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Text File | 1992-08-11 | 22.4 KB | 538 lines

SIMSTAT 1.00c August 9, 1992 Designed and written by Normand Peladeau Copyright (C) 1991,92, N. Peladeau FILES YOU SHOULD HAVE --------------------- Before you start working with SIMSTAT, take a few moments to check the content of the archived file. The program should include 12 files: 4 text files READ.ME -- This file. ORDER.FRM -- Use this file to order copies of Simstat. LISENCE.DOC -- Lisence and warranty information. VENDOR.DOC -- Information for shareware vendors. 3 files for the main program SIMSTAT.EXE -- The simstat statistical program. SIMSTAT.DEF -- The simstat default configuration file. SIMSTAT.HLP -- The simstat help file. 4 sample data files SAMPLE.DAT -- A sample ASCII data file. SAMPLE.SYS -- A SPSS/PC+ system file. SAMPLE.DBF -- A dBASE III data file SAMPLE.WKS -- A Lotus 1-2-3 data file. 1 utility file EXPAND.EXE -- A program to uncompressed listing files INSTALLING AND RUNNING THE PROGRAM ---------------------------------- To install the program, simply copy all the files to the destination disk or directory. There are three command line options that can be used with SIMSTAT: /M or -M Force monochrome color set on a computer with a color card. /E or -E Display 43 lines on an EGA or 50 lines on a VGA monitor. /C or -C Save the listing file in a compressed format. This option is useful for saving disk space when running on a laptop. The listing file will take up to 75% less disk space. You must use the EXPAND.EXE utility to uncompress the listing file. PROGRAM MAINS FEATURES ---------------------- SIMSTAT is a menu driven statistical program that provide many basic descriptive and comparative statistics including: o Summary statistics (mean, variance, standard deviation, etc.) o Crosstabulation - normal crosstabulation and inter-raters agreement table - nominal statistics including: - chi-square - Pearson's Phi - Goodman-Kruskall's Gamma - Contingency coefficient - ordinal statistics - Kendall's tau-b - Kendall's tau-c - Pearson's R - Symetric and asymetric Somers' D, Dxy and Dyx - inter-raters agreement statistics including: - percentage of agreement - Cohen's Kappa - Scott's Pi - Krippendorf's r - Krippendorf's R-bar - free marginal correction for nominal and ordinal measure o Frequencies analysis including: - frequencies table - barchart - histogram - descriptive statistics - percentile table o Breakdown analysis o Oneway analysis of variance o Paired and independent sample t-tests o Pearson correlation matrix, covariance and cross product deviation o Regression analysis including: - Linear and 7 nonlinear regressions including: - quadratic - cubic - 4th degree polynomial - 5th degree polynomial - logarithmic - exponential - inverse - X and Y scatterplot - regression equation - analysis of variance - residuals plot o Nonparametric analysis including: - Mann-Whitney U test - Wilcoxon T-test - Sign test - Kruskall-Wallis ANOVA - Kolmogorov-Smirnov test for 2 samples - Moses test of extreme reactions - Median test (2 or more samples) o nonparametric association matrix including - Spearman's R - Sommer's D, Dxy and Dyx - Goodman Kruskall's Gamma - Kendall's Tau-a, Tau-b - Kendall Stuart's Tau-c BOOTSTRAP ANALYSIS ------------------ SIMSTAT also gives the user access to an innovative and extremely powerful statistical technique called bootstrap simulation. This technique developed by Efron (Efron, 1981; Diaconis & Efron, 1983) can be used to assess various properties of statistical estimators such as their accuracy, their sampling variability, etc.. Typical applications include the computation of nonparametric estimates of sampling distributions, the assessment of the stability of statistical estimators and the construction of nonparametric confidence intervals. SIMSTAT also allows the computation of nonparametric power estimates and Type I error rates for various estimators. The following section provides a short non-technical introduction to the bootstrap technique followed by a description of SIMSTAT particular implementation of bootsrapping methodology. Potential applications for researchers, statistical consultants and for students and teachers in statistics are also presented. For further information about bootstrap methods and its application you can read the articles of Efron and his colleagues (Diaconis & Efron, 1983; Efron, 1981; Efron & Gong, 1983). Wasserman and Bockenhold (1989) also provide an