Multinomial
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Multinomial | |||
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Input Output License Warranty Download The multinomial program is the exact solution to the Chi-square Goodness of fit test of testing for a difference between an observed and an expected distribution in a one-dimensional array. For example, the test can be used to compare the distribution of diseases in a certain locality with an expected distribution on the basis of national or international experiences using an ICD classification. In a two-category array the multinomial test provides a two-sided solution for the Binomial test. For example, Multinomial {10 20 0.20 0.80} gives the two-sided probability (0.105) for the single sided Binomial {0.20 10 30} probability (0.061). The multinomial allows you to work with empty '0' observation cells although you must have an expectation about a cell. The program recognizes two types of input. Observed values are integers in the range 0, 1 and >1. Non-integers that could potentially be an observed value are truncated to the nearest integer less than the given value. Expected values are proportions in the range >0 and <1. The sum of all the expected values should be 1.0, if this is not so the program gives you a warning. Note that the value 0, zero, nothing, can be an observed but not an expected value. The program will consider that the number of expected values it finds is the number of valid categories to evaluate. In the case of too many observed values the program will ignore observed values, and the program will add zeros if there are too few observed values. The program will read the data in the order in which they are presented, the first observed value considered pertaining to the first category, same for the first expected value. You can cut and paste the data into the input field from a spreadsheet or type it into the input field manually. Please be careful with continental European style decimal commas, they are not accepted as valid, should be decimal dots. Any character that does not have a numerical function will be considered to be a separator between two numbers. There is a maximum of 20,000 cases or 500 categories. However, the program will probably give up long before that. As for all exact procedures, sometimes a very large number of calculations are required to find a solution. The program will issue a warning if calculations might take too long for normal patience. Consider that sometimes it might take your computer a few hours to find a solution to your problem. If you put (cut and paste) the following table into the input field and click calculate: 10 50 30 5 .10 0.55 .20>.15 This will be part of the reply: The (Two-sided) CUMULATIVE PROBABILITY for this or a larger difference: 0.0041541 The output reads easier if you make it full screen first, tick the appropriate button in the top right corner of your screen. In the output field first a table of the data as read is presented, followed by a table of the data but now the observed data as a distribution of proportions and the expected proportions as expected numbers. Mean Absolute Difference, a measure of difference between the observed and the expected distribution follow this. Following this the Pearson (GFX) and the likelihood ratio (LRX) Chi-square are presented. These Chi-squares give you an approximate (two-sided) probability of the difference between the observed and the expected distribution having been caused by chance fluctuation. After this the point-probability, the likelihood of this very specific table is presented. Next the number of calculations required for calculating the cumulative probability is presented. At this point the program issues a warning if the number of calculations required is very large. The cumulative probability is the most important statistic presented by the program. It gives you the probability of this or a more extreme table having been produced on the basis of chance considering a certain expectation regarding the distribution. Additionally, it gives you the probability of a more extreme table and the mid-p probability. The mid-p probability is less conservative compared with the usual "the same and larger than" probability and is mostly closer to approximate statistics. The use of the mid-p value is not recommended. The method of the sum of small p-values is used in the calculations and the probabilities are two-sided. The Chi-squares are also two-sided so both methods should produce the same probability, asymptotically. TOP of pageThis is free software. It can be freely distributed and installed. This program is provided to you by Quantitative Skills Research and Statistical Consultancy. Although this program has been tested extensively, no program is ever bug or error free, and you should always check your results carefully. This software and the accompanying files are sold "as is" and without warranties as to performance or merchantability or fitness for a particular purpose. The entire risk arising out of use or performance of the software remains with you. Copyright: Quantitative Skills and Daan Uitenbroek PhD, 2008. TOP of pageAlthough this program has been tested extensively, no program is ever bug or error free, and you should always check your results carefully. This software is provided "as is" and without warranties as to performance or merchantability or fitness for a particular purpose. The entire risk arising out of use or performance of the software remains with you. TOP of pageDownload the program here by double clicking this link and saving the program to a directory of your choice.
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Multinomial | |||
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