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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 $15.00 to cover the costs

of the development of these programs and the development of future programs.

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developing programs of this and other types.

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MODERN MICROCOMPUTERS

Dr. Robert Knodt

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The group of statistical tests called MODSTAT2 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, Rinehard 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, Rinehard 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, Rinehard 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, Rinehard 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, Rinehard 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, Rinehard 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.

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