Difference between revisions of "Manuals/calci/KSTESTNORMAL"

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<div style="font-size:25px">'''KSTESTNORMAL(XRange,ObservedFrequency,Mean,Stdev,Test,Logicalvalue)'''</div><br/>
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<div style="font-size:25px">'''KSTESTNORMAL (XRange,ObservedFrequency,Confidence,DoMidPointOfIntervals,NewTableFlag)'''</div><br/>
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*<math>xRange</math> is the array of x values.
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*<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.
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*<math>Mean</math> is the mean of set of values.
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*<math>Confidence</math> is the mean Value.
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*<math>Stdev</math> is the standard deviation of the set of values.
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*<math>DoMidPointOfIntervals</math> is the standard deviation of the set of values.
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*<math>Test</math> is the type of the test.
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*<math>NewTableFlag</math> is either TRUE or FALSE.
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*<math>Logicalvalue</math> is either TRUE or FALSE.
 
  
 
==Description==
 
==Description==
Line 25: Line 24:
 
*3.Largest empirical estimate of fraction of points falling below <math>x_i</math> and computed as <math>\frac{i}{n}</math> for i=1,...,n.
 
*3.Largest empirical estimate of fraction of points falling below <math>x_i</math> and computed as <math>\frac{i}{n}</math> for i=1,...,n.
 
*4.Theoretical estimate of fraction of points falling below <math>x_i</math> and computed as <math>F(x_i)</math>, where    F(x) is the theoretical distribution function being tested.
 
*4.Theoretical estimate of fraction of points falling below <math>x_i</math> and computed as <math>F(x_i)</math>, where    F(x) is the theoretical distribution function being tested.
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5.Find the absolute value of difference of Smallest and largest empirical value  with the theoretical estimation of points.
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*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.
 
*This is a measure of "error" for this data point.
 
*6.From the largest error, we can compute the test statistic.  
 
*6.From the largest error, we can compute the test statistic.  
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*The Kolmogorov-Smirnov test statistic for the cumulative distribution F(x) is:<math> D_n=Sup_x|F_n(x)-F(x)|</math>,where <math>sup_x</math> is the supremum of the set of distances.
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*The Kolmogorov-Smirnov test statistic for the cumulative distribution F(x) is:<math> D_n=Sup_x|F_n(x)-F(x)|</math>where <math>sup_x</math> is the supremum of the set of distances.
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*<math>F_n(x)</math> is the empirical distribution function for n,with the observations <math>X_i</math> is defined as:<math>F_n(x)=\frac{1}{n}\sum_{i=1}^n I_{X_i\le x}</math>,where <math>I_{X_i\le x}</math> is the indicator function, equal to 1 if <math>X_i\le x</math> and equal to 0 otherwise.
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*<math>F_n(x)</math> is the empirical distribution function for n,with the observations <math>X_i</math> is defined as:<math>F_n(x)=\frac{1}{n}\sum_{i=1}^n I_{X_i\le x}</math>where <math>I_{X_i\le x}</math> is the indicator function, equal to 1 if <math>X_i\le x</math> and equal to 0 otherwise.
 +
 
 +
==Example==
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! 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)
 +
{| class="wikitable"
 +
|+KOLMOGOROV-SMIRNOV TEST
 +
|-
 +
!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
 +
|}
 +
{| class="wikitable"
 +
|+TEST STATISTICS
 +
!ANALYSIS
 +
|-
 +
|MEAN|| 17.21569
 +
|-
 +
|STANDARDDEVIATION || 2.95761
 +
|-
 +
|COUNT ||5
 +
|-
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|D || 0.23665
 +
|-
 +
|D-CRITICAL|| #ERROR
 +
|}
 +
 
 +
'''KS TEST'''
 +
''TYPE NORMALDIST''
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*CONCLUSION - THE DATA IS NOT A GOOD FIT WITH THE DISTRIBUTION.
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|9Of2LTy5Sq0|280|center|K-S Test}}
 +
 
 +
==See Also==
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*[[Manuals/calci/LEVENESTEST| LEVENESTEST]]
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*[[Manuals/calci/MOODSMEDIANTEST| MOODSMEDIANTEST]]
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*[[Manuals/calci/RIEMANNZETA| RIEMANNZETA]]
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*[[Manuals/calci/MANNWHITNEYUTEST| MANNWHITNEYUTEST]]
 +
 
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==References==
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*[http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm Kolmogorov-Smirnov Goodness of Fit test]
 +
 
 +
 
 +
 
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*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 15:50, 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

Spreadsheet
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)
KOLMOGOROV-SMIRNOV TEST
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
TEST STATISTICS
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

K-S Test

See Also

References


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