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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
      • new.gif 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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