PS204 - Statistics

Obtaining Knowledge

• Intuition - get a “feeling”

• Tenacity - hear it over and over

• Authority - we are “told”

• Rationalism - use of reason

• Empiricism - direct observation

There are several ways by which we obtain “knowledge:”

Our everyday observations are empirical in nature, but generalizations based on those observations can be misleading because they are not made in a “systematic” manner (e.g., rock is the most popular kind of music in America).

Obtaining Knowledge (con’t)

• Who/what to study (e.g., effectiveness of a new drug)

• How to observe (e.g., survey, SAT)

• When to study (e.g., day/evening, rush hour)

• Conditions under which observations are made (e.g., drug dosage, warm/cool temp.)

Empirical research is the systematic application of the empirical approach. With a theory or hypothesis in mind, researchers design a research project to test their idea:

Once the observations have been made, they must be analyzed. The primary function of statistics is to summarize and interpret data.

Experiments and Non-Experiments

• What is something like (e.g., How do people feel about increased security measures at the airport?)

• To what degree are things related (e.g., Is there an association between dreaming and creativity?

• What causes something (e.g., Do PowerPoint presentations enhance understanding?)

There are three general types of questions researchers may ask:

The first two questions are addressed using non-experimental methods which allows one to describe the nature of things. The last type of question is addressed using experimental methods which allows one to determine “cause-and-effect.”

This Course

The previous types of questions are analyzed using different techniques. We will, throughout this semester, examine the kinds of analyses used in each case.

To begin, however, we will consider some basic concepts that are essential for all the analyses.

Basic Concepts

• person = John Andrews

• animal = Killer Whale

• test score = 43

• gender = male

• etc.

Element/Observation - a single object or data value.

Basic Concepts

• all Ohio registered voters (N = 13,283,948)

• all LEC students (N = 709)

• all 1957 Corvettes (N = 8,361)

• other examples?

Population - the collection of all elements having one or more specified characteristics.

The symbol “N” is typically used to indicatethe size of the population.

Basic Concepts

• Ohio registered voters (n = 6,387,542)

• LEC students (n = 930)

• 1957 Corvettes (n = 63)

• etc.

Sample - part of a population which may range in size from 1 to N-1. The symbol “n” is typically used to indicate the size of the sample.

Sample ofLEC

Students(n = 50)

AllLEC

Students(N = 739)

observation

Type of SamplesRandom sample - a sample selected in such a way that every observation in the population has an equal chance of being selected for the sample.

?How would you go about selectinga random sample if the populationwas defined as “students in this class?”

Things to RememberAbout Random Samples

• truly random samples are seldom obtained in the real world.

• large random samples tend to be representative of their populations.

• random samples are influenced by “chance” which leads us to the first of the four most important concepts in statistics...

Random Sampling Variability

...the observation that sample values vary from sample to sample because of chance.

DO NOT FORGET THIS!

Other Types of Samples

Stratified Random Sample - a sample which represents observations from each of several different groups or classes (i.e., strata) of a population.

• Freshmen, Sophomore, Junior, Senior

• Methodist, Catholic, Jewish, Islamic, etc

• male/female

• other examples?

Other Types of SamplesProportionate Stratified Random Sample - a sample which represents the relative frequencies of observations from each of several different groups or classes of a population.

N nSenior 1,000 8

Junior 2,000 17Sophomore 4,000 33Freshman 5,000 42

12,000 100

1. 100 ÷ 12,000 = .008333

2. 1,000 x .008333 = 8 (Seniors)

Basic Concepts

• • number of minutes in an hour (60)

• speed of light (186,000 mi/sec)

• other examples?

Constant - an object whose value does not change.

Basic Concepts

• eye color (brown, green, blue, etc)

• weight (123lbs., 87oz., 3 tons, etc)

• IQ scores (100, 130, 85, etc)

• other examples?

Variable - dimensions of categories of objects, events, or manipulations that can have different values.

Classifying VariablesQualitative variable - one whose range of values consists of groups or classes.

Ordered - the values (i.e., groups) can be placed in a meaningful sequence (e.g., letter grades).

Unordered - the values cannot be placed in a meaningful sequence (e.g., make of automobile).

Classifying VariablesQuantitative variable - one whose range of values consists of a count or numerical measurement of a characteristic.

Discrete - contains a finite number of values or an infinite number of values that are countable (e.g., number of gifts received for birthday).

Continuous - contains an “uncountably infinite” number of values (e.g., distance).

Basic Concepts

• to serve as labels (e.g., Drug A)

• to indicate rank (e.g., 3rd place)

• to represent quantity (e.g., 14 parking tickets)

Measurement - assigning values to objects according to a set of rules.

Uses:

Levels of Measurement

• gender

• political affiliation

• other examples?

Nominal - assignment of observations to mutually exclusive, exhaustive, and non-ordered equivalence classes.

Note. When we talk of an “equivalence class,” we simply mean that any observation within that class or category is as good an example as any other observation in that class or category (e.g., one observation of “brown” eyes is considered equal to all other observations of “brown” eyes.

Levels of Measurement

• military ranks

• Top 10 best movies

• other examples?

Ordinal - assignment of observations to ordered equivalence classes, but does not imply equal intervals.

Levels of Measurement

• degrees Fahrenheit

• spelling test scores

• other examples?

Interval - assignment of observations to ordered equivalence classes with equal intervals and an arbitrary value of zero.

Levels of Measurement

• speed

• height

• other examples?

Ratio - assignment of observations to ordered equivalence classes with equal intervals and an absolute zero.