stats 216 chaper 1 (triola, 2014) - capital high...

Stats216_Chapter1_notes.notebook

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Stats216Chaper1(Triola,2014)

1-1 Review and Preview pg. 5 fill in what you need to understand these terms before Monday. CVDOT (read your book)

1. Data:

2. Statistics:

3. Population:

4. Census:

5. Sample:

Homework for the week

Read Chapter 1 and take fill in the following notes


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Statistical Thinking pg. 6


1.2

Voluntary Response Sample (or Self-Selected sample): The respondents themselves decide whether to be included

Analyzing Data: Potential Pitfalls

Misleading Conclusions:

Reported Results:

Small Samples:

Loaded Questions:

Order of questions

Non-response

Missing Data

Precise numbers

Percentages


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1.3TypesofDataParameter: Think of this as population Parameter

Statistic: Think of this like sample statisticBranches of statisticsDescriptive Stats: is the branch of stats that involve the organization, summarization, and display of dataInferential Stats: is the branch of stats that involves using a sample to draw conclusions about a population. A basic tool in the study of inferential stats is probability.

Vocab:Qualitative Data: Consist of attributes, labels or non numerical entriesQuantitative Data: Consist of numerical measurements or countsDiscrete: Quantitative number values are countableContinuous: Numerical data infinitely many possible quantitative values not countable

Levels of Measurement: the level of measurement determines which statistical calculation are meaningful. 4 levels in order from lowest to highestNominal, Ordinal, Interval, Ratio

Nominal level of measurement: are qualitative only. Data at this level are categorized using names, labels, or qualities. NO math computation can be madeOrdinal level of measurement: are qualitative or quantitative. Data at this level can be arranged in order, or ranked, but differences between data entries are not meaningfulInterval level of measurement: Can be ordered, and you can calculate meaningful differences between data entries. At the interval level, a zero entry simply represents a position on a scale, the entry is not an inherent zeroRatio level of measurement: Are similar to data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data values can be formed so that one data value can be meaningfully expressed as a multiple of anotherinherent zero: Is a zero that implies "none" FOR example, the amount of money you have in a savings account could be zero dollars. The zero represents NO MONEY it is called an inherent zeroExample of a zero that is NOT an inherent zero: the temperature 0 degrees, it is a position on the scale, it doesn't mean no heat present


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Example 2 Classifying Data by levelTwo data sets are shown on pg. 12. Which data set consists of data at the nominal level? Which data set consists of data at the ordinal level? Explain

try it yourself #2Consider the following data set, decide whether the data are at a nominal level or at an ordinal levela. Identify what each data set representsb. Specify the level of measurement and justify your answer1. The final standings for the Pacific Division of the NBA2. A collection of phone numbers

Example 3 Classifying data by leveltwo data sets are show on pg. 13. Which data consists of data at the interval level? Which data set consists of data at the ratio level? ExplainBoth of these data sets contain quantitative data. The Dates of Yankee's World Series victories. You could make sense to find the differences between the years. Like the difference between the first and the last 2000-1923= 77 years BUT it doesn't make since to say that one year is a multiple of another SO.... The data is NOT at the interval level

HOME RUN DATAyou can find the differences and WRITE ratios. From the data you can see Detroit hit 31 more home runs then Seattle hit and that Chicago hit about twice as many home runs as Kansas City SO..... these data are at a RATIO level

Try it yourself #3Decide whether the data are at the interval level or at the ratio levela. Identify what each data set representsb. Specify the level of measurement and justify

1. The body temperature (in Fahrenheit) of an athlete during an exercise session

2. the heart rate (in beats per min) of an athlete during an exercise session

The fist set of data set lists the RANK of 5 Tv Shows. They are ranked 1,2,3,4,5. Because the rankings can be listed in order the data is at Ordinal Level 1-5 has no mathematical meaningThe second set of data consists of the call letters or each networkthe call letters are simply the names so they are at the nominal level

Stats216Chaper1(Triola,2014)1.3TypesofData


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GuidelinesDesigning a statistical study1. Identify the variable(s) of interest (the focus) and the population of the study2. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population3. Collect the data4. Describe the data, using descriptive stat techniques5. Interpret the data and make decisions about the population using inferential stats6. Identify any possible errors

Data Collection:*Do an observational study a researcher observes and measures characteristics of interest of part of a population but doesn't change existing conditions. Example:a study in which the researchers observed and recorded the mouthing behavior on nonfood objects of children up to 3 years old.

*perform and experiment: A treatment is applied to part of a population and the responses observed. You may have a CONTROL GROUP: which no treatment is givenExperimental units: subjects are called Placebo: Harmless, unmedicated treatment, that is made to look like the actual treatmentThe responses of both the control group and treatment group

*Use a simulation: the use of a mathematical or physical model to reproduce the conditions of a situation or process. Allows you to study situations that are impractical or even dangerous to create in real life, and often they are cheaper. You will use computers or calculators to simulate statistical process on a computer.

