Statistical Analysis

C. Hall Jones & Associates, Inc., can employ a number of statistical analysis tools to aid in the collection, organization, classification, summarization, and presentation of data, making inferences, testing hypotheses, determining relationships, making predictions about a population or populations, and making decisions under uncertainty.

Statistics is often defined as the science of collecting, organizing, summarizing, analyzing, and making inferences from data. Statistics is a collection of theories and methods that are applied for the purpose of understanding data.

The application of statistics may be beneficial:

• in conjunction with certain types of research in order to fully understand the results and how those results affect future training course and/or program design and application
• to determine various factors from sets of data that have been obtained from tests that have been applied to a single group
• to determine various factors from sets of data that have been obtained from tests that have been applied to different groups

The application of statistics is divided into three broad categories:

• descriptive statistics
• inferential statistics
• decision theory

Descriptive statistics includes collecting, organizing, classifying, summarizing, and presenting data. A partial list of descriptive statistical tests includes:

• mean (standard, weighted, geometric)
• median
• mode
• range (standard, interfractile, interquartile)
• mean deviation
• variance
• standard deviation
• coefficient of variation
• z score
• Pearson r
• Spearman rho

Inferential statistics includes making inferences, hypothesis testing, determining relationships, and making predictions about a population by analyzing a sample from that population. A partial list of inferential statistical tests includes:

• t distribution
• Fisher z transformation
• F distribution and F ratio
• ANOVA (Analysis of Variance)
• Tukey Method (HSD Test - Honesty Significant Difference Test)
• Newman-Keuls Method
• Tukey/Kramer (T/K) Method
• Scheffe Method
• Linear Regression Analysis
• Multiple Linear Regression Analysis
• ANCOVA (Analysis of Covariance)
• Pearson Product-Moment Correlation Coefficients
• Chi-Square Test
• Median Test
• Mann-Whitney U Test
• Kruskal-Wallis One-Way Analysis of Variance (Kruskal-Wallis H Test)
• Wilcoxon Matched-Pairs Signed-Rank Test

Decision theory includes making decisions under uncertainty. A partial list of decision theory tests includes:

• Probability Theory
• Expected Value
• Decision Tree Analysis
• Bayes’ Theorum
• Monte Carlo Simulation