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General Statistical Analysis
General Statistical Analysis Using the SCA Statistical System
Comes with Expert & Workbench 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
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Analysis of Variance
- Plots and descriptive statistics
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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
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
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
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 entrie
s
- Summary table statistics
- Chi-square
- Cramer's V
- Tau B and C
- Contingency coefficient
- Lambda statistics
- Uncertainty coefficients
- Conditional gamma Somer's D statistics
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
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)
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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