*Use a survey: An investigation of one or more characteristics of a population. surveys are carried out on people by questioning. Most common interview, mail, telephone and now Internet. You have to be careful to word the questions so you don't have a biased responses.

Example 1 Deciding on methods of Data CollectionConsider the following statistical studies. Which method of data collection would you use to collect data for each study. Explain1. A study of the effects of changing flight patterns on the number of plane accidents.

2. A study of the effect of eating oatmeal on lowering blood pressure.

3. A study on how fourth grade students solve a puzzle

4. a Study of US residents' approval rating of the US president.

Very impractical to create the situation, so use a simulation

You want to measure the effect a treatment (eating oatmeal) has on patients, so you would perform an experiment

you want to observe and measure a certain characteristic of part of a population, you could do an observational study

-Use a survey, Ask "DO you approve of the way the President is handling the job?"

Try it yourself 1a. First identify the focus of the studyb. Identify the population of the studyc. Choose an appropriate method of data collection

1. A study of the effect of exercise on relieving depression

2. A study of the success of graduates of a large university finding a job within one year of graduation

Stats216Chaper1(Triola,2014)1.4CollectingSampleData


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1.4 continued Look at page 25Sampling techniques VOCABCENSUS: is a count or measure of an ENTIRE population, it provides complete information, but it is very costly and difficultSAMPLING: is a count or measure of PART of a population, it is more commonUNBIASED DATA: a researcher must ensure that the sample is representative of the population. You must use appropriate techniques to ensure inferences about the populationSAMPLING ERROR: you have to keep in mind that when a study is done with faulty data, the results are questionable and sometimes even with the best methods of sampling error will occurRANDOM SAMPLE: one in which every member of the population has an equal chance of being selected.SIMPLE RANDOM SAMPLE: a sample in which every possible sample of the same size has the same chance of being selected.

Example 3 Using a Random SampleThere are 731 students currently enrolled in Statistics in your school. You wish to perform a sample of 8 students to answer some survey questions. Select the students who will belong to the simple random sampleUSE A RANDOM NUMBER GENERATOR ONCALCULATOR

Try it yourself #3A company employs 79 people. Choose a simple random sample of five to survey

Sampling with Replacement and without replacement: You need to decide whether it is acceptable to have the same population member selected more than once. if that is acceptable then the sample is with replacement if not acceptable the it is said to be without replacement

Common sampling techniques look on pg. 25 GREAT PICTURES OF THESE1. Stratified Sample: use when it is important for the sample to have members from each segment of the population. Depending on the focus of the, study, members of the population the members are divided in to two or more subsets, called STRATA, they share a similar characteristic such as age, gender, ethnicity or even political preference. A sample is then randomly selected from each STRATA. This ensures that each segment of the population is represented 2. Cluster Sampling: When a population falls into naturally occurring subgroups, each having similar characteristics. To select a cluster sample, divide the population into groups called clusters, and select all the members in one or more (BUT NOT ALL) of the clusters. Example pg. 233. Systematic Sample: a sample in which each member of the population is assigned a number. The members of the population are ordered in some way, a starting number is randomly selected and then sample members are selected at regular intervals from the starting number. 4. Convenience sample: LEADS to biased studies it consists of only available members of the population... DON'T USE

Example 3 Identify sampling techniquesYou are doing a study to determine the opinion of students at your school regarding stem cell research. Identify the sampling technique you are using if you select the sample listed

1. You select a class at random and question each student in the class

2. You divide the students with respect to majors and randomly select and question some students in each major.

3. you assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

Your class is a natural cluster (a subgroup) and you question each student .... CLUSTER SAMPLE

Students are divided into a Strata (Majors) and a sample is selected and each student has an equal chance of being selected it is .... Stratified Sample

Each Sample of the same size has an equal Chance of being selected and each student has an equal chance of being selected, so..... Simple random sample

Try it yourself 4same situation as abovea. Determine HOW the sample is selectedb. Identify the corresponding sampling technique

1. You select students who are in your Stats class

2. You assign each student a number and, after choosing a starting number, question every 25th student


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1.4 continued

Randomization

Replication:

Blinding:

placebo effect

double-blind


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Attachments

Stats216TriolaCh1book.pdf

Ghapter 1 Introduction to Statistics

Trepare1. Context

WhaL do the d,atra mean?WhaIiEthe goal of sludy?

2. SourceottheDataAre the dala from a eource wi)h a special inLerest, eo thalthere is preseure to obtainresultrs trhat are f avorable Lo lhe eource?

