ROBERT MORRIS UNIVERSITY Statistics Alan D. Smith ROBERT MORRIS UNIVERSITY Alan D. Smith

What is Statistics? Chapter 1

TODAY’s GOALS DEFINE STATISTICS. CITE SOME USES OF STATISTICS IN BUSINESS AND OTHER AREAS. EXPLAIN WHAT IS MEANT BY DESCRIPTIVE STATISTICS AND INFERENTIAL STATISTICS. DISTINGUISH BETWEEN NOMINAL, ORDINAL, INTERVAL AND RATIO LEVELS OF MEASUREMENT.

WHAT IS MEANT BY STATISTICS? Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data for the purpose of assisting in making a more effective decision. WHO USES STATISTICS? Statistical techniques are used extensively by marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc.

TYPES OF STATISTICS Descriptive Statistics: These are statistical methods used to describe data that have been collected. EXAMPLES: According to J. D. Powers, Lexus LS400 owners reported 32 problems per 100 cars during 1994. The statistic 32 describes the number of problems out of every 100 cars. A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer.

TYPES OF STATISTICS (continued) Inferential Statistics: These are statistical methods used to find out something about a population, based on a sample. A population is a collection of all possible individuals, objects, or measurements of interest. A sample is a portion, or part, of the population of interest.

Examples of Inferential Statistics TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers. The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company. Wine tasters sip a few drops of wine to make a decision with respect to all the wine waiting to be released for sale.

TYPES OF VARIABLES Qualitative or Attribute variable: when the characteristic or variable being studied is categorical or non-proportional. EXAMPLES: Gender (male, female), religious affiliation, type of automobile owned, state of birth, eye color, etc. Quantitative variable: when the variable can be reported non-categorical or proportional. EXAMPLES: Balance in your checking account, salaries of faculty members, number of children in a family etc.

TYPES OF VARIABLES (continued) Quanitative variables can be classified as either discrete or continuous. Discrete Variables: can only assume certain values and there are usually “gaps” between the values. EXAMPLE: The number of bedrooms in a house (1, 2, 3, ..., etc.). Continuous Variables: can assume any value within a specific range. EXAMPLE: The time it took to fly from New York to Guyana (South America).

SUMMARY OF TYPES OF VARIABLES Data Qualitative or attribute Quantitative or numerical Type of car owned. Color of pens. Discrete Continuous Number of children. Time taken for an exam.

SOURCES OF STATISTICAL DATA Researching problems involving topics such as crime, health, imports and exports, production, hourly wages etc. generally requires published data. Statistics on these and information on thousands of other topics can be found in published articles, journals, magazines, WWW. Published data are not always available on a given subject. In such cases, information will have to be collected and analyzed. One way of collecting data is through questionnaires.

Conclusion? Missed Days of Work Percent of Total Man-Days in Qtr

LEVELS OF MEASUREMENT The four general types, or levels, of measurement are nominal, ordinal, interval, and ratio. NOMINAL LEVEL (SCALED): Data that can only be classified into categories and cannot be arranged in an ordering scheme. EXAMPLES: Eye color (blue, brown, black etc.); Gender (male, female); Religious affiliations (Hindu, Catholic, Jewish, etc.).

LEVELS OF MEASUREMENT ( terms) Mutually exclusive: When an individual, object, or measurement is included in only one category, then they are mutually exclusive. For example - eye color, gender (male, female), etc. Can only appear in one category Exhaustive: When each individual, object, or measurement must appear in one category, then they are exhaustive. For example - religion. Must appear in at least one category Mutually Exclusive and Exhaustive?

LEVELS OF MEASUREMENT (continued) ORDINAL LEVEL: This involves data that may be arranged in some order, but differences between data values cannot be determined or are meaningless. EXAMPLE: During a taste test of 4 colas, cola 3 was ranked number 1, cola 2 was ranked number 2, cola 1 was ranked number 3, and cola 4 was ranked number 4. Cola 3 is not four times better than cola 4

LEVELS OF MEASUREMENT (continued) INTERVAL LEVEL: This is similar to the ordinal level, with the the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point. EXAMPLE: Temperature on the Fahrenheit scale. Differences can be computed and remain constant. 100 degrees is not twice as hot as 50 degrees

LEVELS OF MEASUREMENT (continued) RATIO LEVEL: This is the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement. EXAMPLES: Heights of the NBA players; Money etc. 100 dollars is twice as much as 50 dollars 100 dollars is 50 more than 50 dollars