Statistics powerpoint chapter 11 slides

8/12/2019 Statistics powerpoint chapter 11 slides

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1.1 - 1Copyright 2010, 2007, 2004 Pearson Education, Inc.

Lecture Slides

Elementary Statistics Eleventh Edition

and the Triola Statistics Series

by Mario F. Triola


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Chapter 1 Introduction to Statistics

1-1 Review and Preview

1-2 Statistical Thinking1-3 Types of Data

1-4 Critical Thinking

1-5 Collecting Sample Data


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1.1 - 3

Statistics

Statistics the science of planning studies andexperiments, obtaining data, and then organizing,summarizing, presenting, analyzing, interpreting, anddrawing conclusions based on the data

Copyright 2010, 2007, 2004 Pearson Education, Inc.


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Data

collections of observations (such asmeasurements, genders, surveyresponses)

Data


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Population

Population the complete collection of allindividuals (scores, people,measurements, and so on) to bestudied; the collection is completein the sense that it includes all ofthe individuals to be studied


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Census versus Sample

CensusCollection of data from every

member of a population SampleSubcol lec t ion of membersselected from a population


7/651.1 - 7Copyright 2010, 2007, 2004 Pearson Education, Inc.

Chapter Key Concepts

Sample data must be collected in anappropriate way, such as through aprocess of r andom selection.

If sample data are not collected inan appropriate way, the data may be

so completely useless that noamount of statistical torturing cansalvage them.



Sampling Method

Does the method chosen greatlyinfluence the validity of theconclusion?

Voluntary response (or self-selected)samples often have bias (those withspecial interest are more likely to

participate). These samples resultsare not necessarily valid.Other methods are more likely toproduce good results.



Conclusions

Make statements that are clear tothose without an understanding ofstatistics and its terminology.

Avoid making statements not justified by the statistical analysis.



Statistical Significance

Consider the likelihood of getting theresults by chance.If results could easily occur bychance, then they are no t s tat i s t ical lys ign i f ican t .If the likelihood of getting the results

is so small, then the results ares ta ti s t ica lly s ig ni f icant .



Key Concept

The subject of statistics is largelyabout using sample data to make

inferences (or generalizations) aboutan entire population. It is essential toknow and understand the definitionsthat follow.



Parameter a numerical measurementdescribing some characteristic of apopulation .

population

parameter

Parameter



Statistic

Statistic a numerical measurement describingsome characteristic of a sample .

sample

statistic



Quantitative Data

Quantitative (or numerical) data

consists of n u m b e r s representing countsor measurements.

Example: The weights of supermodels

Example: The ages of respondents



Categorical Data

Categorical (or qualitative orattribute) data

consists of names or labels (representingcategories)

Example: The genders (male/female) ofprofessional athletesExample: Shirt numbers on professionalathletes uniforms - substitutes for names.



Working with Quantitative Data

Quantitative data can further be

described by distinguishingbetween discrete and continuous types.



Discrete data result when the number of possible valuesis either a finite number or a countable

number(i.e. the number of possible values is

0, 1, 2, 3, . . . )

Example: The number of eggs that a henlays

Discrete Data


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Continuous (numerical) dataresult from infinitely many possible valuesthat correspond to some continuous scalethat covers a range of values without gaps,interruptions, or jumps

Continuous Data

Example: The amount of milk that a cowproduces; e.g. 2.343115 gallons per day


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Levels of Measurement

Another way to classify data is to use

levels of measurement. Four ofthese levels are discussed in thefollowing slides.


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Nominal level of measurement characterized by data that consist of names,

labels, or categories only, and the data cannotbe arranged in an ordering scheme (such aslow to high)

Example: Survey responses yes , no ,undecided

Nominal Level


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Ordinal level of measurement involves data that can be arranged in some

order, but differences between data valueseither cannot be determined or aremeaningless

Example: Course grades A, B, C, D, or F

Ordinal Level


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Interval level of measurement like the ordinal level, with the additionalproperty that the difference between any two

data values is meaningful, however, there isno natural zero starting point (where none ofthe quantity is present)

Example: Years 1000, 2000, 1776, and 1492

Interval Level


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Ratio level of measurement the interval level with the additional propertythat there is also a natural zero starting point

(where zero indicates that none of the quantityis present); for values at this level,differences and ratios are meaningful

Example: Prices of college textbooks ($0represents no cost, a $100 book costs twice

as much as a $50 book)

Ratio Level


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Summary - Levels of Measurement

Nominal - categories only

Ordinal - categories with some order

Interval - differences but no naturalstarting 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 this section we have looked at:


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Misuses of Statistics

1. Evil intent on the part ofdishonest people.

2. Unintentional errors on the partof people who dont know anybetter.

We should learn to distinguish betweenstatistical conclusions that are likely to bevalid and those that are seriously flawed.


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To correctly interpret a graph, you must analyze the numericalinformation given in the graph, so as not to be misled by thegraphs shape. READ labels and units on the axes!

Graphs


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Part (b) is designed to exaggerate the difference by increasingeach dimension in proportion to the actual amounts of oilconsumption.