3. SamplingMethodWere the daLa collected in a way Nhat, is unbiaeed, or were trhe datra colleched in a waythat is biased (such as a procedure in which respondenNs volunteer No participale)?

I

vAnalyze'1 . GraphtheData2. ExploretheData

AreNhere any oulliere (numbersvery far away from almoeL all ofLhe other dala)?What importan, otaXiel;ice summarize the data (such as Lhe mean and, eXandarddeviation describ ed in later)?How arebhe data dieLribuhed?Arethere miseinq daLa?Did many selected eubjects refuse No respond?

3. Apply Stat istical M ethodsUse trechnology ta obtain resulLs.

I

YConclude1 . gLat iatical 9rignifi cance

D o the resulte hav e eLatisti cal signifi cance?Do lhe results have praclical sianificance?

Figure 1-2 Statistical Thinking

PrepareContext Let's consider the data in Table 1- 1. (The data are from Data Set 6 in Appen-dix B.) The data in Table 1-1 consist of measured IQ scores and measured brainvolumes from 10 different subjects. The data are matched in the sense rhat each in-dividual "IQ/brain volume" pair of values is from the same subject. The first subjecthad a measured IQscore of 96 and a brain volume of 1005 cm3. The format ofTable 1-1 suggests the following goai: Determine whether there is a reiationship be-tween IQ score and brain volume. This goal suggests a possible hypothesis: Peoplewith larger brains tend to have higher IQ scores.

Table 1-1 lQ Scores and Brain Volumes (cm3)lQ 96

Brain Volume (cm3) 1005

101 103 127 96 BB

1281 1051 1034 1079 1104

87

1 035

85 97

1439 1029

124

1 160

I

1.4 Collecting Sample Data

34, Scale for Rating Food A group ofstudents develops a scale for rating the qualiry ofcaf-eteria food, with 0 representing "neutral: not good and not bad." Bad meals are given negativenumbers and good meals are given positive numbers, with the magnitude of the number cor-responding to the degree of badness or goodness. The first three meals are rated as2,4, and-5. \fhat is the level of measurement for such ratings? Explain your choice.

35, Interpreting Temperature Increase In the Born Loser cartoon strip by Art Sansom,Brutus expresses joy over an increase in temperature from 1' to 2'. t{4-ren asked what is so good about2", he answers that "it's wice as warm as this morning." Explain why Brutus is wrong yet again.

Collecting Sample Data

Key Concept An absolutely critical concept in applying methods of statistics is con-sideration of the method used to collect the sample data. Of particular importance isthe method of using a simple random sample. We will make frequent use of this sam-pling method throughout the remainder of this book.

As you read this section, remember this:

If sample data are not collected in an appropriate way, the data may be soutterly useless that no amount of statistical torturing can salvage them.

Part 1 of this section introduces the basics of data collection, and Part 2 describessome common ways in which observational studies and experiments are conducted.

Part 1: Basics of Collecting DataStatistical methods'are driven by the data that we coliect. We typically obtain datafrom two distinct sources: obseruationa/ studies and experiments.

DEFINITIONSIn an observational study, we observe and measure specific characteristics, butwe don't attempt to modify the subjects being studied.

ln an experiment, we apply some treatment and then proceed to observe itseffects on the subjects. (Subjects in experiments are called experimental units.)

Experiments are often better than observational studies, because experiments typi-cally reduce the chance of having the results affected by some variable that is not partof a study. (A lurking variable is one that affects the variables included in the study,but it is not included in the study.) In one classic example, we could use an observa-rional study to incorrectly conclude that ice cream causes drownings based on datashowing that increases in ice cream sales are associated with increases in drownings.Our error is to miss the lurking variable of temperature and thus fail to recognize that\\-armer months result in both increased ice cream sales and increased drownings. If,instead of using data from an observational study, we conducted an experimentwithone group treated with ice cream while another group got no ice cream, we would see:hat ice cream consumption has no effect on drownings.

Observational Study and Experiment

Observational Study: The typical survey is a good example of an observationalsrudy. For example, the Pew Research Center suryeyed 2252 adults in the UnitedStates and found that 59o/o of them go online wirelessly. The respondenrs wereasked questions, but they were not given any treatment, so this is an example of anobservational study.

23

34. Either ordinol or infervol is 0 re0s0n-

oble onswer, but ordinol mokes more

sense becouse differences belween

volues ore not likely to be meoning{ul.

For exomple, the differenre beMeen o

food roted I cnd o fooel roted 2 is notneressorily ihe some os the difference

belween o food roied 9 ond o food

roted I 0.

35. With no notur0l slorling point, lem-

perotures ore oi the intervol level of

meosurement, so rolios sucii os "iwice"

ore meoningles.

