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1 EPISTAT Statistical Package for the IBM Personal Computer Version 3.0, 1984 Written by: Tracy L. Gustafson, M.D. Copyright 1984 2 INTRODUCTION EPISTAT is a collection of programs written in BASICA for statistical analysis of small to medium-sized data samples ( < 28 samples or variables and < 2000 total data entries per file). The 25 programs in EPISTAT perform more than 40 common statistical tests or functions and provide utilities for data entry, editing, printing, graphing, sorting, selecting, transforming and crosstabs. The programs are intended to be as self-explanatory and user- friendly as possible. You do not need to memorize this guide before using the programs. On the other hand, neither the programs nor this manual purport to TEACH the proper use or interpretation of statistics. The user must have some familiarity with the kinds of data required and the underlying assumptions appropriate to each statistical test. For further explanations of tests, refer to: 1. Colton, Theodore. Statistics in Medicine. Little, Brown and Co. Boston, 1974. 2. Fleiss, Joseph. Statistical Methods for Rates and Proportions. John Wiley and Sons. New York, 1981. 3. Snedecor, George W. and Cochran, William G. Statistical Methods. Iowa State Univ. Press. Ames, Iowa, 1978. 4. Schlesselman, James. Case-Control Studies. Oxford Univ. Press. New York, 1982. CAVEAT: These programs have been tested extensively, but I cannot guarantee that they will work correctly with every possible data set. Incorrect results are usually due to errors in format or type of data entered. If you believe you have discovered an error in the programs, please write me. I intend to correct any bugs that are brought to my attention. It is good practice to regularly compare the results obtained by programs in EPISTAT with results obtained by your previous method of calculation. ANY unexpected result should be questionned and double-checked by reference to tables or another method of calculation. 3 INDEX TO EPISTAT The following statistical tests and functions are available: TEST or FUNCTION PROGRAM NAME ---------------- ------------ Analysis of variance (1 and 2-way)...................ANOVA Bayes' theorem.......................................BAYES Binomial distribution................................BINOMIAL Chi-square test and distribvtion.....................CHISQR Correlation coefficients.............................CORRELAT F distribution.......................................ANOVA Fisher's exact test..................................FISHERS Linear regression analysis...........................LNREGRES Mantel-Haenszel Chi-square test......................MHCHISQR Mantel-Haenszel for multiple controls................MHCHIMLT McNemar's test.......................................MCNEMAR Mean, median and standard deviation..................DATA-ONE Normal distribution..................................NORMAL Poisson distribution.................................POISSON Random sample generator..............................RANDOMIZ Rank sum test........................................RANKTEST Rates adjusted (direct and indirect).................RATEADJ Sample size calculations..........,..................SAMPLSIZ Signed rank test.....................................RANKTEST Student's T-test and T distribution..................T-TEST The following data-handling capabilities are provided: DATA MANIPULATION PROGRAM NAME ----------------- ------------ Determine best test and program names................EPISTAT Graph histograms.....................................HISTOGRM Graph scattergrams...................................SCATRGRM Perform data transformations.........................LNREGRES Print data (sorted or input order)...................DATA-ONE Print crosstab reports...............................XTAB Select specific records..............................SELECT Transfer data between EPISTAT files..................FILETRAN Transfer data from FORTRAN to EPISTAT files..........FORTRANS 4 SYSTEM REQUIREMENTS FOR EPISTAT MINIMUM OPTIMAL IBM PC with 64K RAM IBM PC with 96K RAM One 160K disk drive Two 320K disk drives Monochrome monitor Color graphics adapter BASICA Hi-res color monitor BASICA IBM, Epson, Okidata, or Prowriter printer with graphics capability OVERALL PROGRAM DESCRIPTION All calculations in EPISTAT are performed using single precision. Although it may first appear that double precision would be more appropriate for statistical tests, "double" precision makes little or no real improvement in precision in these programs. Many of the algorithms used to evaluate p values use trigonometric functions which are calculated in single precision anyway. For best