M ARIO F. T RIOLA 3rd E DITION Essentials of S TATISTICS.

UNIVERSITEIT VAN AMSTERDAM

MARIO F. TRIOLAMARIO F. TRIOLA3rd3rd EDITIONEDITION

Essentials of STATISTICS

Programma vandaag

Organisatie en opzet van de cursus Waarom Statistiek? Vooruitblik op de stof hoofdstukken 1,2 en 3

Website cursus:

Literatuur:Mario Triola:

Essentials of Statistics, 3rd edition

Addison-Wesley Higher Education, 2008

Rooster

Organisatie en opzet (1)

Kijk zelf op website naar:– Introductie– Beoordeling en deadlines– Ziekteregeling– Rooster– Etc.

Uitdelen en inleveren:– Week 1: Opdrachten hoofdstuk 1, 2 en 3– Week 2: uitwerkingen hoofdstuk 1,2 en 3 en maak

een kopie voor de zelfbeoordeling bij de bespreking

Werkcolleges verplicht? Succes garantie?

Samenhang?

relatie pr.cf en tnt.cf stat 0708

0,0 2,0 4,0 6,0 8,0 10,0

tentamencijfer

Reeks1

Waarom Statistiek?

Lezen en schrijven artikelen vakgebied IK– Voorbeeld artikel MIS Quarterly

Lezen en schrijven in het dagelijks leven– Voorbeeld: tabel actiecommitee in de buurt

Baisvoorwaarde: logisch denken en redeneren– Voorbeeld: het Monty Hall-probleem

Tabel (1) artikel MIS Quarterly

Tabel (2) artikel MIS Quarterly

Tabel buurtcomité

Intuïtie is onbetrouwbaar

Monty Hall probleem– Quiz: er zijn 3 gesloten deuren, – Achter één deur staat een auto, achter beide

andere deuren is niets,– Jij mag een deur kiezen..– Welke kans op de hoofdprijs?

Maar dan …

De quizmaster opent NA UW KEUZE een van de twee overgebleven deuren en laat zien dat daar niets achter zit.

Probleem: U mag nu nog van deur wisselen. Doet U dit?

Analyse

Stel de hoofdprijs zit achter deur 1:

1. U koos deur 1 (auto). De quizmaster opent een andere deur waarachter niets staat. Ruilen levert verlies op…

2. U koos deur 2 (leeg). De quizmaster opent deur 3 waarachter niets staat. Ruilen levert hoofdprijs!

3. U koos deur 3 (leeg). De quizmaster opent deur 2 waarachter niets staat. Ruilen levert hoofdprijs!

Aanpak hoorcolleges

Geen uitgebreide bespreking Wel vooruitblik op de stof en bespreking van

mogelijke knelpunten Nu: hoofdstuk 1, 2 en 3

Sekties hfst 1, 2 en 3

1.1 Overzicht 1.2 Datatypen 1.3 Kritisch denken 1.4 Ontwerp experimenten

2.1 Overzicht 2.2 Frequentieverdeling 2.3 Histogrammen 2.4 Grafische weergave

3.1 Overzicht 3.2 Centrummaten 3.3 Variatiematen 3.4 Relatieve afwijking 3.5 Exploratieve data-

analyse

Triola, hoofdstuk 1

Belangrijke definities voor gebruik bij de statistiek

Sektie 1.1 Belangrijke definities

Data Statistiek Populatie Census Steekproef

Definitie Statistiek

a collection of methods for- planning studies and experiments,- obtaining data, - and then organizing, summarizing, presenting, analyzing, interpreting, - and drawing conclusions based on the data

Chapter Key Concepts

Sample data must be collected in an appropriate way, such as through a process of random selection.

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

Sektie 1.2 Data typen

Definities:– Populatie parameter versus steekproef statistic– Kwantitatieve versus kwalitatieve data– Discrete versus continue data– Meetnivo’s: nominaal, ordinaal, interval, ratio

Levels of Measurement

1. Nominal - categories only

2. Ordinal - categories with some order

3. Interval - differences but no natural starting point

4. Ratio - differences and a natural starting point

Sektie 1.3 Kritisch denken

Misbruik, ondeskundig gebruik, verkeerd gebruik van de statistiek

Misuse # 1- 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 be made only about the specific group of people who agree to participate.

