Southwest Technology Consultants

  Excellence In:
Statistical Consulting
Statistical Training
Data Analysis
Applied Statistical Methods
Introduction

The subject of statistics is broad, but often centers on the collection of information-laden data and methods that can be used to analyze these data. Thus, statistics is the discipline that will help an individual acquire good data skillsócollecting, summarizing, displaying, and interpreting data. These skills are fundamental to test and evaluation programs and to making intelligent decisions.

Statistics is intimately involved with data analysis. The types of analyses that can be performed are quite diverse and require statistical methods that are equally diverse. Statistical methods presented in this short course have been selected on the basis of their proven usefulness in a wide variety of test and evaluation applications.

What You Will Learn

Course participants will gain an understanding of how to obtain, display, analyze, and interpret statistical data. In particular, attendees will learn:

  • How to collect, display, and summarize data
  • The role of probability models in statistics
  • Estimation and hypothesis testing
  • How to analyze enumerative (count) data
  • Methods for correlation and regression
  • Methods for quality control
  • How to analyze test results for experimental designs
  • How to interpret results of statistical tests
  • How to communicate results to decision makers
Course Outline
The course can be modified to cover some or all of the following topics depending on participant needs.

Data Analysis

1. Data Collection: The Role of Sampling in Statistics

  • Populations and samples

  • The importance of random samples

  • Experiments and data types

2. Data Display: Graphical Techniques

  • Dotplots and stem-and-leaf plots

  • Histograms

  • Cumulative relative frequency

  • Scatterplots

  • Displaying multivariate data

3. Data Summarization: Descriptive sample statistics

  • The sample mean

  • The sample standard deviation

  • Modes, quantiles, proportions, and boxplots

Probability and Distributions

4. Probability, Discrete and Continuous Populations

  • Probability

  • Discrete random variables

  • Continuous random variables

  • Population parameters

  • Additional topics in probability

5. Some Useful Discrete and Continuous Distributions

  • The binomial distribution

  • The normal distribution

  • The normal approximation to the binomial and checking for normality

  • The distribution of the sample mean

  • The Poisson, exponential, and hypergeometric distributions

Estimation and Hypothesis Testing

6. Estimation (One Sample)

  • General remarks about estimation

  • Estimating the true proportion in a population

  • Estimating the mean

  • Estimating the population median

  • Estimating the population standard deviation

7. Hypothesis Testing

  • Hypotheses, test statistics and p-values

  • The decision rule and power

  • The binomial test and acceptance sampling

  • Testing hypotheses about the population mean and standard deviation

  • Testing hypotheses about the population median

8. Two Related Samples (Matched Pairs)

  • The paired t-test

  • The Wilcoxon signed ranks test

9. Estimation and Hypotheses Testing with Two Independent Samples

  • Large samples: inferences about the difference between two means

  • Difference between two means: normal populations with equal variance (two-sample t-test)

  • Difference between two means: normal populations with unequal variances (Satterthwaite's test)

  • Difference between two means: general populations

  • (Wilcoxon-Mann-Whitney rank sum test)

Enumerative Data

10. Analysis of Enumerative Data

  • 2 x 2 contingency tables

  • The r x c contingency table

  • The chi-square goodness of fit test

Correlation and Regression

11. Correlation

  • Introduction to correlation

  • The rank correlation coefficient: Spearman's rho

12. Simple Linear Regression

  • An introduction to linear regression

  • Inference for linear regression

  • Monotone regression

13. Multiple Linear Regression

  • Tests of hypothesis in multiple regression

  • Methods for selecting a regression model in the presence of several independent variables

  • General linear models with qualitative variables

  • General linear models with interaction

Quality Control

14. Techniques for Monitoring Product Quality

  • Shewhart control charts

  • A combined Shewhart-CuSum scheme

  • An exponentially weighted moving average (EWMA)

Analysis of Experimental Designs

15. Analysis of Variance for One-Factor Experiments

  • An overview of completely randomized designs

  • The analysis of variance for the completely randomized design

  • Comparing population means in a completely randomized design

  • A comparison of means for general populations: The Kruskal-Wallis test

16. Analysis of Variance for Two-Factor Experiments

  • The analysis of variance for the randomized complete block design

  • Interaction in two-factor experiments

  • Analysis of two-factor experiments for general populations: The Friedman test

17. Other Useful Topics in Experimental Design

  • Analysis of variance for three-factor experiments

  • The analysis of covariance

  • Methods for use with general populations

 

 


Contact Information

Phone: 505 856-6500

Email: stc@swtechcon.com

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