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YOUR MODERN MICROCOMPUTERS' STATISTICS LICENSE Even though the program is ShareWare, and can be freely copied, there are still some limitations to protect the quality of the distribution of the program and to support future development. Users of MODERN MICROCOMPUTERS' STATISTICAL software may make copies of this program for trial use by others on a PRIVATE NON-COMMERCIAL BASIS. By accepting and using this software, you acknowledge that this software may not suit your particular requirements or be completely trouble-free. With proper application, this software will perform as described. However, MODERN MICROCOMPUTERS is not responsible for your specific application or any problems resulting from use of this software. If the software does not perform as described, our liability to you is limited to replacing the software or refunding the purchase price (if pur chased and registered). We have no liability to you or any other person or entity for any damage or loss, including special, incidental, or consequen tial damages, caused by this software, directly or indirectly. Some states do not allow the limitation or exclusion of liability for incidental or con sequential damages, so the above limitation or exclusion may not apply to you. This Agreement is governed by the laws of the State of Virginia. Should any part of this agreement be held invalid, the remainder of the Agreement will still be in effect. This Agreement can only be modified by written state ment signed by MODERN MICROCOMPUTERS. Under this license, you may NOT: 1) Distribute the program in connection with any other product or service, or as part of a corporate or institutionally sponsored distribution. Site licenses and bundling agreements are available upon request. 2) Charge anything for these MODERN MICROCOMPUTERS' programs. An excep- tion is made for registered user groups who may charge a cost-based fee (not to exceed $10) to cover their own costs. 3) Distribute the program in modified form. 4) Copy or reproduce the printed documentation in any form. THE SHAREWARE CONCEPT MODERN MICROCOMPUTERS' STATISTICS is distributed through a unique marketing approach called ShareWare. The diskette with programs on it can be freely copied and shared. It is also available from us, MODERN MICROCOMPUTERS, for $20.00. We ask you to help us distribute MODERN MICROCOMPUTERS' MODSTAT3 by sharing unmodified copies of the diskette with others. We also encourage you and those to whom you have distributed the program to register your copy. Registration has a number of benefits to you: 1) You will receive the latest copy of the programs, including all recent updates, and additions. 2) Automatic notice of future updates and additions. 3) You will be supporting the concept that allowed you to receive MODERN MICROCOMPUTERS' MODSTAT3 in the first place. Only through user support can be continue to improve MODERN MICROCOMPUTERS' MODSTAT3 and perhaps develop other products. Only by supporting the program's authors who release valuable programs as ShareWare can you encourage others to do the same. NO-QUIBBLE LICENSE AGREEMENT YOU ARE IMPORTANT TO US AS A CUSTOMER AND WE RESPECT YOUR NEEDS We know that it's extremely important to you that our software be easy to use, and so our disks contain only standard unprotected files with no 'fingerprints' and requiring no special installation routines. This means that you can install our files on hard disks with no fear of future problems. Our only concession to copy protection is that our program code is encrypted with serial number and/or user's name which appears on the screen and makes each disk traceable. Our software license restriction is essentially that each licensed copy of the software must be used on ONLY ONE COMPUTER AT A TIME. BY USING THIS SOFTWARE YOU INDICATE YOUR ACCEPTANCE OF THE THIS SOFTWARE LICENSING AGREEMENT. We hope you will find the program useful and will support the ShareWare concept by registering your copy with us. Please use the registration form on the next page. In the event that the REGISTRATION FORM is missing, you can receive one from us by writing to: MODERN MICROCOMPUTERS 6446 Kim Shelly Court Mechanicsville, Virginia 23111 or by calling: (804) 746-4352 There is no charge for the registration form. Even if you do not decide to send in the $20.00 donation, you should register your copy with us. We only want those who find the program useful to donate. We appreciate your passing of the programs on to friends and fellow workers. SYSTEM REQUIREMENTS: IBM PC/XT/AT OR IBM COMPATIBLE computer with hard disk. MS-DOS 2.1 (PC-DOS 2.1) or higher. 