excellent introduction to bootstrap methodology, while Stine (1989) offers an comprehensive presentation of it's potential application. WHAT IS BOOTSTRAP SIMULATION? Bootstrap simulation is a resampling technique whereby initial sample subjects are treated as if they constitute the population under study. By replicating those data an infinite number of time, we then draw at random from that population a large number of samples, each the same size as the original sample. By computing, for every bootstrap sample, a statistical estimator of interest (such as a mean or a correlation between two variables), this resampling procedure recreates an empirical sampling distribution of this statistics. The main advantage of such a procedure is that the sampling distribution is not mathematically estimated but empirically reconstructed based on all the original characteristics of the data. So, it automatically takes into account distribution properties that are generally considered as contaminating factors, such as skewness, ceiling effects, outliers, etc. This feature makes bootstrap estimations adequate even when data are not normally distributed. In fact, bootstrapping can even be used to describe the sampling distribution of estimators for which sampling properties are unknown or unavailable. SIMSTAT IMPLEMENTATION OF BOOTSTAPPING SIMSTAT provides bootstrap analysis for seven descriptive estimators of a single variable and twenty estimators involving two variables. Those estimators are: One variable estimators: - Mean - Median - Variance - Standard deviation - Standard error - Skewness - Kurtosis Two variables estimators: - Kendall's Tau-A and B - Kendall-Stuart's Tau-C - Symmetric and asymmetric Somers' D - Goodman-Kruskal's Gamma - Student's t and F - Pearson's r - Spearman's R - Regression slope and intercept - Mann-Whitney's U - Wilcoxon's W - Difference between means - Difference between variances - Sign test - Kruskal-Wallis ANOVA - Median test The number of bootstrap samples for a single analysis can range from 100 to 20,000. The output of a simulation analysis can consist of various results, including descriptive statistics, frequency tables, histograms and percentile tables. The program also computes bootstrap confidence intervals. For estimators which can be tested for significance, SIMSTAT also displays nonparametric power estimates for up to four alpha levels. Power estimation with the bootstrap technique is straightforward: while performing bootstrap on a given data set, the proportion of redrawn samples that lead to a statistically significant estimator (at some given alpha level) is computed and used as a power estimate. In addition to simulation results, the program displays the value of the seed used to initialize the random number generator. This value may then be used to regenerate the same data at a later time or to compare various estimators using the same bootstrap samples. EXTENSIONS TO BOOTSTRAP To achieve an even greater range of potential application SIMSTAT implements two extensions to standard bootstrap simulation. 1) Variable sample size One typical aspect of bootstrap simulation is that it generally involves redrawn samples of the same size as the original one. However (de son cot ), SIMSTAT offers the possibility to modify the dimension of the bootstrap samples, thus allowing to compare estimator distributions obtained from different sample sizes. The user can set bootstrap simulations involving sample sizes that range from 10 to 20,000 observations. 2) Randow sampling Another aspect of bootstrapping is that it assumes that the original sample is representative of the population. SIMSTAT offers a modified bootstrap sampling process that makes the null assumption that there is no difference or relation in the population. While in bootstrap sampling the drawing is achieved on subjects, the RANDOM procedure extracts the data for each variable independently. Consequently, while a standard bootstrap simulation on a correlation between two variables would yield coefficients that fluctuate around the correlation that exists in the original sample, the RANDOM procedure would produce correlations that vary around a null correlation. In this procedure, the proportion of redrawn samples that lead to a statistically significant estimator at a given alpha level are use to assess the type I error rate. BOOTSTRAP APPLICATIONS We have already seen that standard bootstrap resampling can be use to obtain various measure of sampling variability such as nonparametric confidence intervals. The capability to alter the bootstrap sample size and to replicate the condition of the null hypothesis also establish numerous new applications. The following topic gives some examples of such applications. 