Pictographs


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Bad Samples

Voluntary response sample(or self-selected sample)

one in which the respondents themselves

decide whether to be included

In this case, valid conclusions can bemade only about the specific group ofpeople who agree to participate and notabout the population.


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Correlation and Causality

Concluding that one variable causes theother variable when in fact the variablesare linked

Two variables may seemed linked,smoking and pulse rate, this relationshipis called correlation. Cannot conclude theone causes the other.Corre lat ion d oes no t imp ly causa l ity .


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Small Samples

Conclusions should not be basedon samples that are far too small.

Example: Basing a schoolsuspension rate on a sample ofonly three students


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Order of Questions

Questions are unintentionally loaded bysuch factors as the order of the itemsbeing considered.

Would you say traffic contributes moreor less to air pollution than industry?Results: traffic - 45%; industry - 27%

When order reversed.Results: industry - 57%; traffic - 24%


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Missing Data

Can dramatically affect results.

Subjects may drop out for reasonsunrelated to the study.People with low incomes are less likelyto report their incomes.

US Census suffers from missing people(tend to be homeless or low income).


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Self-Interest Study

Some parties with interest to promotewill sponsor studies.

Be wary of a survey in which thesponsor can enjoy monetary gain fromthe results.

When assessing validity of a study,always consider whether the sponsormight influence the results.


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Precise Numbers

Because as a figure is precise, manypeople incorrectly assume that it is alsoaccura te .

A precise number can be an estimate,and it should be referred to that way.


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Deliberate Distortion

Some studies or surveys are distortedon purpose. The distortion can occurwithin the context of the data, thesource of the data, the samplingmethod, or the conclusions.


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Section 1-5Collecting Sample Data


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Key Concept

If sample data are not collected in anappropriate way, the data may be socompletely useless that no amount ofstatistical torturing can salvage them.

Method used to collect sample datainfluences the quality of the statistical

analysis.Of particular importance is s implerando m samp le .


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Observational study observing and measuring specificcharacteristics without attempting to modify the subjects being studied

Observational Study


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Experiment apply some treatment and then observe its

effects on the subjects; (subjects inexperiments are called experimental units )

Experiment


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Simple Random Sample

Simple Random Sampleof 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 Sample members from the population are selectedin such a way that each individual member in the population has an equal chance ofbeing selected

Random & Probability Samples

Probability Sampleselecting members from a population in sucha way that each member of the populationhas a known (but not necessarily the same)chance of being selected


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Random Samplingselection so that each

individual member has anequal 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 each

subgroup (or stratum)


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Cluster Samplingdivide the population area into sections

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


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Multistage Sampling

Collect data by using some combination of thebasic sampling methods

In a multistage sample design, pollsters select a

sample in different stages, and each stage mightuse different methods of sampling

M h d f S li S


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Random

Systematic

Convenience Stratified

Cluster

Multistage

Methods of Sampling - Summary

d h f


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Different types of observational studies andexperiment design

Beyond the Basics ofCollecting Data

f


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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 (examine records,interviews, )

Prospective (or longitudinal or cohort) study

data are collected in the future from groupssharing common factors (called cohorts )

Types of Studies

R d i i


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Randomizationis used when subjects are assigned todifferent groups through a process ofrandom selection. The logic is to usechance as a way to create two groups thatare similar.

Randomization

R li i


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Replicationis the repetition of an experiment on morethan one subject. Samples should be largeenough so that the erratic behavior that ischaracteristic of very small samples will notdisguise the true effects of differenttreatments. It is used effectively when thereare enough subjects to recognize the

differences from different treatments.

Replication

Use a sample size that is large enough to let ussee the true nature of any effects, and obtainthe sample using an appropriate method, such

as one based on r andomness .

Bli di


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Blinding is a technique in which the subject doesntknow whether he or she is receiving atreatment or a placebo. Blinding allows usto determine whether the treatment effect issignificantly different from a placebo effect ,

which occurs when an untreated subjectreports improvement in symptoms.

Blinding

D bl Bli d


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Double-Blind Blinding occurs at two levels:

Double Blind

(1) The subject doesnt know whether he orshe is receiving the treatment or aplacebo

(2) The experimenter does not knowwhether he or she is administering thetreatment or placebo

C f di


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Confoundingoccurs in an experiment when theexperimenter is not able to distinguishbetween the effects of different factors.

Try to plan the experiment so thatconfounding does not occur.

Confounding


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S


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Three very important considerations in the designof experiments are the following:

Summary

1. Use randomiza t ion to assign subjects to

different groups2. Use replication by repeating the experiment on

enough subjects so that effects of treatment or

other factors can be clearly seen.3. Contro l the e ffec ts of var iab les by using such

techniques as blinding and a completelyrandomized experimental design

E


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Sampling error

the difference between a sample result andthe true population result; such an errorresults from chance sample fluctuations

Nonsampling error sample data incorrectly collected, recorded,or analyzed (such as by selecting a biasedsample, using a defective instrument, orcopying the data incorrectly)

ErrorsNo matter how well you plan and execute

the sample collection process, there islikely to be some error in the results.

R


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Recap

In this section we have looked at: Types of studies and experiments

Controlling the effects of variables

Randomization

Types of sampling

Sampling errors

Statistics powerpoint chapter 11 slides

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