
CHI SQUARE GOODNESS OF FIT TESTName:
NOTE: This command has been replaced with the unified GOODNESS OF FIT command.
The primary advantage of the chi square goodnes of fit test is that it is quite general. It can be applied for any distribution, either discrete or continuous, for which the cumulative distribution function can be computed. Dataplot supports the chisquare goodness of fit test for all distributions for which it supports a CDF function. There are two primary disadvantages:
In order to apply the chisquare goodness of fit test, any shape parameters must be specified. For example,
WEIBULL CHISQUARE GOODNESS OF FIT TEST Y The name of the distributional parameter for families is given in the list below. Location and scale parameters can be specified generically with the following commands:
LET CHSSCALE = <value> The location and scale parameters default to 1 if not specified. Dataplot supports the chisquare goodness of fit test for either binned or unbinned data. For unbinned data, Dataplot automatically generates binned data using the same rule as for histograms. That is, the class width is 0.3*s where s is the sample standard devition. The upper and lower limits are the mean plus or minus 6 times the sample standard deviation (any zero frequency bins in the tails are omitted). As with the HISTOGRAM command, you can override these defaults using the CLASS WIDTH, CLASS UPPER, and CLASS LOWER commands. Prebinned data can be specicied in two ways. If your bins are of equal size, then you specify a single X variable that contains the midpoints of the bins. If your bins may be of unequal size, then two X variables are given. The first contains the lower limit of each bin and the second contains the upper limit of each bin. Unequal bin sizes usually result from combining classes with small (less than 5) expected frequency.
where <y> is a response variable; <dist> is one of the following distributions: This syntax is used for the case where you have unbinned data.
where <y> is a variable of precomputed frequencies; <x> is a variable containing the midpoints of the bins; <dist> is as above; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have binned data with equal size bins.
where <y> is a variable of precomputed frequencies; <x1> is a variable containing the lower limits of the bins; <x2> is a variable containing the upper limits of the bins; <dist> is as above; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have binned data with unequal size bins.
NORMAL CHISQUARE GOODNESS OF FIT TEST Y SUBSET GROUP > 1 CAUCHY CHISQUARE GOODNESS OF FIT TEST Y LOGNORMAL CHISQUARE GOODNESS OF FIT TEST X EXTREME VALUE TYPE 1 CHISQUARE GOODNESS OF FIT TEST X LET LAMBDA = 0.2 TUKEY LAMBDA CHISQUARE GOODNESS OF FIT TEST X
SET MINMAX = 1
LET LAMBDA = 3
NORMAL CHISQUARE GOODNESS OF FIT TEST Y X
EV1 and GUMBEL are synonyms for EXTREME VALUE TYPE 1. FATIGUE LIFE is a synonym for FL. RECIPROCAL INVERSE GAUSSIAN is a synonym for RIG. IG is a synonym for INVERSE GAUSSIAN. The word TEST is optional. CHISQUARE, CHISQUARE, and CHI SQUARE can all be used.
read zarr13.dat y . let m = mean y let s = standard deviation y let chsloc = m let chsscale = s normal chisquare goodness of fit test y The following output is generated. ************************************************ ** normal chisquare goodness of fit test y ** ************************************************ CHISQUARED GOODNESS OF FIT TEST NULL HYPOTHESIS H0: DISTRIBUTION FITS THE DATA ALTERNATE HYPOTHESIS HA: DISTRIBUTION DOES NOT FIT THE DATA DISTRIBUTION: NORMAL SAMPLE: NUMBER OF OBSERVATIONS = 195 NUMBER OF NONEMPTY CELLS = 20 NUMBER OF PARAMETERS USED = 2 TEST: CHISQUARED TEST STATISTIC = 5.506083 DEGREES OF FREEDOM = 17 CHISQUARED CDF VALUE = 0.004063 ALPHA LEVEL CUTOFF CONCLUSION 10% 24.76903 ACCEPT H0 5% 27.58711 ACCEPT H0 1% 33.40867 ACCEPT H0 CELL NUMBER, BIN MIDPOINT, OBSERVED FREQUENCY, AND EXPECTED FRQUENCY WRITTEN TO FILE DPST1F.DAT  
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Date created: 06/05/2001 