256K RANDOM ACCESS MEMORY REGISTRATION FORM ----------------- If you purchased MODERN MICROCOMPUTERS' MODSTAT3 directly from MODERN MICROCOMPUTERS in your own name, then your copy is already registered and you will receive all the benefits of registration. You do not need to send in a registration form. If you received MODERN MICROCOMPUTERS' MODSTAT3 some other way, you may register your copy by filling out the following form and mailing it to the listed address along with $20.00. You will promptly receive the latest version of MODERN MICROCOMPUTERS' MODSTAT3. We will also place you on our update list so that you will automatically be notified of any changes to the programs. Once your copy of MODERN MICROCOMPUTERS' MODSTAT3 is registered, you will be entitled to unlimited telephone support bye calling (804) 746-4352 during business hours (10:00 a.m. - 3:00 p.m. Virginia time). In addition, you will be supporting software distributed under the ShareWare concept and will be contributing to the further development of MODERN MICROCOMPUTERS' MODSTAT3 and other ShareWare products. Mail To: MODERN MICROCOMPUTERS 6446 Kim Shelly Court Mechanicsville, VA 23111 NAME ______________________________________________ COMPANY ___________________________________________ ADDRESS ___________________________________________ CITY/STATE ________________________________________ ZIP ______________________________ How did you first learn about MODERN MICROCOMPUTERS' MODSTAT3 or where did you first obtain a copy of MODERN MICROCOMPUTERS' MODSTAT3? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ What additional programs would you like to see developed? _______________ _________________________________________________________________________ _________________________________________________________________________ THIS IS THE MODERN MICROCOMPUTERS' STATISTICAL SOFTWARE These programs were developed during the teaching of various courses in statistics at the university level by Dr. Robert C. Knodt. Their development was the direct result of work instituted to make statistics a more understandable and usable subject. Early in my work with statistics I realized that almost any student can learn to apply the statistical tests and successfully complete the mathematics necessary to arrive at the correct answer to any of these tests. What proved to be the biggest problem that the students had revolved around the problem of selecting the correct statistical test to meet the proposed investigation. With this in mind the first program was developed. The aim of the program is to help in the selection of the proper statistical test. This program is called 'FIND' is the first one listed on the first menu. FIND allows the investigator to answer some simple questions and the program will indicate the correct statistical test. In addition, the program will then branch to that test so that the investigator can immediately perform the test. Over the course of years the various programs increased in number so that today there are over 40 programs in the package. Of course, not all will be needed by any one investigator, but they do cover a wide range of situations. These programs are not strictly free. The author, Dr. Knodt, requests that you send the registration form along with $20.00 to cover the costs of the development of these programs and the development of future programs. If you find these programs useful, $20.00 is a small price for the collection of programs. Your donation will allow the author to continue developing programs of this and other types. As a registered user you will be kept up-to-date on any future programs and will be offered them at comparably low prices. Please send your donation to: MODERN MICROCOMPUTERS Dr. Robert Knodt 6446 Kim Shelly Court Mechanicsville, VA 23111 If you experience any difficulty or find that you need any personal help in your investigations or the analysis of data from you investigations, please do not hesitate to call (804) 746-4352 from 10:00 a.m. to 3:00 p.m. Virginia time. Dr. Knodt will make every effort to help. THE SHAREWARE CONCEPT ALLOWS THE DEVELOPMENT OF POWERFUL, USEFUL, AND HIGHLY AFFORDABLE COMPUTER SOFTWARE. SUPPORT THE CONCEPT. REGISTER AND SEND YOUR $20.00 TODAY. The group of statistical tests called MODSTAT3 include the following tests. * ONE-WAY ANALYSIS OF VARIANCE BETWEEN GROUPS FOLLOWED BY t-TESTS. (Up to seven groups - any number in a group) One of the best tests, if not the best, for determining of there is a significant difference between groups. There should only be one independent variable involved. The test assumes that the scores are from a population with a normal distribution but studies have shown that this requirement can be violated to a great extent without altering the outcome of the analysis. The test produces a summary table and gives the F value as well as the significance of that value. The degrees of freedom are taken from the table as the degrees of freedom of the between variable and the