To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the graph’s shape.

Misuse # 3- Graphs

Loaded Questions Order of Questions Refusals Correlation & Causality Self Interest Study Precise Numbers Partial Pictures Deliberate Distortions

Other Misuses of Statistics

Sektie 1.4 Ontwerp van het onderzoek

Soorten studies– Observationeel– Experimenteel– Retrospectief– Prospectief (longitudinaal, cohort)

Confounding occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors

Definition

Voorbeeld: confounding effects

Controlling Effects of Variables

Blinding– subject does not know he or she is receiving a

treatment or placebo Rigorously Controlled Design

– subjects are very carefully chosen Blocks

– groups of subjects with similar characteristics Completely Randomized Exp. Design

– subjects are put into blocks through a process of random selection

Steekproeven

Definitions

Random Sample– members of the population are selected in

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

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

Random

Systematic

Convenience

Stratified

Cluster

Methods of Sampling

Triola, hoofdstuk 2

Statistiek voor het samenvatten en weergeven van data

1. Center: A representative or average value that indicates where the middle of the data set is located.2. Variation: A measure of the amount that the values vary among themselves. 3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed).4. Outliers: Sample values that lie very far away from the vast majority of other sample values.5. Time: Changing characteristics of the data over time.

Sektie 2.1 OverviewImportant Characteristics of Data

Sektie 2.2 Frequentieverdelingen

Gewone (rechte) telling van waarden in een tabel

Samenvoegen van waarden in categorieën (classes)

Frequency Distribution Ages of

Best Actresses

Frequency DistributionOriginal Data

Samenhangende definities

Lower class limits Upper class limits Class boundaries Class midpoints Class width Relatieve frequenties Cumulatieve frequenties (cumulatieve percentages)

Frequency Tables

Sektie 2.3 Histogrammen

Grafische weergave van verdelingen

HistogramA bar graph in which the horizontal scale represents the classes of data values and the vertical scale represents the frequencies

Relative Frequency Histogram Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies

One key characteristic of a normal distribution is that it has a “bell” shape. The histogram below illustrates this.

Critical ThinkingInterpreting Histograms

Sektie 2.4 Statistical graphics

Andere vormen van visuele weergave– Polygon– Ogive– Dot plot– Stemplot– Pareto chart– Pie chart– Scatter plot– Time series

A line graph that depicts cumulative frequencies

Insert figure 2-6 from page 58

Dot PlotConsists of a graph in which each data value is plotted as a point (or dot) along a scale of values

Other Graphs

Triola, hoofdstuk 3

Statistiek voor het beschrijven, verkennen en vergelijken van data

Sektie 3.1 Overzicht

Descriptive Statistics– summarize or describe the important

characteristics of a known set of data

Inferential Statistics– use sample data to make inferences (or

generalizations) about a population

Sektie 3.2 Centrummaten

Gemiddelde (mean) – Van steekproef (x-streep) en van populatie (mu)

Mediaan (x-tilde) Modus Midrange Gewogen gemiddelde

Notation

µ is pronounced ‘mu’ and denotes the mean of all values in a population

x is pronounced ‘x-bar’ and denotes the mean of a set of sample values

Carry one more decimal place than is present in the original set of values.

Round-off Rule for Measures of Center

use class midpoint of classes for variable x

Mean from a Frequency Distribution

Best Measure of Center

Skewness

Sektie 3.3 Variatiematen

Range Standaard deviatie

– steekproef (s) en populatie (sigma) Variantie (s-kwadraat)

Variatiecoëfficiënt (CV)

Key Concept

Because this section introduces the concept of variation, which is something so important in statistics, this is one of the most important sections in the entire book.

Place a high priority on how to interpret values of standard deviation.

Definition

The standard deviation of a set of sample values is a measure of variation of values about the mean.