results, data entries should be numbers between 1E+7 and 1E-7. Larger or smaller numbers should be multiplied by an appropriate power of 10 before entry and analysis in EPISTAT. All EPISTAT programs are written so that as much pertinent information about the test as possible can fit on the final screen. This feature allows a summary printed copy to be produced simply by pressing <Shift-PrtSc>. This will work any time there is a pause in the program display. Six programs, "DATA-ONE", "HISTOGRM", "RANDOMIZ", "SCATRGRM", "SELECT", and "XTAB" produce printed reports without using <Shift-PrtSc>. In these, follow program instructions to route output to your printer. EPISTAT is the introductory program in the EPISTAT package. DATA-ONE is the major data entry, editing, and printing program. Most of the programs in EPISTAT can evaluate data entered and saved using DATA-ONE. Many of the programs can, in addition, evaluate summary data. The programs marked with a star (*) below can evaluate data entered in DATA-ONE. Non-starred programs provide their own data entry routines. The EPISTAT disk should be placed in drive A (or other default drive) when loading any program because "EPIMRG" and "EPISETUP.DAT" are used by every program. Once a program is running, EPISTAT can be removed from drive A if necessary. 5 INDIVIDUAL PROGRAM DESCRIPTIONS (1) "EPISTAT" This introductory program lists the available programs and aids the user in selecting the best statistical test. It also allows one to specify hardware configuration and colors for a color monitor. Choose colors 7,0,0 if you have a monochrome monitor connected to the color/graphics adapter. If yours is not one of the listed printers, check your printer's codes for the typeface you want. For example, the code for elite type on the Prowriter is ESC "E". If you press Escape then E, the display will show the decimal ASCII codes: 27 69. An alternate method is to press <Alt> and enter the decimal code on the numeric keypad. Press <Enter> when the complete code is entered. "DATA-ONE" * DATA ENTRY: This is the central keyboard data entry program for the EPISTAT package (for non-keyboard data entry, see FILETRAN and FORTRANS). Initial data entry (Option 1) first asks you to name your samples or variables. Then type in the data, pressing <Enter> twice after each entry. The maximum number of samples or variables (S) allowed is 28 with a color adapter and 7 with a monochrome adapter. The maximum number of records in each sample is 2000/S. A blank record can be entered by pressing <Enter> then key F2. To exit, press <Enter> then key F10. The mean, median and (n-1) standard deviation are then displayed. When you return to the main menu, SAVE your datafile to disk (Option 5) for future modification or use by other programs in the EPISTAT package. Although all entries in a datafile are treated as numbers by DATA-ONE, it is possible to enter characters (names) in a record. Characters will be treated as zeros in calculations. Nevertheless, it improves data readability to use the "Sample 1" column for record or case names. Thus, DATA-ONE allows one to specify a name for each column (variable) and each row (case) in the datafile. DATA MODIFICATION: APPEND (Option 2) allows one to add more observations to a sample at a later session. EDIT (Option 3) allows one to delete or replace incorrect data entries and to change sample or variable names. When you return to the main menu, SAVE modified data to disk again. PRINTING DATA: To view or review a datafile, a printout to screen or printer can be selected (Option 4). To print a datafile exactly as it was keyed in, request the printout in INPUT order. DATA-ONE can also print the data SORTED by any selected sample. Only numeric data is sorted by DATA-ONE, so it will not alphabetize a character field. Blank records are not sorted, either. SAVING DATAFILES and LOADING DATAFILES: SAVING data (Option 5), writes your data to disk in a sequential file for later editing, review, or use by another program. DATA MUST BE SAVED TO DISK before it can be used by other programs in EPISTAT. Since EPISTAT must be in drive A: (or other default drive) to begin, you will probably want to SAVE datafiles on drive B. To do so, precede each datafile name with B: (e.g. B:TESTDATA). Do not enclose filenames in quotation marks. 