degrees of freedom of the within variable. You can check the significance level in the F-table using these degrees of freedom but the program gives you the exact value. The program then shows the t-test values for each group compared to each other group. The mean and standard deviation of each group is also displayed. The test can be used for comparing two groups and gives the F value which, in that case, is the Z score (or for small groups, the t-test) squared. Most statistics books give the computational method but many do not stress the value and ease of the test. Usually the t-test is emphasized for comparing two groups and the ANOVA (ANalysis Of VAriance) tests left for later in the course work. In all probability, the ANOVA should be taught first since it includes the t-test calculations. In most other ANOVA tests the number of subjects in each group must be equal but this is not the case for the One-Way ANOVA. You can test up to 7 groups and have unequal numbers in each group. The first basic assumption is that the scores must be from a genuine interval scale, that is, each score should be equal distant from the next score. For example the distance from 84 to 85 should be the same as the distance from 23 to 24. The second assumption is that the scores must be normally distributed in the population. As noted above, this assumption can be violated to a great extent without changing the conclusions of the test. The third assumption is that the variance in the groups must be homogeneous. This assumption can also be violated to a great extent. There are some tests that have been developed to determine non-normalcy and heterogeneity of variance but most of them are less robust than the ANOVA and many are themselves more susceptible to distortion than the ANOVA. Most are also tedious and time-consuming to perform. Hamberg, Morris, Basic Statistics: A Modern Approach. New York: Harcourt Brace Jovanovich, Inc., 1974 Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946 * TWO-WAY ANALYSIS OF VARIANCE BETWEEN GROUPS (Up to 9 levels of each variable) The same assumptions exist for this test as exist for the One-Way ANOVA with the added condition that you must have equal numbers of scores in each condition of the test. The test is used when you have a between subjects design and two independent variables. The program produces the summary table, shows all F scores and shows the significant level of each F score. The degrees of freedom are the degrees of freedom for the item in question and the degrees of freedom for the error factor. The main effects of Variable A and Variable B are evaluated and the interaction of Variable A with Variable B (AxB) is shown. In the event that only one score is tabled per test condition then the error term is not shown and all F scores are calculated by dividing by the mean square value of the triple interaction term. If more than one score is entered under each test condition, the error term is shown and F scores are calculated using the mean square value of the error term. All summary totals are shown and the average of scores in each cell are shown. These averages can be used when doing the Turkey's (a) test. For information on this test refer to: Cicchetti, Dominic V. Extensions of multiple-range tests to interaction tables in the analysis of variance: A rapid approximate solution. Psychological Bulletin, 1972, 77, 405-408. McNemar, Quinn, Psychological Statistics. New York: John Wiley & sons., Inc., 1949. Richmond, Samuel B., Statistical Analysis. New York: The Ronald Press Company, 1964. * THREE-WAY ANALYSIS OF VARIANCE BETWEEN GROUPS (Up to 4 levels of each variable) This analysis also requires an equal number of scores in each condition of the test. The summary table is shown along with all the significant levels for the F values shown. In the event that only one score is tabled per test condition then the error term is not shown and all F scores are calculated by dividing by the mean square value of the triple interaction term. If more than one score is entered under each test condition, the error term is shown and F scores are calculated using the mean square value of the error term. Linton, Marigold, and Philip S. Gallo, The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. McNemar, Quinn, Psychological Statistics. New York: John Wiley & sons., Inc., 1949. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. * ONE WAY-ANALYSIS OF VARIANCE WITHIN GROUPS FOLLOWED BY CORRELATED t-TESTS * TWO-WAY ANALYSIS OF VARIANCE WITHIN GROUPS * THREE-WAY ANALYSIS OF VARIANCE WITHIN GROUPS These tests are similar to the ANOVA for between groups but involve investigations involving a within groups situation. This type of test involves tested the same individuals more than once. It can be used as a before and after investigation. Each individual is tested once under each of the conditions. With the one-way ANOVA after the completion of the summary table for the ANOVA you can do a correlated t-test between any two of the test conditions. Edwards, Allen L., Experimental Design in Psychological Research. New York: Holt, Rinehart and Winston, Inc., 1968. (Please note that the example in Edwards listed as a between ANOVA is actually the within ANOVA.) Linton, Marigold, and Philip S. Gallo, The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. * ANALYSIS OF VARIANCE MIXED DESIGN TWO FACTOR BETWEEN-WITHIN * ANALYSIS OF VARIANCE MIXED DESIGN THREE FACTOR BETWEEN-BETWEEN-WITHIN * ANALYSIS OF VARIANCE MIXED DESIGN THREE FACTOR BETWEEN-WITHIN-WITHIN These tests involve a mixed design ANOVA. There are three tests of which the two factor design is the most often used. The subjects are usually divided into groups and each individual is tested under a number of conditions. The test allows for an analysis of both the between groups and the within groups. The other two tests involve either the between group factor or the within group factor to be compared to two of the other type factor. In all cases the subjects are tested under various conditions. Linton, Marigold, and Philip S. Gallo, The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. Edwards, Allen L., Experimental Design in Psychological Research. New York: Holt, Rinehart and Winston, Inc., 1968. * ANALYSIS OF VARIANCE LATIN SQUARE DESIGN, 3x3, 4x4, 5x5 This program handles three different sized Latin square designs. You indicate where in the design each individual tested is located and the program does the complete ANOVA. The significance level of the calculated F score is shown. Edwards, Allen L., Experimental Design in Psychological Research. New York: Holt, Rinehart and Winston, Inc., 1968. * ONE-WAY CHI SQUARE ANALYSIS * TWO-WAY CHI SQUARE ANALYSIS 2x2 USING YATES CORRECTION FACTOR * FISHER'S EXACT PROBABILITY TEST FOR 2x2 TABLE WITH SMALL VALUES * TWO-WAY CHI SQUARE ANALYSIS AxB * THREE-WAY CHI SQUARE ANALYSIS 2x2x2 * THREE-WAY CHI SQUARE ANALYSIS AxBxC Although the Chi Square analysis is one of the most often used non- parametric tests, it is possible to select the incorrect test for your data. You are advised to use the FIND program which is choice 1 on the first menu to make sure you have selected the correct Chi Square test. The Yates correction factor is used wherever necessary and if the 2x2 analysis has limited numbers in each cell of the table, you are offered the option of running the Fisher's exact probability test as an alternative. All these tests assume a between subjects analysis. * REPEATED MEASURES CHI SQUARE ANALYSIS * McNEMAR'S CHI SQUARE ANALYSIS OF CHANGES These two Chi Square tests are used when you have a within subjects or a mixed design analysis. Boker, A. H., A test for symmetry in contingency tables. J. American Statistical Association, 43, 1948. Linton, Marigold, and Philip S. Gallo, The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. McNemar, Quinn, Psychological Statistics, 2nd Ed. New York: John Wiley & Sons Inc., 1955. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. * THE SIGN TEST The sign tests gets its name from the fact that is uses plus or minus signs rather than quantitative measures as its data. You can either enter the raw data or a summary of the data indicating only the number of individuals who changed in each direction. The test is based on the binomial distribution. The significance level is shown. A more detailed test is the Wilcoxon match-pairs signed-ranks test. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. McNemar, Quinn, Psychological Statistics, 2nd Ed. New York: John Wiley & Sons Inc., 1955. * WILCOXIN RANK-SUMS TEST This test utilizes information about the direction and magnitude of the differences between the scores of individuals over time. If only the direction of the change is known, then the proper test is the Sign test. The idea of using rank values in place of the measurements themselves for the purpose of significance tests came from Professor Spearman in 1904. Mood, A. M., Introduction to the theory of statistics. New York: McGraw- Hill Book Company, 1950. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. Spearman, C., American Journal of Psychology, 15:88, 1904. Wilcoxon, F., Individual comparisons by ranking methods. Biometrics Bulletin, 1, 1945. Wilcoxon, F., Probability tables for individual comparisons by ranking methods. Biometrics Bulletin, 3, 1947. * KRUSKAL WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS This test extends the range of Wilcoxon's Sum of Ranks Test to cases where there are more than two sets of measurements. The test uses the Chi Square distribution. This test determines whether k independent samples are from different populations. Langley, Russell, Practical Statistics Simply Explained. New York: Dover Publications, Inc., 1970 Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. Kruskal, W. H. and W. A. Wallis, Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47, 1952. * FRIEDMAN'S TEST This test compares three or more random samples which are matched. The test involves ranking each set of matched measurements. Friedman, Milton, Journal of the American Statistical Association, 1937. