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General Statistical Analysis Using the SCA Statistical System


Almost anyone with a need to analyze data can benefit from the general statistical analysis capabilities of the SCA System. Practitioner, instructor, student . . . all will appreciate its wide range of features. The SCA General Applications Package (SCA-GSA) provides you with versatility. It can be used on mainframes, workstations and personal computers. It is an integratable component of the SCA Statistical System.

The SCA-GSA module provides a wide range of general statistical capabilities from graphical to selected advanced analysis features. The SCA-GSA module provides features such as:

A key feature of SCA-GSA is its regression capabilities. In addition to standard regression analysis, models with serially correlated errors can be analyzed. These include lagged regressions with autoregressive or moving average noise terms. Other important enhancements to the standard regression model include:

Applications of Box-Cox transformations
Weighted least squares
Ridge regression
Piecewise fitting
Nonparametric statistics



Regression output is concise and easy to understand. You can control the amount of information you wish to view to include diagnostic tools such as:

Residual and studentized residuals
Cook distance
Studentized deleted residuals
Durbin-Watson statistic
Leverage




The SCA-GSA module provides all standard analysis of variance measures, including:

Two-sample t-tests
One-way to N-way analysis of variance
One-way to N-way analysis of covariance
Confidence interval plots
Analysis of balanced and unbalanced designs



In addition, the SCA-GSA module offers a capability not readily found in other statistical packages, Box-Cox transformation analysis. This powerful tool permits the user to incorporate the transformation of the response variable into an analysis. Analyses are often simplified and improved with this valuable addition. Lambda plots (plots of MSE or effects against transformation values) are also available for greater understanding of transformations.


The key part of any analysis is the beginning. Data should be displayed, and in a variety of ways. Basic descriptive measures should be calculated adnd examined. Only then will you best know how to proceed. The SCA-GSA module provides numerous data displays, including:

Single and multiple time series plots
Histograms
Stem-and-leaf displays
Pareto diagrams
Scatter plots
Probability plots
Box-and-whisker plots
Shewart plots
Autocorrelation and Partial-autocorrelation plots
others



All basic descriptive statistics are available, as well as more advanced descriptive measures. These include:

Mean and median
Coefficient of variation
Sample quartiles
Variance and standard deviation
Skewness and kurtosis
Correlation




Data are easily cross-classified in the SCA-GSA module, permitting an investigation of relationships between two or more variables. Capabilities encompass:

One-way to N-way tables
Statistics of variables associated with cross tabulated entries
Summary table statistics
Chi-square
Cramer's V
Tau B and C
Contingency coefficient
Lambda statistics
Uncertainty coefficients
Conditional gamma Somer's D statistics




Most standard nonparametric tests are provided in the SCA-GSA module. These tests encompass:

One sample (binomial, runs, chi square and Kolmogorov-Smirnov tests)
Two independent samples (median, Mann-Whitney U, and Kolmogorov-Smirnov tests)
Several independent samples (median and Kruskal-Wallis H tests)
Two related samples (sign, Wilcoxin, Kendall's rank correlation and Spearman's rank correlation tests)
Several related samples (Cochran's Q and Friedman's two-way ANOVA tests; Kendall's coefficient of concordance)




 

Statistical capabilities within the SCA-GSA module are augmented with extensive mathematic and statistical functions and operators. These capabilities include:

Mathematical operators (addition, subtraction, multiplication, division, exponentiation, logical comparison and logical operators)
Trigonometric and hyperbolic functions
Mathematic functions (absolute value, exponential, square root, factorials, gamma function, and modular arithmetic)
Matrix functions (matrix multiplication, Kronecker product, transpose, trace, determinant, inverse, eigen values, and Cholesky decomposition)
Statistic operators (sum, arithmetic and geometric mean, median, variance, and standard deviation)
Cumulative distribution functions and inverse distribution functions (standard normal, student's-t, chi-square, F, and beta distributions)




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