Nole fo Instructor

This section con be reod by studenls on

their own. Ihe previous edition included

seporote definitionstor simple rondorn

sonple ond rondam sample.See lhe noie

in porenlheses included with the definition

of simple rondom sornple. Al lhis sfoge, it

is not so importonl to distinguish between

o simple rondorn somple ond o rondom

somple. But it is crllicolly imporlonl lo

slres lhe imporlonre of good sompling

tethniques. Reinforce the ronrepl lhot

voluntory response somples ore unsuiloble

for sound sloiislicol methods. lf the som-

pling is not done rorreclly, even very lorge

somples moy be totolly worthles.

Lurking variableis mentioned in lhis

serlion. l/onrondom sompling error ond

two other sompling errors ore now included

in lhis seclion.

Chapter f

;,:-:l r=,Fi.i llLliWClinical l?ials vs.ObservationalStudiesln a New York Times article about

hormone therapy for women, re-

porter Denise Grady wrote about

randomized clinical trials that in-

volve subjects

who were

ranoomry

tceidnoa{ tn

Such

randomized clinical trials are

often referred to as the "gold

standard" for medical research.

In contrast, observational studies

can involve patients who decide

themselves to undergo some

treatment. Subjects who decide

themselves to undergo treatments

are often healthier than other

subjects, so the treatment group

might appear to be more suc-

cessful simply because it involves

healthier subjects, not neces"-

sarily because the treatment is

effective. Researchers criticized

observational studies of hormone

therapy for women by saying that

results might appear to make the

treatment more effective than it

really is.

24 lntroduction to Statistics

Experiment In the largest public health experiment ever conducted,200,745children were given a trearment consisting of the Salk vaccine, while 20I,229 otherchildren were given a placebo. The Salk vaccine injections constitute a treatment

that modified the subjects, so this is an example of an experiment.

tMhether one is conducting an observational studv or an experiment, it is impor-rant ro select the sample of subjects in such a way that the sample is iikely to be repre-sentative of the larger population. In Section 1-2 we saw that in a voluntary responsesample, the subjects decide themselves whether to respond. Although voluntary re-sponse samples are very common, their results are generally useless for making validinferences about larger populations. The following defintion refers to one commonand effective way to collect sampie data.

DEF INITIORI A simple random sample of n subjects is selected in such away that every possible sample of the same sZe n has the same chance of beingchosen. (A simple random sample is often calted a random sample. but strici'yspeak;ng, a random sample has the weaker requirement that all men'be's o'Lhepopulation have the same chance of being selected. That distinctlon is not soimportant in this text.)

Throughout, we will use various statistical procedures, and we often have arequirement that we have collected a simple random sample, as defined above.

The definition of a simple random sample requires more than selecting subjectsin such a way that each has the same chance of being selected. Consider the selectionof three students from the class of six students depicted below. If you use a coin tossto select a row, randomness is used and each student has the same chance of beingselected, but the result is not a simple random sample. The coin toss will produceonly two possible samples; some samples of three students have no chance of beingselected, such as a sample consisting of a female and two males. This violates therequirement that all samples of the same size have the same chance of being selected.Instead of the coin toss, you could get a simple random sample of three students bywriting each of the six different student names on separate index calds, rvhich couldthen be piaced in a bowl and mixed. The selection of three index cards will yield asimple random sample, because every different possible sample of three students now

has the same chance of beine selected.

Aeade:

Taile:

\fith random sampling we expect all components of the population to be (approx-imately) proportionately represented. Random samples are selected by many differentmethods, including the use of computers to generate random numbers. Unlike care-less or haphazard sampling, random sampling usually requires very careful planningand execution. Vayne Barber of Chemeketa Communiq. College is quite correct whenhe tells his students that "randomness needs help."

*th*r S*rrnBiing flfiethsds In addition to simple random sampling, here are someother sampling methods commonly used for suffeys. Figure i-3 illustrates these dif-ferent sampling methods.

:1,

-t

n+n,il,1T,il

m,*

,sd*r*F,

1-4 Collecting Sample Data

1?th

Random Sampling:

Each memb,zr o{ the populafion hasan equal chance of being selected.Compufers ar,z oflen used logenerole random telephone numbe.rs.

Simple Rctndom Sctmpling:

A sample of n subiects isselecfed in such a woy fhaf everypossible somple of lhe some size nhas fhe same chance of being chosen

Syslematic Sampling:Selecf some sforltnet noinf. fl^1sp:"'- ""J I'""'

26 Chapter 1 lntroduction to Statistics

DEFInIITIOI\ISIn systematic sampling, we select some starting point and then select every kth(such as every 50th) element in the population,

With convenience sampling, we simply use results that are very easy to get.