Sample Standard Deviation Formula

(x - x)2

n - 1s =

Population Standard Deviation

2 (x - µ)

This formula is similar to the previous formula, but instead, the population mean and population size are used.

Standard Deviation - Important Properties

The standard deviation is a measure of variation of all values from the mean.

The value of the standard deviation s can increase dramatically with the inclusion of one or more outliers (data values far away from all others).

The units of the standard deviation s are the same as the units of the original data values.

Variance - Notationstandard deviation squared

}Notation

Sample variance

Population variance

Estimation of Standard DeviationRange Rule of Thumb

For estimating a value of the standard deviation s,

Where range = (maximum value) – (minimum value)

Estimation of Standard DeviationRange Rule of Thumb

For interpreting a known value of the standard deviation s, find rough estimates of the minimum and maximum “usual” sample values by using:

Minimum “usual” value (mean) – 2 X (standard deviation) =

Maximum “usual” value (mean) + 2 X (standard deviation) =

The Empirical Rule

Definition

The coefficient of variation (or CV) for a set of sample or population data, expressed as a percent, describes the standard deviation relative to the mean.

Sample Population

sxCV = 100%

Sektie 3.4 Maten van relatieve afwijking

Z-scores Quartielen Percentielen

Key Concept

This section introduces measures that can be used to compare values from different data sets, or to compare values within the same data set. The most important of these is the concept of the z score.

z Score (or standardized value)

the number of standard deviations that a given value x is above or below the mean

Definition

Sample Population

x - µz =

Round z to 2 decimal places

Measures of Position z score

z = x - xs

Interpreting Z Scores

Whenever a value is less than the mean, its corresponding z score is negative

Ordinary values: z score between –2 and 2 Unusual Values: z score < -2 or z score > 2

Q1, Q2, Q3 divide ranked scores into four equal parts

Quartiles

25% 25% 25% 25%

Q3Q2Q1(minimum) (maximum)

(median)

Percentiles

Just as there are three quartiles separating data into four parts, there are 99 percentiles denoted P1, P2, . . . P99, which partition the data into 100 groups.

Sektie 3.5 EDA

Uitbijters (outliers) Boxplot

Important Principles

An outlier can have a dramatic effect on the mean.

An outlier can have a dramatic effect on the standard deviation.

An outlier can have a dramatic effect on the scale of the histogram so that the true

nature of the distribution is totally obscured.

Definitions

For a set of data, the 5-number summary consists of the minimum value; the first quartile Q1; the median (or second quartile Q2); the third quartile, Q3; and the maximum value

A boxplot ( or box-and-whisker-diagram) is a graph of a data set that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at the first quartile, Q1; the median; and the third quartile, Q3

Boxplots

Boxplots - cont

Einde vooruitblik 1, 2 en 3

Volgende week: – Vragenuur hoofdstukken 1, 2 en 3– Vooruitblik hoofdstukken 4 en 5

M ARIO F. T RIOLA 3rd E DITION Essentials of S TATISTICS.

Documents

Transcript of M ARIO F. T RIOLA 3rd E DITION Essentials of S TATISTICS.

1 Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

1 Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION.

1 Chapter 7. Section 7-1 and 7-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION.

1 Chapter 2. Section 2-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

1 Chapter 10. Section 10.1 and 10.2 Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION.

1 Chapter 6. Section 6-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 3-6 Counting.

1 Chapter 1. Section 1-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

s tatistics talk…

1 Chapter 1. Section 1-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

1 Chapter 10. Section 10-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E.

1 Chapter 4. Section 4-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

1 Chapter 6. Section 6-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

S TATISTICS 1 Regression & Correlation. S TATISTICS 2 Outline X, Y & Regression Models Simple linear regression (SLR) The logic of SLR: SST=SSR+SSE.

统计学原理 S tatistics

1 Chapter 4. Section 4-1 and 4-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION.

Il percorso riola

1 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

1 Chapter 1. Section 1-1 and 1-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION.

WHAT IS THE MAJOR POWER LINKING TATISTICS DATA MINING