Chapter 1: The Nature and Probability of Statistics

Lesson 1:

The Nature and Probability of Statistics

What is statistics?

The science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data.

Two types of statistics:

1. Descriptive - collection, organization, summation & presentation of data

2. Inferential - generalizing, testing, determining relationships, making predictions, all from samples to populations - using probability theory

Some definitions:

Variables –mathematical symbols that represent a number, but have no fixed value
Data - Value(s) that variables can assume (numbers, types, colors, etc.)
Data set - A collection of data values
Random Variables - Variables whose values are determined by chance
Population - all data values being studied
Sample - A subgroup of a given population

Questions

1. Give some examples of variables

a: Qualitative - can be placed into distinct categories: gender, color, religion

b: Quantitative - numerical, can be ordered or ranked: age, temperature, height

c: Discrete - assume values that can be counted (number of kids, days in a cycle)

d: Continuous - can assume all values between any two specific values (temp)

2. Boundaries - useful when considering continuous variables, allows us to more easily group them

Measurement Scales

1. Nominal: Classifies data into mutually exclusive categories in which NO order or ranking can be imposed on the data

University departments
Gender
Hair color
Marital status
Race
Political party
Religion
Zip codes!
Area codes

2. Ordinal: Classifies data into categories that CAN be ranked; however, precise differences between the ranks do not exist

Course Grades (A,B,C,D,F)
Rating Scales (poor, average, good, excellent)
Rankings (1st, 2nd...)

3. Interval: Same as above, except precise differences between the ranks DO exist; however, there is no meaningful zero

IQ scores (there IS a difference between 120 and 121)
Temperature (Zero degrees does NOT mean that there is no temperature!)

4. Ratio: Same as above, except a true zero exists. True ratios exist when the same variable is measured on two different members of the population

Weight (He’s 300lbs, she’s 150lbs, thus he’s twice as heavy as she
Height
Age
Time
Salary

Data Collection and Sampling Techniques

1. Data collection techniques

        a. Direct observations (should be self explanatory)
        b. Reviewing records (weather temperatures over the last 50 years, etc.)
        c. Surveys -

I. Telephone:

Advantages: cheap, people more candid w/o face-to-face contact

Disadvantages: Those w/o phones, those not at home or no answer

II. Mailed questionnaire:

Advantages: Cover a wider area, respondents anonymous

Disadvantages: Low # of responses, incorrect reading of questions

III. Personal interview:

Advantages: Can get in-depth responses

Disadvantages: Interviewers must be trained (Q&A), expensive, interviewer may be biased in selection of respondents

2. Sampling Techniques

a. Random - Selected by using chance methods or random numbers

b. Systematic - Numbering each subject of the population and picking each kth number
(See page 12 for example- need 50 out of 2000, every 40th w/1st picked at random)

c. Stratified - Divide population into groups according to some characteristic, then random sampling from each group (sample from freshmen, sophomores, juniors and seniors; sample from officers and enlisted personnel, etc.)

d. Cluster - Using intact groups that are representative of a population, such as the residents in a retirement home, kids in one school, nurses in a hospital

e. Convenience - Use subjects that are convenient to study

Please Go to Lesson 2