In stratified sampling, we subdlvide the population into at least two differentsubgroups (or strata) so that subjects within the same subgroup share the same

characteristics (such as age bracket). Then we draw a sample from each subgroup(or stratum).

In cluster sampling, we first divide the population area into sections (or clusters).Then we randomly select some of those clusters and choose a// the members from+h^^a aalanra;

^1,,^+^LI luse seteuLeu L;lusLefS.

It is easy to confuse stratified sampling and cluster sampling, because they both usesubgroups. But cluster sampling uses all members from a sample of clusters, whereasstratified sampling Lrses a sample of members from all xrata. An example of cluster sam-pling is a preelection poll, in which pollsters randomly select 30 election precincts froma large number of precincts and then survey all voters in each of those precincts. This isfaster and much less expensive than selecting one voter from each of the manv precinctsin the popularion area. Pollsters can adjust or weight the results of stratified or clustersampling to correct for any disproportionate representation of groups.

For a fixed sample size, if you randomly select subjects from different strata, youare likely to get more consistent (and less variable) results than by simply selecting arandom sample from the general population. For that reason, pollsters often use strat-ified sampling to reduce rhe variation in the results. Many of the methods discussedlater in this book require that sample data be derived from a simple random samPle,and neither stratified sampling nor cluster sampling satisfies thaf requirement.

Multistage $arnpling Professional pollsters and government researchers often col-lect data by using some combination of the basic sampling methods. In a multistagesample design, pollsters select a sample in different stages, and each stage might usedifferent methods of sampling. For example, one multistage sample design might in-

volve the random selection of clusters, but instead of surveying all members of thechosen clusters, you might randomly select 50 men and 50 women in each selectedcluster; thus you begin with cluster sampling and end with stratified sampling. SeeExample 2 for an actual multistage sample design that is complex, but effective.

Multistage Sample Design

The U.S. governmenr's unemployment statistics are based on surveyed househoids. Itis impractical to personally visit each member of a simple random sample, because in-

dividuai households are spread all over the country. Instead, the U.S. Census Bureau

and the Bureau of Labor Statistics collaborate to conduct a survey called the Current

Population Survey. This survey obtains data describing such factors as unemploy-

ment rates, college enrollments, and weekly earnings amounts. One recent sutvey

incorporates a multistage sample design, roughly following these steps:

r. The entire United States is partitioned into 2025 different regions calledprimary sampling uni* (PSlJs). The primary sampling units are metropolitanareas, large counties, or combinations of smaller counties. These primarysampling units are geographically connected . -Ihe 2025 primary samplingunits are then grouped into 824 different strata.

.:i.-{,..ftF,"+.Fi.e+ffiHawthorne andExperimenterEffectsThe well-known placebo effect

occurs when an untreated subject

incorrectly believes that he or

she is receiving a

'lt, real treatment and::r:t reports an improve-.:

* ment in symptoms.&,.n' *,4,*

The rlawthorne ef-

'.1 e= ' J fect occurs when-.-'-* treated subiects'l''l ...,. .- somehow

respond differently, simply

because they are part of an

experiment. (This phenomenon

was called the "Hawthorne effect"

because it was first observed

in a study of factory workers at

Western Electric's Hawthorne

plant.) An experimenter effect

(sometimes called a Rosenthal

cffcet\ oe.r rrs when the researcher

or experimenter unintentionally

influences subjects through such

factors as lacial expression, tone

of voice, or attitude.

iliote to ingtc'ileto!'

The leiinitions ci stratt{ied sanpiing andtluster scr,'plinrl inny rcruse some ionfusion

hecor,se lfe'/ llcii irvolve slmpling fromd:lfer:rt u c:r:s. il,rrircle tne tonfusion

by noting thoi'riih cluster somcling, we

use o#members {rom the selerieri rlusters,

wherecs slrciified soiirpl!nq irses only r

sanpieol members Irom eoch slrrlc.

Assotiote "rirsiei"' wilh "nli."

ffi

wffi

1-4 Collecting Sample Data

In each of the 824 different strata, one of the primary sampling units isselected so that the probability of selection is proportional to the size of thepopulation in each primary sampling unit.

In each of the 824 selected primary sampling units, census data are used toidentif' a census enumeration district, with each containing about 300 house-holds. Enumeration districts are then randomly selected.

In each of the selected enumeration districts, clusters of about four addresses(contiguous whenever possible) are randomly selected.

Respondents in the 60,000 selected households are interviewed about theemployment status of each household member of age 16 or older.

This muldstage sample design includes random, stratified, and cluster sampling atdifferent stages. The end result is a very complicated sampling design, but it is much morepractical and less expensive than using a simpler design, such as a simple random sample.