6 (3) "ANOVA" * Provides ONE-way and TWO-way analysis of variance. One-way ANOVA compares the means of 3 or more samples. Two-way ANOVA compares the combined effects of 2 variables on a third (ROW and COLUMN effects). All samples in two-way ANOVA must have the same number of elements. ANOVA prints sample means, (n-1) variances and sums of squares. It also evaluates a known F value. (Snedecor, pp. 258-338) (4) "BAYES" Using Bayes' theorem, this program calculates the rates of false positive and false negative tests given different sensitivities, specificities and outcome incidences. Using the formula in a different way, it calculates the prior probability of several outcomes given a positive test. (Fleiss, p. 5) (5) "BINOMIAL" The binomial distribution allows calculation of the probability of an observed number compared to the expected. It assumes the variable is dichotomous and has an equal probability of occurring in each trial. This program calculates the ONE-tailed probability of the observed number and all more extreme situations. For example, in the case of 2 heads in 10 tosses of a coin, the ONE-tailed probability includes the sum of the probabilities for 0,1 and 2 heads. (Colton, p. 151) (6) "CHISQR" The Chi-square program evaluates a table of data or a known chi-square value. 2 by 2 tables are evaluated using Yates' correction and the odds ratio and its confidence limits are calculated using Cornfield's method (Schlesselman, p. 175,177). A Chi-square test for trend can also be performed. (Sclesselman, p. 201) (7) "CORRELAT" * Pearson's correlation coefficient and Spearman's rank correlation assess the relationship between paired variables. The probability of a given Pearson R value is evaluated using the T distribution. (Colton, p. 212) (8) "FILETRAN" * On occasion, it may happen that you want to compare 2 samples or variables that are in separate datafiles. Or you may have a data set with more than 28 variables that you split between two or more datafiles. Since EPISTAT programs only allow analysis of samples that are in the same datafile, FILETRAN allows you to transfer samples between two datafiles. You may create a new datafile by selecting one sample from DATAFILE #1 and another from DATAFILE #2. FILETRAN can also combine two samples by APPENDING one to the other. 7 (9) "FISHERS" Fisher's exact test evaluates 2 by 2 tables of discrete variables. It is particularly valuable when the Chi-square test is inappropriate because the expected value for a cell is < 5. However, this program can evaluate some tables where A+B+C+D > 200. (10) "FORTRANS" If your data was previously entered into a FORTRAN or other SDF sequential card image file, FORTRANS may be able to transform it into an EPISTAT datafile. You must know the record length, appropriate column numbers, number of decimal places and missing value code. (11) "HISTOGRM" * The histogram program graphs a data sample according to user specifications on the high resolution graphics screen. To obtain a printed copy on the IBM, Epson, Okidata or Prowriter (specified in "EPISTAT") press key F1. Press F10 to return to the program. (12) "LNREGRES" * Linear regression analysis calculates the least-squares regression line for paired samples. It then uses the T distribution to determine if the calculated slope is significantly different than zero. (Colton p. 199) LNREGRES also provides a variety of data transformations. Transformed data can be saved to disk for future use or printout. (13) "MHCHISQR" The Mantel-Haenszel Chi-square test evaluates the relationship between two discrete variables while controlling for the effect of a third variable. It also calculates an odds ratio and 95% confidence limits. (Schlesselman, pp. 183,206) (14) "MHCHIMLT" * The Mantel-Haenszel Chi-square test for multiple controls compares a case sample with 2 or more matched control samples, and calculates a probability and an odds ratio. (Fleiss, p. 125) MHCHIMLT can evaluate summary data or raw data entered using DATA-ONE. If using DATA-ONE, data should be coded as "1" for factor present, and "0" for factor absent in each case and control sample. (15) "MCNEMAR" McNemar's test (paired Chi-square test) evaluates 2 by 2 tables of paired discrete variables using Yates' correction and calculates an odds ratio and 95% confidence limits. (Schlesselman, p. 210) (16) "NORMAL" * The normal distribution has innumerable uses in statistics. This program specifically addresses three situations: (1) It compares a sample mean to a population mean. (2) It calculates the proportion of samples that would be expected to fall in any given range under the normal curve. (3) It calculates the two-tailed probability associated with any given value of z. 8 (17) "POISSON" The Poisson distribution applies to dichotomous variables when the number of successes can be counted, but the number of failures cannot. This program calculates a ONE-tailed probability. (18) "RANDOMIZ" This random sample generator aids in the selection of random samples for several purposes. It can provide a random subset of a larger population, or it can assign cases randomly to independent or paired