1) Research planning - Power estimation The possibility to compare various estimator distributions obtained for different sample sizes can prove useful in planning research by allowing the researcher to determine the sample size needed to achieve a desired precision level. It can also be used for power estimation allowing comparison of the power attained using various estimators and/or sample sizes. Researchers thus have an empirical basis for choosing between two different statistical strategies. In addition, unlike standard approaches to power estimation, which rely on numerous assumptions, including normal data distributions, bootstrap power estimates makes no distribution assumptions. 2) Teaching Tool As a teaching tool, bootstrap simulation would be effective in illustrating to new stats students concepts such as sampling theory or central limit theorem. It would provide a simulation of the sampling process of an experiment, allowing the students to visualize the sampling variability of given estimators. By increasing or decreasing sample size, the student can observe how these changes affect the variability of estimators or the statistical power of an experiment. Additionally, bootstrap would be effective in demonstrating how outliers can affect estimation and how data transformation can improve population estimates. 3) Monte Carlo investigations Bootstrap might also be handy for the researcher interested in studying the effect of violation of the normality assumption on some estimators by allowing the evaluation of the Type I and Type II (statistical power) error rate of a test. While Monte Carlo simulations usually analyze data generated by assumed mathematical functions, bootstrap simulation provides a direct assessment of sample distributions from data provided by the researcher. By performing simulation on data distributions more representative of real world data, bootstrap may therefore be a more appropriate evaluation of statistical robustness. BOOTSTRAP REFERENCES DIACONIS, P., & EFRON, S. (1983, May). Computer intensive methods in statistics. SCIENTIFIC AMERICAN, 116-130. EFRON, B. (1981). Nonparametric estimates of standard error: The jackknife, the bootstrap, and other resampling methods. BIOMETRIKA, 68, 589-599. EFRON, B., & GONG, G. (1983). A leisurely look at the bootstrap, the jackknife and cross-validation. AMERICAN STATISTICIAN, 37, 36-48. STINE, R. (1989). An introduction to bootstrap methods: Examples and ideas. SOCIOLOGICAL METHODS AND RESEARCH, 8(2&3), 243-290. WASSERMAN, INPUT AND OUTPUT ---------------- The data may be entered directly from the keyboard or read directly from a dBase file (version III or IV), a LOTUS 1-2-3 file, a SPSS/PC+ file or from a ASCII data file. The keyboard entry may be saved for later analysis. The output can be read on the screen, save on disk in a listing file, and/or send directly to the printer. CAPABILITY ---------- The program can handle up to 500 variables and 20,000 cases. The simulation can contain between 100 and 20,000 sub-sampling. These limitations are the absolute maximum and can be somewhat lower depending on the amount of memory available. SYSTEM REQUIREMENTS ------------------- SIMSTAT will run on any IBM PC/XT, AT, PS/2 and compatible under MS-DOS/PC-DOS version 2.0 or higher. A minimum of 356K of free RAM is necessary. The program does not need a numeric coprocessor but will use it if available. A coprocessor is highly recommended for extensive bootstrap simulation or computation on large samples. SIMSTAT take less than 120K of disk space (including the help file). It can easily be run on a system with a single 360K disk drive or on a LAPTOP computer. CREDIT ------ IBM-PC/XT, AT and PS/2, PC-DOS are trademarks of International Business Machines MS-DOS is a registered trademark of Microsoft Corporation. SPSS/PC+ is a registered trademark of SPSS Inc. DBASE III and IV are trademarks of Ashton-Tate. LOTUS is a trademark of Lotus Corp. RELEASE HISTORY --------------- 1.00c 09-08-92 - Fixed "Invalid printer port" error on 486 computers. (I/O OPTIONS). - Fixed problem with analysis on more that 16,384 valid cases. - Fixed floating point error when performing a logarithmic regression with