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. * PEARSON PRODUCT-MOMENT CORRELATION AND REGRESSION ANALYSIS Single and multiple regression - Curvilinear regression These programs allow you to work with either simple or multiple regression analysis. For a simple regression analysis the program first uses the least squares method and calculates the regression equation, coefficient of correlation 'R' value and the standard error of the estimate. It will also evaluate if the 'R' value is significantly different from zero by calculating either the t-value or the Z value, and finally, it will allow you to make estimates of the dependent variable from the independent variable(s). The program then offers you the ability to check for a curvilinear regression fit using the same data. At the completion of the analysis the program will indicate the F value for divergence from the linear relationship and evaluate the significance of the F value. If the F value is significant you will be shown the significance level of the correlation coefficient and finally offered the ability to make estimates of the dependent variable from various independent values. If the F value is non-significant you are returned to the linear section and offered the opportunity to do estimates. The range of the conditional mean is shown as well as the individual range of the predicted dependent variable. If you select to do a multiple regression the data will be analyzed using two entered independent variables associated with the dependent variable. You are shown the level of significance and given the opportunity to make estimates of the dependent variable based on entering various combinations of the dependent variables. All data is saved in a file. For single linear regression data you can try the data as in choice 2 of the menu to see if you get a better fit as exponential, logarithmic or as a power fit. If you data doesn't match the input data limitations of these tests you will receive an error message. This basic method of curve fitting is attributed to Karl Pearson and a much more complete analysis of this method can be found in the text, Statistical Methods by George W. Snedecor. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. Poole, Lon, Mary Borchers, and David M. Castlewitz, Some Common Basic Programs, Apple II Edition, Berkeley, California: Osborne/McGraw-Hill, 1981. McElroy, Elam E., Applied Business Statistics, 2nd Ed., San Francisco, California: Holden-Day, Inc., 1979. * REGRESSION ANALYSIS EXPONENTIAL * REGRESSION ANALYSIS LOGARITHMIC * REGRESSION ANALYSIS POWER These methods calculate the regression equation when the dependent variable is related to the independent variable in various fashions. When attempting an exponential analysis the dependent variable must be greater than zero. When attempting a logarithmic fit the independent variable must be greater than zero and when attempting a power curve fit, both variables must be greater than zero. The program shows the coefficient of determination, the calculated 'A' and 'B' values, the regression equation and allows you to make estimates of the dependent variable from the independent variable. All data is saved in a file so it is possible to try all three curve fits as well as a linear and curvilinear fit without having to re-enter the data. Hewlett-Packard Company, HP-67 Standard Pac, Cupertino, California * SPEARMAN RANK CORRELATION COEFFICIENT Of all the statistics based on ranks, the Spearman rank correlation coefficient was the earliest to be developed and is perhaps the best known today. This statistic is referred to as 'rho'. Both variables must be measured in at least an ordinal scale so that the objects or individuals under study may be ranked in two ordered series. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. Spearman, C., American Journal of Psychology, 15:88, 1904. * POINT-BISERIAL CORRELATION If one variable is graduated and yields an approximately normal distribution and the other is dichotomized, then if we can assume that the underlying dichotomized trait is continuous and normal, then we can obtain a correlation measure which constitutes an estimate as to what the product moment 'r' would be if both variables were in graduated form. Bernstein, Allen L., A Handbook of Statistics Solutions for the Behavioral Sciences. New York: Holt, Rinehart and Winston, Inc., 1964 McNemar, Quinn, Psychological Statistics. New York: John Wiley & sons., Inc., 1949. * KENDALL'S RANK ORDER CORRELATION The Kendall rank correlation coefficient, tau, is suitable as a measure of correlation when you have rank values for the X and Y variables. It is possible, although the program is not included in this set, to generalize to a partial correlation coefficient. