One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is also called the Kolmogorov-Smirnov D test or Kolmogorov-Smirnov Z test. One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test tests whether or not a given distribution is not significantly different from one hypothesized (on the basis of the assumption of a normal distribution).
One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is a more powerful alternative to chi-square goodness-of-fit tests when its assumptions are met. Chi-square test for goodness-of-fit tests whether or not in general, the observed distribution is not significantly different from the hypothesized one. On the other hand, One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test tests whether or not it is even for the most deviant values of the criterion variable. Thus, One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is a more stringent test.
The observed distribution in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is the distribution of the variable in the sample. The hypothetical distribution in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is the expected distribution of a variable with the same parameters. For One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test, the distribution types, which are supported by SPSS, are the normal, Poisson, exponential, or uniform distributions. The other distributions are supported through graphical methods.
The expected hypothetical distribution in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is calculated by consulting the appropriate distribution table. The D value in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is the largest absolute difference between the cumulative observed proportion and the cumulative proportion expected on the basis of the hypothesized distribution. The computed Z is compared to a table of critical values of D in the One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test, for a given sample size. For samples, which is > 35 in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test, the critical value at the .05 level is approximately 1.36/SQRT(n), where n = sample size. If the computed value of D is less than the critical value in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test, the researcher fails to reject the null hypothesis, that the distribution of the criterion variable is not different from the hypothesized (ex., normal) distribution.
Assumptions
We assume that the sample has been obtained by random sampling in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test. In One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test, continuous interval or ratio data are required for exact results. If approximate results are sufficient, then ordinal data or grouped interval data may be (and commonly are) used. One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test is also used for ordinal data when the large-sample assumptions of the chi-square goodness-of-fit tests are not met.
Hypothetical distribution is specified in advance in One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test. For the normal distribution, the expected sample mean and sample standard deviation must be specified in advance. For the Poisson distribution and the exponential distribution, the expected sample mean must be specified in advance. For the uniform distribution, the expected range (minimum, maximum values) must be specified in advance.
One Sample Kolmogorov-Smirnov Goodness of Fit Test Resources
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