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General Statistical Analysis Using the SCA Statistical
System
Powerful, Yet Easy to Use!
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 also an integratable component of
the SCA Forecasting and Modeling Package and the SCA Quality Improvement
package.
SCA-GSA
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:
Regression analysis, including serially correlated errors
Analysis of Variance
Plots and descriptive statistics
Cross tabulation contingency tables and chi-square tests
Box-Jenkins ARIMA modeling
Nonparametric statistics
Analytical functions and matrix operators
Regression analysis
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
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
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Analysis of Variance
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.
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Plots and descriptive statistics
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
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Cross tabulation contingency tables and chi-square tests
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
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Box-Jenkins ARIMA modeling
Univariate time series analysis using Box-Jenkins autoregressive-integrated
moving average (ARIMA) models are available within SCA-GSA.
The univariate time series analysis features are a subset of
the time series analysis and forecasting capabilities provided
in the SCA-UTS module.
The SCA-GSA module provides:
Identification procedures (sample ACF, PACF, and EACF)
Flexible model specification
Ability to constrain parameters
Conditional and exact likelihood estimation procedures
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Nonparametric 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)
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Analytical functions, matrix operators, and cumulative and
inverse distribution functions
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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