Part 2t Beyond the Basics of Collecting DataIn Part 2 of this section, we refine what we've learned about observational studies andexperiments by discussing different rypes of observational studies and different waysof designing experiments.

There are various types of observational studies in which investigators observeand measure characteristics of subjects. The following definitions identi$, the stan-dard terminology used in professional journals for different types of observationalstudies. These defiriitions are illustrated in Figure 1-4.

27

?ast, periodof time

Retrospeclive {orcase-control) etudy:GobackintimetocollecL data over eomepast period.

Whenarethe

obeewationsmade?

I One pointI intimeY

Cross-sectionaletudy:)ala aremeaeured aa one

poinLinLime.

Forwardintime

7 r o ep e ctiv e (o r I o n gitu din alor cohort) etudy:G o torw ard in Lime and ob e erv eqrou?s sharing common factore,euch as emokers and nonsmokers.

ProspectiveNational Children'sStudyA good example of a prospective

study is the National Children's

Study begun in 2005. lt is track-

ing 100,000

children from

birth to age 21.

The children

are from 96

different

geographic

The objec-

tive is to improve the health of

children by identifying the effects

of environmental factors, such

as'diet, chemical exposure, vac-

cinations, movies, and television.

The study will address questions

such as these: How do genes

and the environment interact

to promote or prevent violent

behavior in teenagers? Are lack

of exercise and poor diet the only

reasons why many children are

overweight? Do infections impact

developmental progress, asihma,

obesity, and heart disease? How

do city and neighborhood plan-

ning and constructlon encourage

or discourage injuries?

Ihis section ond severol olher seclions

ore porliiioned inlo Part I snd Porl 2.The typicol one-semesler course does nol

ollow enough time to cover oll topics in lhis

book, ond Port 2 could be omitted {rom

such courses.

2.

3.

4.

5.

ObsewationalgtudyrObsewe andmeasure,butdo noi modify.

+

Figure 1-4 Types of Observational Studies

28 Chapter I lntroduction to Statistics

DEFINITIONSln a cross-sectional study, data are observed, measured, and collected at onepoint in time, noi over a period of time,

In a retrospective (or case-control) study, data are collected from a past time pe-riod by golng back in time (through examination of records, interviews, and so on).

ln a prospective (or longitudinal or cohort) study, data are collected in the futurefrom groups that share common factors (such groups are called cohorts).

The sampling done in retrospective studies differs from that in prospective studies.In retrospective studies we go back in time to collect data about the characteristic thatis of interest, such as a group of drivers who died in car crashes and another group ofdrivers who did not die in car crashes. In prospective studies lve go forward in time byfollowing a group with a potentialiy causative factor and a group without it, such as agroup of drivers who use cell phones and a group of drivers who do not use cell phones.

Designs of Experiments\7e begin with Example 3, which describes the largest public health experiment everconducted, and which serves as an example of an experiment having a good design.After describing the experiment in more detail, we describe the characteristics of ran-domization, replication, and blinding that typify a good design in experimenrs.

National Ghildren'sStudyThe National Children's Study,

launched in 2009, is designed to

follow 100,000 U.S. children from

before birth to age 21. Subjects

have been selected from 105

different counties

teristics. Because children

are observed from birth into the

future, this is a good example of

a prospective study. The cost of

the study was originally expected

to be $3 billion, but it has grown to

almost $7 billion. Data are being

collected from such varied sources

as breast milk and carpet dust.

The general goal is to collect data

that will enhance our understand-

ing of the effects of genetics and

the environment on children. lt is

hoped that this understanding will

lead to improvements in children's

health. The National Children's

Study is the largest, most expen-

sive. and most comprehensive

study of its type ever undertaken.

It is being sponsored by sevqral

lederal organizations, including the

Department of Health and Human

Services, the National Institutes

of Health, and the Environmental

Protection Agency.

The Salk Vaccine Experiment, In 1954, a large-scaie experiment was designed to test the effectiveness of the Salk,: vaccine in preventing polio, which had killed or paralyed thousands of chiidren. In. that experimenq200,745 chrldren were given a treatment consisting of Salk vaccine

injections, while a second group of 201 ,229 children were injetted with a placebo,' that contained no drug. The children being injected dld not know whether they were,, getting the Sa.lk vaccine or the placebo. Children were assigned to the treatment or, placebo group through a process ofrandom selection, equivalent to flipping a coin.

