Statistics

Statistics is used to summarize and simplify large amounts of numerical data. Using statistics one can draw conclusions about data. Statistics is a discipline that examines data and can calculate numerical estimates of "true" values. It is used to characterize something for which we have only a limited sample- we must therefore estimate the "true" parameters by employing statistical methods. It may reveal underlying patterns in data not normally observable. If used correctly, statistics can separate the probable from the possible.

Types of Data:

• Ratio-scale data: Measurements along a continuous scale whose scale begins at 0
• Interval-scale data. Same as ratio, but data do not have 0 as low end of scale
• Ordinal-scale data. Generally used for irregular scaled data converted to ranks or relative position
• Discrete data. Not continuous.
• Nominal or categorical data. It includes binary data or group data.

Some Basic Definitions:

Variable: Anything that varies and can be measured. Determining the relationships between variables is the realm of R-mode analysis.

Object: Unit of study on which variables can be measured. Determining the relationships between objects is the realm of Q-mode analysis.

Population: The limits of the population should be designated before any analysis. Usually the population is unknowable and must be estimated by a sample.

Sample: Collection of objects which are a subset of the population of interest and are taken as representative of the population.

Sample size: How big must it be for the sample to represent the population? No real answer as it depends upon the variability of the population and the degree of precision one wants to achieve in answering the question.

Parametric statistics: Statistical procedures used on interval or ratio data. Usually many assumptions must be made.

Nonparametric statistics: Statistical procedures used on ordinal data based on ranks. Not so many assumptions are necessary.