence</math> is the mean Value. |
− | *<math> | + | *<math>DoMidPointOfIntervals</math> is the standard deviation of the set of values. |
− | *<math> | + | *<math>NewTableFlag</math> is either TRUE or FALSE. |
− | |||
==Description== | ==Description== | ||
Line 99: | Line 98: | ||
==References== | ==References== | ||
*[http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm Kolmogorov-Smirnov Goodness of Fit test] | *[http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm Kolmogorov-Smirnov Goodness of Fit test] | ||
+ | |||
+ | |||
+ | |||
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ Z3 | Z3 home ]] |
Latest revision as of 16:50, 14 June 2018
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