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# CoStat's Statistical Procedures

CoStat has a wide range of statistical procedures.

• Each procedure has a short description in its dialog box.
• Statistical results are sent to a text editor window (CoText), where they can be viewed, edited, printed, and saved to a file.

Here is a list of the procedures:

• ANOVA (See a description and sample run.)
• CoStat's ANOVA procedure can do ANOVAs with:
• Missing values
• Unbalanced designs
• Contrasts
• Covariance
• Up to 10 factors
• User-specified models
• Sums of Squares Types - CoStat can calculate Type I, Type II, and Type III sums of squares.
• Pre-Defined Models - CoStat comes with numerous models already defined. This makes it very easy to set up the ANOVA -- just pick the model from a list. You don't have to write a Model statement as you do in SAS.
• 1, 2, 3, and 4 way completely randomized
• 1, 2, and 3 way randomized blocks
• 2 and 3 way nested
• Split plot
• Split-split plot
• 2 variations of split block
• Latin square
• Lattice
• Several models with covariance
• Defining Models - If you need a model that hasn't been pre-defined, you can modify an existing model or create your own model. The simple little language which describes the models is fully described in the manual. The system lets you easily:
• Make variations of the existing models
• Create your own new models
• Change the format of the ANOVA table
• Specify which term provides the df and MS values for each F test
• Specify contrasts.
• Re-use the models with other data files
• Bartlett's Test - Before performing the ANOVA, CoStat performs Bartlett's Test for Homogeneity of Variances, one of the assumptions of ANOVA.
• Contrasts - You can specify any contrast that you want (for example, you can compare treatment 1 vs. treatments 2, 3, and 4).
• Means Comparisons Tests - After performing the ANOVA, CoStat can automatically run a means comparisons test (for example, Duncan's, Student-Newman-Keuls (SNK), Tukey-Kramer, Tukey's HSD, or Least Significant Difference (LSD)).

• Compare Means - performs SNK, Duncan's, LSD, Tukey's HSD, or the Tukey-Kramer test for multiple comparisons of means. These test are also available as part or the ANOVA procedure.

• Correlation - calculates correlation coefficient; slope and Y intercept of linear regression; standard errors.

• Descriptive Statistics - calculates n, sum, mean, standard deviation, variance, coefficient of variation, skewness, kurtosis, maximum, minimum, tests of normality (D'Agostino-Pearson K^2 Test), tests for outliers (Dixon's Test, Grubbs' Test, Inter-Quartile-Range). The procedure makes it easy to select subsets of the data for analysis.

• Analysis of Frequency Data (See a description and sample run.)
• Cross tabulation of string or numeric data.
• Calculation of expected frequency of normal, binomial, or Poisson distributions.
• Goodness of Fit Tests - Kolmogorov-Smirnov, Likelihood Ratio (G test), and Chi-square tests of goodness of fit.
• Fisher's Exact Test.
• Log-linear analysis of 3 way tables.

• Miscellaneous Tests
• Confidence Limits of a Correlation Coefficient
• Confidence Limits of a Mean
• Confidence Limits of a Regression Coefficient (Slope)
• Equality of Two Means (equal variances) (t Test)
• Equality of Two Means (unequal variances) (t test)
• Equality of Two Percentages (G test)
• Equality of Two Variances (F Test)
• Homogeneity of Correlation Coefficients
• Homogeneity of Linear Regression Slopes
• Homogeneity of Variances (Using n and Variance Data) (Bartlett's Test)
• Homogeneity of Variances (Using Raw Data) (Bartlett's Test)
• Mean+/-2SD - summarized data in a format that it is easy to plot in CoPlot.
• Single Observation and a Mean (t Test)

• Nonparametric Tests (See a description and sample run.)
• Percentiles - calculates nonparametric descriptive statistics: mode and percentiles.
• Rank Correlation - Kendall's and Spearman's Rank Correlation Tests are analogous to the Pearson product moment correlation coefficient.
• 2 Runs Tests - Up and Down, and Above and Below the Median
• Tied Ranks - ranks the values in a column, replaces ties with the average rank, then inserts a new column with the tied rank values.
• 1 Way, Completely Randomized ANOVA - using the Kruskal-Wallis Test.
• 1 Way, 2 Treatment, Completely Randomized ANOVA - using the Mann-Whitney U-test and Wilcoxon Two Sample Test.
• 1 Way, Randomized Blocks ANOVA - using Friedman's Method for Randomized Blocks.
• 1 Way, 2 Treatment, Randomized Blocks ANOVA - using Wilcoxon's Signed-Ranks Test for Two Groups.

• Regression (Curve-Fitting)
• Polynomial regressions of any order (linear, quadratic, cubic, quartic, ...). (See a description and sample run.)
• Periodic (Fourier) curve fitting ( y = b0 + b1cos(x) + b2sin(x) + b3cos(2*x) + b4sin(2*x) + ...).
• Multiple linear regression.
• Full model (See a description and sample run.)
• One subset
• World's best subset selection in multiple regression
(All Subsets and several approximate procedures, including the Simons2 procedure which does a dramatically better job of finding the best subsets).
(See a description and sample run.)
Different versions of CoStat include different subset selection procedures:
• CoStat includes the All Subsets and Replace 1 procedures.
• CoPlot includes a version of CoStat with the All Subsets, Replace 1, Replace 2, Simons 1, and Simons 2 procedures.
• Linearizable nonlinear regressions (several types): Square Root (y=a+b*x^0.5), Power (y=a*x^b), Inverse (y=a+b/x), Inverse Power (y=a*e^(b/x)), Hyperbola (y=x/(a*x+b)), Exponential (y=a*e^(b*x)), Logarithmic (y=a+b*ln(x)), Hoerl's (y=a*x^b*e^(c*x)), y=1/(a+b*e^-x), y=e^(a+b*x), and y=1-e^(-a*x)
• True nonlinear regressions using the Nelder and Mead Simplex Algorithm. You enter any equation. It will interatively search for the best values for the unknowns. (See a description and sample run.)
• Solve simultaneous linear equations.

• Tables - calculates the probability associated with a given test statistic, or the reverse (the statistic associated with a given probability). The tables included are:
• Chi-square distribution
• F distribution
• Normal distribution
• t distribution (2 tailed)

The procedure can also calculate the z transformation of a correlation coefficient and its inverse.

• Utilities
• Data Area - Given x and y data columns, this calculates the area under the curve.
• Data Interpolate X Y - Given x and y data columns and an x value, this interpolates values between the data points to find the corresponding y value. Or, given y, it finds x.
• Date <-> Julian Date - converts Year-Month-Date date values to/from Julian dates (1899-12-31 = day 1).
• Degrees°Min'Sec" <-> Degrees.dd - converts Degrees°Min'Sec" values to/from decimal degrees values.
• Factorials - Given an integer, n, this calculates n factorial, often written as n!.
• Functions Closest - This finds the x value where two functions are closest.
• Function Equals Y - Given a y value, this finds where the x value where a function evaluates to y. This is useful for calculating an LD50.
• Function Evaluate - This procedure evaluates an equation at a series of x values.
• Function Integrate - This procedure numerically integrates an equation.
• Function Minima - Given an x value, this procedure finds a nearby minima.
• Function Maxima - Given an x value, this procedure finds a nearby maxima.
• Permutations And Combinations - Given the number of items picked and the size of the population, this procedure calculates the number of permutations and combinations.
• Random Numbers - This will create a series of random integers in a specific range.
• Time <-> Seconds - converts Hours:Minutes:Seconds.Decimal time values to/from seconds values.

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