Among the children given the Salk vaccine, 33 later developed parall.tic polio, and

, among the children given a placebo, i 15 later developed paraly'tic polio

Randomization is used when subjects are assigned to different groups through aprocess of random selection. The 407,974 children in the Salk vaccine experiment wereassigned to the Salk vaccine treatment group or the placebo group via a process of ran-dom selection equivalent to flipping a coin. In this experiment, it would be extremely dif-ficult to directly assign children to two groqps having similar characteristics of age, health,sex, weight, height, diet, and so on. There could easily be important variables that wemight not think of including. The logic behind randomization is to use chance as a wayto create two groups that are similar. Although it might seem that we should not leaveanlthing to chance in experiments, randomization has been found to be an extremely ef-fective method for assigning subjects to groups. However, it is possible for randomizationto result in unbalanced samples, especially when very small sample sizes are involved.

Replication is the repetition of an experiment on more than one subject. Sampiesshouid be large enough so that the erratic behavior that is characteristic of very smallsamples will not disguise the true effects of different treatments. Replication is used ef-fectively when we have enough subjects to recognize differences resulting from differenttreatments. (In another context) replicrttizn refers to the repetition or duplication of anexperiment so thar results can be confirmed or verified.) With replication, the largesample sizes increase the chance of recognizing different treatment effects. However, alarge sample is not necessarily a good sample. Although it is important to have a sample

,. i so that it will

T * r'- includasood

f mtx oT cnarac-

ffi

1.4 Collecting Sample Data

that is sufficiently large, it is even more important to have a sample in which subjectshave been chosen in some appropriate way, such as random selection.

Use a sample size that is large enough to let us see the true nature of anyeffects, and obtain the sample using an appropriate method, such as onebased on randomness.

In the experiment designed to test the Salk vaccine, 200,745 children were given theactual Salk vaccine and 20I,229 other children were given a placebo. Because the ac-tual experiment used sufficientiy large sample sizes, the researchers could observe theeFFectiveness of the vaccine,

Blinding is in effect when the subject doesn't know whether he or she is receivinga rrearment or a placebo. Blinding enables us to determine whether the treatment effectis significantly different from a placebo effect, which occurs when an untreated sub-ject reports an improvement in symptoms. (The reported improvement in the placebogroup may be real or imagined.) Blinding minimizes the placebo effect or allows inves-tigators ro account for it. The polio experiment was double-blind, which means thatblinding occurred at nvo leveis: (1) The children being injected didn't know whetherthey were getting the Salk vaccine or a placebo, and (2) the doctors who gave the in-jections and evaluated the results did not know either. Codes were used so that theresearchers could objectively evaluate the effectiveness ofthe Salk vaccine.

Controlling Effects of Variables Results of experiments are sometimes ruinedbecause of co nfou ndi ng.

DEFINITION Confounding occurs in an experiment when the investigatorsare not able to distlnguish among the effects of different factors.

Try to design the experiment in such a way that confounding does not occur.

Designs of Experiments See Figure t-5(a), where confounding can occur when thetreatment group of women shows strong positive results. Here the treatment groupconsists of women and the placebo group consists of men. Confounding has occurredbecause we cannot determine whether the treatment or the gender of the subjectscaused the positive results. It is important to design experiments in such a way as tocontrol and understand the effects of the variabies (such as treatments) . The Salk vac-cine experiment in Example 3 illustrates one method for controlling the effect of thetreatment variable: Use a completely randomized experimental design, whereby ran-domness is used to assign subjects to the treatment group and the placebo group.A completeiy randomized experimental design is one of the following methods thatare used to control effects ofvariables,

Completely Randomized Experimental Design: Assign subjects to different treat-ment groups through a process of random selection, as illustrated in Example 3 andFigure 1-5(b).

Randomized Block Design: A block is a group of subjects that are similar, butblocks differ in ways that might affect the outcome of the experiment. Use the fol-lowing procedure, as illustrated in Figure 1-5(c):

1. Form biocks (or groups) of subjects with similar characteristics.

2. Randomly assign treatments to the subiects within each block.

ZV

Survey PitfallsSurveys constitute a huge and

growing business in the United

States, but survey

results can be

compromised by

many factors. A

growrng numoer

of people refuse

to respond; lthe average

response rale

is now about 22%,

compared to 360/o dround the year

2000. A growing number of people

are more difficult to reach because

they use cell phones (no direc-

tories); about 15% of adults now

have cell phones and no landlines,

and they tend to be younger

than average. There are obvious

problems associated with surveys

that ask respondents about drug

use, theft, or sexual behavior, and

a social desirability bias occurs

when survey respondents are not

honest because they don't want

to be viewed negatively by the

person conducting the interview.

(b)

(d)

30

T

Ghapter I Introduction to Statistics

Treattheee randomlyselecl;ed subjecte and giveLhe others a Vlacebo.

Bad experimental design:Treal all women subjecLsand qiveLhe men a placebo.