a value of zero (REGRESSION) 1.00a 06-19-92 NEW FEATURES AND IMPROVEMENTS ----------------------------- - Added bootstrap simulation analysis for 7 descriptives statistics and 20 bivariate statistics. - More powerful case selection. A single string of up to 250 characters can now be used to select cases. It may consist of a simple expression or include many expressions related by logical operators (AND, OR, XOR). Multiple parentheses level can be used to control the order in which expressions are evaluated. - Added 6 new measures of inter-rater agreement (CROSSTAB) o Scott's pi (nominal) o Adjusted Kappa (nominal) o Krippendorf's r (ordinal) o Krippendorf's R bar (ordinal) o free marginals adjustement (nominal and ordinal). - Added ability displays a listing of the values of the selected dependent and independent variables. - Improved memory management that gives up to 64k more ram for statistical analysis. - Improved monochrome color scheme. - Added user defined page header. - Improved algorithm for automatic histogram scaling when a normal curve is superimposed (FREQUENCIES). - More consistant use of the keyboard keys for the CHOOSE X-Y command (pressing the escape key will cancel the operation and restore previous variable definitions while the F10 key is use to accept the data definition) FIXED PROBLEMS -------------- - fixed problem with the computation of Spearman's R (NPAR MATRIX). - fixed problem with the output of variance and standard error in analysis of variance (ONEWAY). - fixed problem with histogram output with a normal curve (FREQUENCIES). - fixed floating point overflow error (runtime error 205) in the computation of Kolmogorov-Smirnov and chi-square probability (KOLMOGOROV-SMIRNOV, CROSSTAB and KRUSKALL- WALLIS). - fixed problem with variable label printing beyond the listing width (DESCRIPTIVE). - Fixed problem with residual plot in regression analysis (REGRESSION). - Fixed problem with SPSS/PC+ files of more than 500 variables. - Fixed problem with monochrome color scheme (-m switch). - Fixed problem with memory management in regression procedure (REGRESSION). 0.93 (beta) 12-15-91 NEW FEATURES AND IMPROVEMENTS ----------------------------- - Added nonlinear regressions (quadratic, cubic, 4th and 5th degree polynomial, logarithmic, exponential and inverse) (REGRESSION). - The F7 key can be used to toggle the printer on and off. - The F8 key can be used to toggle the disk log on and off. - Improved precision for confidence intervals with small degree of freedom (less than 8) (ONEWAY and REGRESION). - Added capability to browse through the last analysis even if the listing is not saved to disk. - The file listing window displays information on files and directory (OPEN FILE). FIXED PROBLEMS -------------- - Fixed problem with the scatterplot scaling (REGRESSION). - Fixed problem with confidence intervals other than 95% (ONEWAY and REGRESSION). - Fixed problem with barchart on string variables (FREQUENCIES). 0.92 (beta) 09-21-91 NEW FEATURES AND IMPROVEMENTS ----------------------------- - Added option for user defined confidence intervals (ONEWAY and REGRESSION). - The "." caracter in ASCII files is now treated as a missing value. - Added automatic decimal adjustment for very small numbers. - Improved algorithm for choosing scatterplot scaling (FREQUENCIES) FIXED PROBLEMS -------------- - Fixed problem with large number overlapping. - Fixed problem with the computation of the mode (FREQUENCIES). - More typographical errors corrected. 0.91 (beta) 06-25-91 NEW FEATURES AND IMPROVEMENTS ----------------------------- - Added option to eliminate the beep (I/O OPTION). - REGRESSION procedure now includes an anova, standard error and confidence interval of the slope and the intercept. FIXED PROBLEMS -------------- - Fixed problem with printer error message. - Fixed problem with reading Lotus file (OPEN FILE). - Help file corrected. 0.90 (beta) 06-14-91 - First public release. DISTRIBUTION ------------ Since SIMSTAT 1.00 is a shareware product, you are encouraged to experiment with it and share it with your friends as long as the following provisions are met: 1) It is distributed ONLY in its original, unmodified form. 2) No fee is charged for copying or distribution without permission by the author. You can contact the author by writing to the following addresses: By mail: Normand Peladeau Provalis Research 5000, Adam street Montreal, QC H1V 1W5 By electronic mail via CompuServe: Normand Peladeau User# [71760,2103]