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

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Presentatie over: "M ARIO F. T RIOLA 3rd E DITION Essentials of S TATISTICS."— Transcript van de presentatie:

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

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

3 Website cursus:

4

5 Boek Literatuur: Mario Triola: Essentials of Statistics, 3 rd edition Addison-Wesley Higher Education, 2008

6 Rooster

7 Organisatie en opzet (1) Kijk zelf op website naar: – Introductie – Beoordeling en deadlines – Ziekteregeling – Rooster – Etc.

8 Organisatie en opzet (2) 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

9 Organisatie en opzet (3) Werkcolleges verplicht? Succes garantie?

10 Samenhang?

11 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

12 Tabel (1) artikel MIS Quarterly

13 Tabel (2) artikel MIS Quarterly

14 Tabel buurtcomité

15 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?

16 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?

17 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! 123

18 Aanpak hoorcolleges Geen uitgebreide bespreking Wel vooruitblik op de stof en bespreking van mogelijke knelpunten Nu: hoofdstuk 1, 2 en 3

19 Sekties hfst 1, 2 en 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

20 Triola, hoofdstuk 1 Belangrijke definities voor gebruik bij de statistiek

21 Sektie 1.1 Belangrijke definities Data Statistiek Populatie Census Steekproef

22 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

23 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.

24 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

25 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

26 Sektie 1.3 Kritisch denken Misbruik, ondeskundig gebruik, verkeerd gebruik van de statistiek

27 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.

28 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

29  Loaded Questions  Order of Questions  Refusals  Correlation & Causality  Self Interest Study  Precise Numbers  Partial Pictures  Deliberate Distortions Other Misuses of Statistics

30 Sektie 1.4 Ontwerp van het onderzoek Soorten studies – Observationeel – Experimenteel – Retrospectief – Prospectief (longitudinaal, cohort)

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

32 Voorbeeld: confounding effects

33 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

34 Steekproeven

35 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

36  Random  Systematic  Convenience  Stratified  Cluster Methods of Sampling

37 Triola, hoofdstuk 2 Statistiek voor het samenvatten en weergeven van data

38 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 Overview Important Characteristics of Data CVDOT

39 Sektie 2.2 Frequentieverdelingen Gewone (rechte) telling van waarden in een tabel Samenvoegen van waarden in categorieën (classes)

40 Frequency Distribution Ages of Best Actresses Frequency Distribution Original Data

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

42 Frequency Tables

43 Sektie 2.3 Histogrammen Grafische weergave van verdelingen

44 Histogram A bar graph in which the horizontal scale represents the classes of data values and the vertical scale represents the frequencies

45 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

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

47 Sektie 2.4 Statistical graphics Andere vormen van visuele weergave – Polygon – Ogive – Dot plot – Stemplot – Pareto chart – Pie chart – Scatter plot – Time series

48 Ogive A line graph that depicts cumulative frequencies Insert figure 2-6 from page 58

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

50 Other Graphs

51 Triola, hoofdstuk 3 Statistiek voor het beschrijven, verkennen en vergelijken van data

52 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

53 Sektie 3.2 Centrummaten Gemiddelde (mean) – Van steekproef (x-streep) en van populatie (mu) Mediaan (x-tilde) Modus Midrange Gewogen gemiddelde

54 Notation µ is pronounced ‘mu’ and denotes the mean of all values in a population x = n  x x is pronounced ‘x- bar’ and denotes the mean of a set of sample values N µ =  x x

55 Carry one more decimal place than is present in the original set of values. Round-off Rule for Measures of Center

56 use class midpoint of classes for variable x Mean from a Frequency Distribution

57 Best Measure of Center

58 Skewness

59 Sektie 3.3 Variatiematen Range Standaard deviatie – steekproef (s) en populatie (sigma) Variantie (s-kwadraat) Variatiecoëfficiënt (CV)

60 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.

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

62 Sample Standard Deviation Formula  ( x - x ) 2 n - 1 s =s =

63 Population Standard Deviation 2  ( x - µ ) N  = This formula is similar to the previous formula, but instead, the population mean and population size are used.

64 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.

65 Variance - Notation standard deviation squared s  2 2 } Notation Sample variance Population variance

66 Estimation of Standard Deviation Range Rule of Thumb For estimating a value of the standard deviation s, Use Where range = (maximum value) – (minimum value) Range 4 s s 

67 Estimation of Standard Deviation Range 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) =

68 The Empirical Rule

69 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 s x CV =  100%  CV =   100%

70 Sektie 3.4 Maten van relatieve afwijking Z-scores Quartielen Percentielen

71 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.

72  z Score (or standardized value) the number of standard deviations that a given value x is above or below the mean Definition

73 Sample Population x - µ z =  Round z to 2 decimal places Measures of Position z score z = x - x s

74 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

75 Q 1, Q 2, Q 3 divide ranked scores into four equal parts Quartiles 25% Q3Q3 Q2Q2 Q1Q1 (minimum)(maximum) (median)

76 Percentiles Just as there are three quartiles separating data into four parts, there are 99 percentiles denoted P 1, P 2,... P 99, which partition the data into 100 groups.

77 Sektie 3.5 EDA Uitbijters (outliers) Boxplot

78 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.

79 Definitions For a set of data, the 5-number summary consists of the minimum value; the first quartile Q 1 ; the median (or second quartile Q 2 ); the third quartile, Q 3 ; 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, Q 1 ; the median; and the third quartile, Q 3

80 Boxplots

81 Boxplots - cont

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


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