(Troblem: W e don't know ifeffects are due Lo sex orLo I;reatmenL)

Completely randomizedexperimental design:

Uee randomnessLodetermine who ge1s Lhetreatment and who qeLethe placebo.

Matched paira design:GeL meaeurements from thesame subjects before and after9)me treaLrnenl.

Block of Women

+r4+tt-----.---lf

T r e at r an domly e ele ctedwomen.

Dlock of Men.1 oo)r

i,ilt, qJtWT r.,{l Ln.j I l,rnu-raffit""r"amen.

Defore After- -!_

Atex tl,l _ u,ilLi| l_[Jg

1ob tfotr _ i],llI.JLJ N6

-12-chris tlnl

- [J,/l_rll uJ

Ra n d o miz e d bl o ck d e si gn:1 . Form a block of women

and a block of men.2. Wirhin eachblock

r and omly sele cL subje ct;sLo betreated

Figure 1-5 Designs of Experiments

For example, in designing an experimenr ro test the effectiveness of aspirin treat,menrs on heart disease, we might form a brock of ;; ;;J;"biock of women,because it is known that the tr.irr, oi -.1 and women .", b.h"rr. differentry. By,TJi:::,i:"ffi::* this randomu.a ui..r. d.,is;;ri;;.,,""a* as a possibre

A randomized brock design uses the same basic idea as stratified sampring, butrandomized block designs are" used *h., l.rigrring experimenrs, whereas stratifiedsampling is used for surveys.

Treatment Group:WomenffiTreat all wamen subiecLs.

?Iacebo Group: Men..qgA-a--a-h/1/1/Ij/q/tttlfGive all men a placebo

{-4 Collecting Sample Data

Matched Pairs Design: Compare two treatment groups (such as treatment and pla-

cebo) by using subjects matched in pairs that are somehow related or have similarcharacteristics, as in the following cases.

. Before/After: Matched pairs might consist of measurements from subjects before

and after some trearmenr, as illustrated in Figure 1-5(d). Each subject yields a"before" measurement and an "after" measurement, and each before/after pair ofmeasurements is a matched pair.

. Twins: A test of Crest toothpaste used matched pairs of rwins, where one Wvinused Crest and the other used another toothpaste.

Rigorously Controlled Design: Carefully assign subjects to different treatmentgroups, so rhat those given each treatment are similar in the ways that are importantto the experiment. In an experiment testing the effectiveness of aspirin on heart dis-ease, if the placebo group includ es a 27 -year-old male smoker who drinks heavily andconsumes an abundance of salt and fat, the treatment group should also include aperson with these characteristics (such a Person would be easy to find). This approachcan be extremely difficult to implement, and often we can never be sure that we haveaccounted for all ofthe relevant factors.

Sampling Errors In an algebra course, you will get the correct result if you usethe correct methods and apply them correctly. In statistics, you could use a goodsampling method and do everl'thing correctly, and yet it is possible for the result tobe wrong. No matter how well you plan and execute the sample collection process,there is likely to be some error in the results. Suppose that you randomly select 1000adults, ask them whether they use a cell phone while driving, and record the sample

percenrage of "yes" fesponses. If you randomly select another sample of t0OO adults,it is likely that you will obtain a dffirent sample percentage. The different types ofsampling errors are described here.

DEFINITIONSA sampling error (or random sampling error) occurs when the sample has been

selected with a random method, but there is a discrepancy between a sample

result and the true population result; such an error results from chance sample fluc-

tuations.

A nonsampling error is the result of human error, includlng such factors as wrong

data entries, computing errors, questions with biased wording, false data provided

by respondents, forming biased conclusions, or applying statistical methods that

are not appropriate for the circumstances.

A nonrandom sampling error is the result of using a sampling method that is not

random, such as using a convenience sample or a voluntary response sample.

Iiwe carefully collect a random sample so that it is representative of the population,ive can use methods in this book to analyze the sampling error, but we must exercise

Sreat care to minimize nonsampling error.Experimental design requires much more thought and care than we can describe

.n this relatively brief section. Taking a complete course in the design of experiments

-s a good start in learning so much more about this important topic.

JI

MisleadingStatistics inJournalismN ew York Ti me s reporter Daniel

Okrant wrote that although every

senlence

in his

newspaper

rs copy-

edited for

clarity and

good writing, "numbers, so alien

to so many, don't get nearly this

respect. The paper requires

no specific training to enhance

numeracy and [employs] no spe-

cialists whose sole job is to foster

it." He cites an example of the

N ei York Times reporting aboutan estimate of more than $23

billion that New Yorkers spend

tor counterfeit goods each year.

Okrant writes that "quick arith-

metic would have demonstrated

that $23 billion would work out to

roughly $8000 per city household,

a number ludicrous on its face."

SMART Notebook

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