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, Replace 1, and Replace 2 procedures.
      • CoPlot includes a version of CoStat with the All Subsets, Replace 1, Replace 2 and Simons 1 procedures.
      • CoPlot Pro 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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