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. Kendall, M. G., Rank Correlation Methods. London: Griffin Press, 1948. * KENDALL'S COEFFICIENT OF CONCORDANCE When you have k sets of rankings of N objects or individuals it is possible to determine the association among them by using the Kendall coefficient of concordance, W. Friedman, M., A comparison of alternative tests of significance for the problem of m rankings. Annual Mathematical Statistician, 11, 1940. Kendall, M. G., Rank Correlation Methods. London: Griffin Press, 1948. * PARTIAL CORRELATION ANALYSIS This technique is used to asses the relationships between two variables when another variable's relationship with the initial two has been held constant or "partialed out." Popham, W. James, Educational Statistics, Use and Interpretation. New York: Harper & Row, Publishers, 1967. Richmond, Samuel B., Statistical Analysis. New York: The Ronald Press Company, 1964. * MULTIPLE CORRELATION ANALYSIS It is possible to use this program to determine the extent of the relationship between one variable and a combination of two or more other variables considered simultaneously. Popham, W. James, Educational Statistics, Use and Interpretation. New York: Harper & Row, Publishers, 1967. Richmond, Samuel B., Statistical Analysis. New York: The Ronald Press Company, 1964. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. * DETERMINE THE DIFFERENCE BETWEEN TWO CORRELATIONS This will determine if the correlation coefficient computed for one sample is significantly different than the correlation coefficient computed for a second sample. Richmond, Samuel B., Statistical Analysis. New York: The Ronald Press Company, 1964. * COVARIANCE WITH ONE VARIABLE * COVARIANCE WITH TWO VARIABLES In a single-classification analysis of covariance model there is one dependent variable, one independent variable and at least one control variable. There may be several control variables which can be employed if the researcher feels that they are strongly related to the dependent variable in the study. This design can statistically compensate for differences between the independent variable groups with respect to the control variables. Edwards, Allen L., Experimental Design in Psychological Research. New York: Holt, Rinehart and Winston, Inc., 1968. Popham, W. James, Educational Statistics, Use and Interpretation. New York: Harper & Row, Publishers, 1967. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. * ETA TEST FOR USE AFTER ONE-WAY ANALYSIS OF VARIANCE The eta test performed after a one-way ANOVA can tell how much (percentage) of the variance was accounted for by the conditions of the test. Linton, Marigold, and Gallo, Philip S., The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. McNemar, Quinn, Psychological Statistics. New York: John Wiley & sons., Inc., 1949. * ETA TEST FOR USE AFTER RANK-SUMS OR KRUSKAL TEST This test is similar to the previous one in that it can also tell how much (percentage) of the variance was due to the conditions of the test. It is used in one of two forms after either the Rank-sums or Kruskal-Wallis test. Linton, Marigold, and Philip S. Gallo, The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. McNemar, Quinn, Psychological Statistics. New York: John Wiley & sons., Inc., 1949. * CONTINGENCY COEFFICIENT FOR USE AFTER CHI SQUARE ANALYSIS The contingency coefficient is a measure of the degree of association or correlation which exists between variables for which we have only categorical information. It is included as part of some of the Chi Square analysis but it can be run directly from this program. McNemar, Quinn, Psychological Statistics. New York: John Wiley & sons., Inc., 1949. * DETERMINATION OF MEAN AND STANDARD DEVIATION OF GROUPED DATA * DETERMINATION OF MEAN AND STANDARD DEVIATION OF UNGROUPED DATA * COMBINING THE MEANS AND STANDARD DEVIATIONS OF TWO GROUPS These three techniques are very useful when you have raw data which must be analyzed before it is entered into other tests. The standard deviations calculated in the first two tests will show both the population standard deviation and the sample deviation. The third test can be used to combine any number of groups with known means and standard deviations into one over-all group. Many texts give the basic calculation methods. Edwards, Allen L., Experimental Design in Psychological Research. New York: Holt, Rinehart and Winston, Inc., 1968. Richmond, Samuel B., Statistical Analysis. New York: The Ronald Press Company, 1964. