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Copyright © 2004 Pearson Education, Inc.

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Chapter 1Introduction to Statistics

1-1 Overview

1-2 Types of Data

1-3 Critical Thinking

1-4 Design of Experiments

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Created by Tom Wegleitner, Centreville, Virginia

Section 1-1Overview

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Overview

A common goal of surveys and other data collectingtools is to collect data from a smaller part of a larger group so we can learn something about the larger

group.

In this section we will look at some of ways to describedata.

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Data

observations (such as measurements,genders, survey responses) that have

been collected.

Definitions

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Statistics

a collection of methods for planningexperiments, obtaining data, and then

then organizing, summarizing, presenting,

analyzing, interpreting, and drawingconclusions based on the data.

Definitions

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Definitions

Population

the complete collection of allelements (scores, people,measurements, and so on) to bestudied. The collection is complete

in the sense that it includes allsubjects to be studied.

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Census

the collection of data from everymember of the population.

Samplea sub-collection of elements drawnfrom a population.

Definitions

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Key Concepts

Sample data must be collected in anappropriate way, such as through a

process of random selection.

If sample data are not collected in anappropriate way, the data may beso completely useless that noamount of statistical torturing can

salvage them.

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Section 1-2Types of Data

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Parameter a numerical measurement describing

some characteristic of a population

population

parameter

Definitions

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Definitions

Statistica numerical measurement describing

some characteristic of a sample.

sample

statistic

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Definitions

Quantitative data

numbers representing counts or measurements.

Example: weights of supermodels.

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Definitions

Qualitative (or categorical or

attribute) data

can be separated into different categoriesthat are distinguished by some nonnumericcharacteristics.

Example: genders (male/female) of professional athletes.

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Working withQuantitative Data

Quantitative data can further be distinguished betweendiscrete and continuous types.

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Discretedata result when the number of possiblevalues is either a finite number or aµcountable¶ number of possible values.

0, 1, 2, 3, . . .

Example: The number of eggs that hens lay.

Definitions

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Continuous(numerical) data result from infinitely many possiblevalues that correspond to some continuous scalethat covers a range of values without gaps,

interruptions, or jumps.

Definitions

2 3

Example: The amount of milk that a cow produces;

e.g. 2.343115 gallons per day.

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Levels of Measurement

Another way to classify data is touse use levels of measurement.

Four of these levels arediscussed in the following slides.

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nominal level of measurement

characterized by data that consist of names,labels, or categories only. The data cannot be

arranged in an ordering scheme (such as low

to high)

Example: survey responses yes, no,

undecided

Definitions

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ordinal level of measurement

involves data that may be arranged in someorder, but differences between data values

either cannot be determined or are meaningless

Example: Course grades A, B, C, D, o r F

Definitions

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interval level of measurement

like the ordinal level, with the additional property that the

difference between any two data values is meaningful.

However, there is no natural zero starting point (where

none of the quantity is present)

Example: Years 1000, 2000, 1776, and 1492

Definitions

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ratio level of measurement

the interval level modified to include the natural

zero starting point (where zero indicates that

none of the quantity is present). For values at

this level, differences and ratios are meaningful.

Example: Prices of college textbooks ($0

represents no cost)

Definitions

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Summary -Levels of Measurement

Nominal - categories only

Ordinal - categories with some order

Interval - differences but no natural

starting point

Ratio - differences and a natural startingpoint

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Recap

Basic definitions and terms describing data

Parameters versus statistics Types of data (quantitative and qualitative)

Levels of measurement

In Sections 1-1 and 1-2 we have looked at:

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Section 1-3Critical Thinking

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Success in Statistics

Success in the introductory statistics course typicallyrequires more common sense than mathematical

expertise.

This section is designed to illustrate how commonsense is used when we think critically about data and

statistics.

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Misuses of Statistics

Bad Samples

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Definitions

Voluntary response sample

(or self-selected survey)

one in which the respondents themselves decide whether to be

included.

In this case, valid conclusions can be made only about the specific

group of people who agree to participate.

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Misleading Graphs

Bad Samples

Small Samples

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Figure 1-1

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To correctly interpret a graph,we should analyze the numericalinformation given in the graphinstead of being mislead by its

general shape.

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Bad Samples

Small Samples

Misleading Graphs

Pictographs

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Figure 1-2

Double the length, width, and height of a cube,

and the volume increases by a factor of eight

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Bad Samples

Small Samples

Misleading Graphs

Pictographs

Distorted Percentages

Loaded Questions

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97% yes: ³Should the Presidenthave the line item veto to

eliminate waste?´

57% yes: ³Should the President

have the line item veto, or not?´

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Bad Samples

Small Samples

Misleading GraphsPictographs

Distorted Percentages

Loaded Questions

Order of Questions

Refusals

Correlation & Causality

Self Interest StudyPrecise Numbers

Partial Pictures

Deliberate Distortions


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Recap

Reviewed 13 misuses of statistics.

Illustrated how common sense can play abig role in interpreting data and statistics

In this section we have:

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Section 1-4Design of Experiments

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Major Points

If sample data are not collected in anappropriate way, the data may be so

completely useless that no amount of statistical tutoring can salvage them.

Randomness typically plays a criticalrole in determining which data tocollect.

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Observational Studyobserving and measuring specific

characteristics without attempting to modifythe subjects being studied

Definitions

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Experiment

apply some treatment and then observe itseffects on the subjects

Definitions

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Cross Sectional Study

Data are observed, measured, and collectedat one point in time.

Retrospective (or Case Control) Study

Data are collected from the past by goingback in time.

Prospective (or Longitudinal or Cohort) StudyData are collected in the future from groups(called cohorts) sharing common factors.

Definitions

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Confoundingoccurs in an experiment when the

experimenter is not able to distinguishbetween the effects of different factors

Try to plan the experiment so confounding does not occur!

Definitions

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Controlling Effectsof Variables

Blinding

subject does not know he or she is receiving atreatment or placebo

Blocksgroups of subjects with similar characteristics

Completely Randomized Experimental Design

subjects are put into blocks through a processof random selection

Rigorously Controlled Design

subjects are very carefully chosen

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Replicationrepetition of an experiment when there are

enough subjects to recognize the differencesin different treatments

Replication andSample Size

Sample Size

use a sample size that is large enough to seethe true nature of any effects and obtain thatsample using an appropriate method, such asone based on randomness

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Random Samplemembers of the population are selected in

such a way that each individual member hasan equal chance of being selected

Definitions

Simple Random Sample (of size n)

subjects selected in such a way that every

possible sample of the same size n has the

same chance of being chosen

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Random Samplingselection so that each has an

equal chance of being selected

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Systematic SamplingSelect some starting point and then

select every K th element in the population

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Convenience Samplinguse results that are easy to get

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Stratified Samplingsubdivide the population into at

least two different subgroups that share the samecharacteristics, then draw a sample from eachsubgroup (or stratum)

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Cluster Samplingdivide the population into sections

(or clusters); randomly select some of those clusters;choose all members from selected clusters

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Random

Systematic

Convenience

Stratified

Cluster

Methods of Sampling

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Sampling Error the difference between a sample result and the truepopulation result; such an error results from chancesample fluctuations

Nonsampling Error sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using adefective instrument, or copying the data incorrectly)

Definitions

R

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Slide 54Recap

In this section we have looked at:

Types of studies and experiments

Controlling the effects of variables

Randomization

Types of sampling

Sampling Errors

Documents

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