Chapter 1

Statistic: Descriptive measure of a sample. Usually represented by Roman letter

: sample mean : sample variance : sample standard deviation

Sample

A portion or subset of the population. (Caution: Sample must be large enough to represent the whole.)

Parameter

Descriptive measure of the population. Usually represented by Greek letters.

Branches of Statistics

Descriptive statistics, Inferential statistics

Census

Gathering data from the entire population

σ2(sigma squared)

population variance

Ratio Level Data

Ratio data have the same properties as interval data, but ratio data have an absolute zero, and the ratio of two numbers is meaningful. e.g. height, weight, time, volume, distance, # of people, age, Profit and Loss, Revenue, Expenses, Financial ratios (P/E Ratio, Inventory Turnover, Quick Ratio)

Population

The whole collection of persons, objects, or items under study

Accounting

auditing and cost estimation

Finance

investments and portfolio management

Economics

regional, national, and international economic performance

Parametric Statistics

require that data be interval or ratio.

Classify each of the following as nominal, ordinal, interval, or ratio data. a. The ranking of a company by Fortune 500 -- ordinal b. The number of tickets sold at a movie theater on any given night -- ratio c. The identification number on a questionnaire -- nominal d. Per capita income -- ratio

INFO

Nominal data are the most limited data in terms of the types of statistical analysis that can be used with them. Ordinal data allow the researcher to perform any analysis that can be done with nominal data and some additional analyses. With ratio data, a statistician can make ratio comparisons and appropriately do any analysis that can be performed on nominal, ordinal, or interval data. Some statistical techniques require ratio data and cannot be used to analyze other levels of data.

INFO

Nonparametric Statistics

If the data are nominal or ordinal, nonparametric statistics must be used. Nonparametric statistics can also be used to analyze interval or ratio data.

Statistical techniques can be separated into two categories

Parametric Statistics, Nonparametric Statistics

Statistics

a science dealing with the collection, analysis, interpretation, and presentation of numerical data

Nominal Level Data

can be used only to classify or categorize. The categories can be numbered, but no ordering of the cases is implied. e.g. gender, religion, ethnicity, ethnicity, political affiliation, geographic location, place of birth, job, SS#, telephone numbers, ZIP codes.

Ordinal Level Data

can be used to rank or order object. e.g. The instructor displayed a personal interest in students and their learning. 1 = Hardly Ever, 2 = Occasionally, 3 = Sometimes, 4 = Frequently, 5 = Almost Always e.g. Position within an organization 1 for President, 2 for Vice President, 3 for Plant Manager, 4 for Department Supervisor, 5 for Employee

Management

human resources, compensation, and quality management

Interval Level Data

if the data are always numerical and the distances between consecutive numbers are equal. And, location of origin(zero) is arbitrary. e.g. Fahrenheit Temperature and Celsius Temperature (Note: Zero degree is just another point on the scale and does not mean the absence of the temperature)

Marketing

market analysis and consumer research

International Business

market and demographic analysis

Management Information Systems

performance of systems which gather, summarize, and disseminate information to various managerial levels

μ (mu)

population mean

σ(sigma)

population standard deviation