groups for case-control studies. (19) "RANKTEST" * Two non-parametric tests of significance are performed by this program. They are appropriate for small samples which are clearly NOT normally distributed. They also specifically apply when quantitative variables are not available but qualitative ranks are. The RANK SUM TEST compares 2 independent samples. The SIGNED RANK TEST compares the medians of paired samples. RANKTEST calculates the TWO-tailed exact probability associated with the various rank sums. Note that for samples larger that 20 observations, the latter calculation can take several minutes. (Colton, pp. 219-222) (20) "RATEADJ" * The rate adjustment program will adjust sample rates by either the direct or indirect methods.(Colton, pp. 47-51) For the direct method, the datafile must include the study sample rates and the standard population figures. For indirect adjustment, the datafile used must include the study population figures and the standard population rates. For indirect rate adjustment, RATEADJ evaluates the probability of the observed number of cases using the ONE-tailed Poisson distribution for small numbers, or the Chi-square distribution for large numbers. (21) "SAMPLSIZ" The sample size program calculates the approximate sample sizes required to achieve statistical significance given certain specified levels of certainty. Adjustments are made if the user desires more than one control per case. (Schlesselman, p. 168) For a survey: TP = total population pi = population proportion d = maximum acceptable error in sample proportion n = [ z(a)*SQR(pi*(1-pi)) / d ] squared N = n / (1+n/TP) For a paired case-control study: (Colton, p. 161) N = [(z(a)*SQR(pi*(1-pi)) + |z(b)|*SQR(PT*(1-PT))) / (PT-pi)] squared For an unpaired case-control study: (Fleiss, p. 41) [(z(a)*SQR(2*pi*(1-pi)) + |z(b)|*SQR(PT*(1-PT)+PC*(1-PC))] N = [-----------------------------------------------------------] squared (PT - PC) 9 (22) "SCATRGRM" * The scattergram program graphs paired variables according to user specifications on the hi-res graphics screen. To add the linear regression line, press key F5. To obtain a printed copy on the IBM, Epson, Okidata or Prowriter (specified in "EPISTAT"), press key F1. Press key F10 to return to the program. (23) "SELECT" * This program allows the user to select any combination of records for printout. It can also create a new disk datafile that is a select subset of the original. One can select on any variable with "AND" and "OR" specifications. As many as 10 selection criteria can be set at one time. SELECT assumes that "AND"s are in parentheses. For example: "SELECT IF Sample #1>10 AND Sample #2=1 OR Sample #1<Sample #3" is interpreted as meaning: "SELECT IF (Sample #1>10 AND Sample #2=1) OR Sample #1<Sample #3" (24) "T-TEST" * The Student's T-test compares the means of two samples. The program provides both paired and unpaired T-test calculations. Variances (n-1) are displayed and, for independent samples, the equality of variances is tested to be sure that the assumptions of the T-test are met.(Snedecor, p. 116) T-TEST will also evaluate a known T value. (25) "XTAB" * The crosstab program generates 1,2 or 3-way crosstab reports. It allows the user to specify the crosstab criteria as well as a name for each row and column so that the report will be readable and easily interpreted. NOTICE --------------------------------------------------------------------- Users may copy EPISTAT and distribute it to others on the following conditions: 1. The programs are not modified in any way. 2. Individual programs are not distributed separately. 3. No fee is charged for copying or distribution. --------------------------------------------------------------------- 10 ====USER-SUPPORTED SOFTWARE==== The concept of user-supported software is based on three principles: 1. The value and utility of a software package is best assessed by each user on his or her own system with his or her own data. Only after using a program can one determine whether it serves one's personal applications, needs, and tastes. 2. The creation of independent personal computer software requires a substantial commitment of time and effort. Rather than duplicate this effort time after time, the computing community can and should support individual creative efforts. 3. By encouraging users to copy programs, rather than spending large sums on copy-protection, authors can supply quality software at reduced cost. Users will support useful programs. If after using EPISTAT, you find it of value, your contribution in any amount will be appreciated ( $25 suggested ). Send contributions to: Tracy L. Gustafson, M.D. 1705 Gattis School Road Round Rock, Texas 78664 Thank you, and good luck.