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. Weinberg, George H., and John A. Schumaker, Statistics, An Intuitive Approach. Belmont, California: Wadsworth Publishing Co., Inc., 1965. * ZM TEST This compares a random sample of one or more measurements with a large parent group whose mean and standard deviation is known. It is useful if you have a small sample, as small as one individual, and want to determine if it came from a population about which you know both the mean and standard deviation. Langley, Russell, Practical Statistics Simply Explained. New York: Dover Publications, Inc., 1970 * ZI TEST This test is essentially an adaptation of the ZM test for use with numbers of instances instead of measurements. The test allows for comparing a sample of isolated occurrences and an average, for comparing two samples of isolated occurrences with each other, or for comparing a binomial sample and a large parent group. Langley, Russell, Practical Statistics Simply Explained. New York: Dover Publications, Inc., 1970 * DETERMINING THE SIGNIFICANT DIFFERENCE BETWEEN TWO LARGE GROUPS * DETERMINING THE SIGNIFICANT DIFFERENCE BETWEEN TWO SMALL GROUPS * DETERMINING THE SIGNIFICANT DIFFERENCE BETWEEN TWO PROPORTIONS * STUDENT'S t-TEST * SIGNIFICANT DIFFERENCE BETWEEN A SAMPLE AND A POPULATION USING PROPORTIONS This group of tests allows for the determination of significant differences between two groups. The calculation methods are listed in several texts. They should allow you to handle all situations involving the comparison of groups. The first two require that you know the mean and standard deviation of both groups along with the number in each group. You can calculate this data by using choice 1 of menu number four. When determining the significant difference between proportions you need only to know the number in the sample and the number or proportion within the sample which are under consideration. * DETERMINING THE PROPER SAMPLE SIZE TO USE This test is described in many books. In order to estimate the proper sample size to use it is important that you estimate the PROBABLE standard deviation involved in the population from which you intend to take the sample. One way is to take a small pilot sample, calculate the mean and standard deviation and then using those numbers estimate the population standard deviation. You are offered various options to the program. The first option will determine the sample size for a large population without replacement, the second option takes into account the finite population factor if you are sampling from a small sample. You can also use proportions and the last two options offer you the chance to estimate from a large population or a small population. One further option is provided. If you use the options to estimate the proportion of the population the program also calculates the worst case situation. When you enter the estimated error or estimated answer you will also be shown the worst case situation which is based on 50%. Levin, Richard I., Statistics for Management, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1978. McElroy, Elam E., Applied Business Statistics, 2nd Ed., San Francisco, California: Holden-Day, Inc., 1979. * DETERMINING THE CONFIDENCE INTERVAL OF A POPULATION FROM A PROPORTION This program finds the standard error of the proportion and then, given the sample size and the proportion of the same in which the investigator is interested, calculates the upper and lower confidence limits. You must indicate the significance level wanted. You must indicate if the sample is being taken from a small population without replacement. If this is the case various correction factors come into use. After indicating if the population is small or large you enter the number in the sample size and the number in the sample which is of interest. This can be entered either as a proportion (by indicating a decimal point in front of the number) or as the actual number in the sample. Levin, Richard I., Statistics for Management, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1978. * DETERMINING THE CONFIDENCE INTERVAL OF A POPULATION FROM A SAMPLE There are a number of different estimates of a population which can be made from information acquired from a sample. The simplest estimate is called a POINT estimate. It is simply using the sample mean as the best estimator of the population mean. It is also possible to use the standard deviation of the sample to estimate the standard deviation of the population. This is done by dividing the sample standard deviation by the square root of the number in the sample. In some cases the finite population correction factor must be used. An interval estimate describes a range of values within which a population parameter is