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Addison Wesley Longman 1

Elementary Elementary StatisticsStatistics

Addison Wesley Longman

Introduction To Introduction To StatisticsStatistics

Chapter 1Chapter 1

1-1 Overview

1-2 The Nature of Data

1-3* Uses and Abuses of Statistics

1-4 Design of Experiments

Chapter 1 Introduction to Statistics

Statistics

Two Meanings Actual numbers Methods of analysis

1-1 Overview

Actual numbersnumerical measurements determined by a

set of data

Statistics

Methods of analysisa collection of methods for planning

experiments, obtaining data, and then

analyzing, interpreting, and drawing

conclusions based on the data

Statistics

Population

the complete collection of elements (scores, people, measurements, etc.) to be studied

Sample

Definitions

Population

the complete collection of elements (scores, people, measurements, etc.) to be studied

Sample

a subset of a population

Definitions

Parameter

a numerical measurement describing some characteristic of a population

Parameter

a numerical measurement describing some characteristic of a population

population

parameter

Definitions

Statistic

a numerical measurement describing some characteristic of a sample

Definitions

Statistic

a numerical measurement describing some characteristic of a sample

sample

statistic

• Population

Definitions

Population Parameter

Definitions

Sample

Definitions

Sample Statistic

Definitions

Sample Statistic

Census

Definitions

Quantitative data

numbers representing counts or measurements

Qualitative (attribute) datanonnumeric data that can be separated into different categories

The Nature of Data

Definitions

Discrete data which results from either a finite number of

possible values or a countable number of possible values

0, 1, 2, 3, . . .

Definitions

Discrete data which results from either a finite number of possible

values or a countable number of possible values

0, 1, 2, 3, . . .

Continuous data which results from infinitely many possible values that

can be associated with points on a continuous scale in such

as way that there are no gaps or interruptions

Definitions

Discrete - Countable

Quantitative Data

Discrete - Countable

Continuous - Measurements with no gaps

Quantitative Data

nominal level of measurement

characterized by data that consist of names,

labels, or categories only. Data cannot be

arranged in an ordering scheme (such as low

to high)

Definitions

E.g. Blood types: O, A, B, AB

Genders: Male & Female

ordinal level of measurementinvolves data that may be arranged in some

order, but differences between data values

either cannot be determined or are meaningless

Definitions

E.g. Taste of food: bad, so-so, good, delicious

Grades: A, B, C, D, F

interval level of measurement like the ordinal level, with the additional property

that we can determine meaningful amounts of

differences between data. However, there is no

inherent (natural) zero starting point (where none

of the quantity is present.)

Definitions

E.g. year 2000, temperature 96.2 F etc.

ratio level of measurement

the interval level modified to include the inherent

zero starting point where zero indicates that

none of the quantity is present. For values at

this level, differences and ratios are meaningful.

Definitions

E.g. weights of grains, heights of people

Levels of Measurement

Nominal - names only

Ordinal - names with some order

Interval - differences but no ‘zero’

Ratio - differences and a ‘zero’

Levels of Measurement

Nominal - names only

Ordinal - names with some order

Interval - differences but no ‘zero’

Ratio - differences and a ‘zero’

Design of Design of ExperimentsExperiments

Section 1-4Section 1-4

Steps for Designing an Experiment

1. Identify the exact question and exact population

2. Develop a plan for collecting data that is representative of the population

3. Collect data minimizing errors that result in biased data

4. Analyze the data and draw conclusions

Observational Study

Definitions

Observational Study observing and measuring specific characteristics

Definitions

Experiment

Definitions

Experiment application of some treatment and then observe its effects on the subject

Definitions

Treatment Group

Definitions

Treatment Group Control Group

E.g. Drug v.s. placebo

Designing an Experiment

Experimental units (blocks)

Completely randomized design

Rigorously controlled design

Replication

Study the text book Section 1-4 for the details

Confounding

Definitions

Confounding effects from two or more variables that cannot be distinguished from each other

Definitions

Data carelessly collected may be so completely useless that no amount of statistical torturing can salvage them.

Random Sampling - selection so that

each has an equal chance of being selected

Stratified Sampling - subdivide population and draw sample from each stratum

Every K th element

Systematic Sampling

Cluster Sampling - divide into sections; choose a few of those sections; choose all from selected sections

Hey!Do you believe

in the deathpenalty?

Convenience Sampling - use readily available results

Random

Stratified

Systematic

Cluster

Convenience

Methods of Sampling

Sampling Error the difference between a sample result and the

true population result due to chance sample fluctuations

Non-sampling Error sample data that is incorrectly collected, recorded, or analyzed

Definitions

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