likely to lie. In statistics, the probability that we associate with an interval estimate is called the confidence level. It indicates how confident we are that the interval estimate will include the population parameter. The confidence interval is the range of the estimate we are making. It is often expressed as standard errors rather than in numerical values. This program will calculate the mean of a population along with the confidence interval at whatever significance level you desire. It will also handle both finite and infinite populations. You must enter significance level wanted, the mean, the standard deviation and size of the sample. If you enter a small number for the sample you will be reminded to enter the significance value as a student's t value rather than a Z value. Levin, Richard I., Statistics for Management, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1978. McElroy, Elam E., Applied Business Statistics, 2nd Ed., San Francisco, California: Holden-Day, Inc., 1979. * THE POISSON DISTRIBUTION * THE NORMAL DISTRIBUTION * THE CHI SQUARE DISTRIBUTION * THE STUDENT'S t-TEST DISTRIBUTION * THE F-DISTRIBUTION * THE BINOMIAL DISTRIBUTION Although tables are available for most of these distributions, these programs allow you to determine significance values from the raw data. The programs were adapted from the book listed below. All limitations are included as part of the program and where the values are not exactly precise, they are on the conservative side. Poole, Lon, Mary Borchers, and David M. Castlewitz, Some common Basic Programs, Apple II Edition, Berkeley, California: Osborne/McGraw-Hill, 1981. BIBLIOGRAPHY Bernstein, Allen L., A Handbook of Statistics Solutions for the Behavioral Sciences. New York: Holt, Rinehart and Winston, Inc., 1964 Cicchetti, Dominic V. Extensions of multiple-range tests to interaction tables in the analysis of variance: A rapid approximate solution. Psychological Bulletin, 1972, 77, 405-408. Edwards, Allen L., Experimental Design in Psychological Research. New York: Holt, Rinehart and Winston, Inc., 1968. Ehrenfeld, S., and S. Littauer, Introduction to Statistical Analysis, 3rd ed. New York: McGraw-Hill Book Co., 1964 Friedman, Milton, Journal of the American Statistical Association, 1937. Friedman, Milton, A comparison of alternative tests of significance for the problem of m rankings. Annual Mathematical Statistician, 11, 1940. Hamberg, Morris, Basic Statistics: A Modern Approach. New York: Harcourt Brace Jovanovich, Inc., 1974. Hewlett-Packard Company, HP-55 Statistics Programs, Cupertino, California Hewlett-Packard Company, HP-67 Standard Pac, Cupertino, California Kendall, M. G., Rank Correlation Methods. London: Griffin Press, 1948. Kruskal, W. H. and W. A. Wallis, Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47, 1952. Langley, Russell, Practical Statistics Simply Explained. New York: Dover Publications, Inc., 1970 Lapin, L. L., Statistics for Modern Business Decisions. New York: Harcourt Brace Jovanovich, Inc., 1973. Levin, Richard I., Statistics for Management, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1978. Linton, Marigold, and Philip S. Gallo, The Practical Statistician. Monterey, California: Brooks/Cole Publishing Co., 1975. McElroy, Elam E., Applied Business Statistics, 2nd Ed. San Francisco, California: Holden-Day, Inc., 1979. McNemar, Quinn, Psychological Statistics. New York: John Wiley & Sons., Inc., 1949. McNemar, Quinn, Psychological Statistics, 2nd Ed. New York: John Wiley & Sons Inc., 1955. Mood, A. M., Introduction to the Theory of Statistics. New York: McGraw- Hill Book Company, 1950. Poole, Lon, Mary Borchers, and David M. Castlewitz, Some Common Basic Programs, Apple II Edition, Berkeley, California: Osborne/McGraw-Hill, 1981. Popham, W. James, Educational Statistics, Use and Interpretation. New York: Harper & Row, Publishers, 1967. Richmond, Samuel B., Statistical Analysis. New York: The Ronald Press Company, 1964. Shao, Stephen P., Statistics for Business and Economics. Columbus, Ohio: Charles E. Merrill Books, Inc., 1967. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. Snedecor, George W., Statistical Methods., 4th Ed., Ames, Iowa: The Iowa State College Press, 1946. Spearman, C., American Journal of Psychology, 15:88, 1904. Texas Instruments, Calculating Better Decisions, 1977. Weinberg, George H., and John A. Schumaker, Statistics, An Intuitive Approach. Belmont, California: Wadsworth Publishing Co., Inc., 1965. Wilcoxon, F., Individual comparisons by ranking methods. Biometrics Bulletin, 1, 1945. Wilcoxon, F., Probability tables for individual comparisons by ranking methods. Biometrics Bulletin, 3, 1947. MODERN MICROCOMPUTERS 6446 Kim Shelly Court Mechanicsville, VA 23111 (804) 746-4352 Programmer: Dr. Robert C. Knodt Suggested Donation: $20.00 REGISTER YOUR COPY TODAY.