Statistical Data Presentation

8/13/2019 Statistical Data Presentation

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StatisticsLecture and exercises (WS 2012/2013)

22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 1

Dr. Olaf Lenz

Institut fr Angewandte Geowissenschaften

Angewandte SedimentgeologieTechnische Universitt Darmstadt


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Structure


Basics (3 lectures with exercises)Introduction on StatisticsData PresentationRequirements of Data for Statistical Analysis

Elementary Statistics (6 lectures with exercises)t-tests and F-testsAnalysis of VarianceCorrelation and Regression

Chi-square TestsNon-parametric TestsMultivariate ANOVA/Repeated Measures

Analysis of Multivariate Data (3 lectures with exercises)Cluster-AnalysisPrincipal Component Analysis

(Detrended) Correspondence Analysis

Time Series Analysis (1 lecture with exercises)Analysis of stationary data: Spectral AnalysisAnalysis of non-stationary data: Wavelet Analysis

Final exam

17.10.2012

24.10.201231.10.2012

07.11.201214.11.201221.11.2012

28.11.201205.12.201212.12.2012

16.01.201323.01.2013

30.01.2013

06.02.2013

13.02.2013


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Summary Statistics


Measures of location:

Measures of spread:

Measures of shape:

MeanMedianMode

Quartiles

location of the center

of the distribution

location of the other partsof the distribution

VarianceStandard deviationInterquartile range

variability of thedata values

Coefficent of skewnessCoefficient of variationKurtosis

symmetry

length of the tail


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Exercise 1


Exercise 1: Find the median and the mean of these three data sets. Use the PAST software.a) 11 8 6 11 10 8 7 5 6

mean: (72/9) = 8 median: 8

5 6 6 7 8 8 10 11 11

b) 7 15 9 8 12 6 3 2

mean: (62/8 = 7.75) median: (7+8)/2 = 7.5

2 3 6 7 8 9 12 15

c) 7 100 9 8 12 6 3 2

mean: (147/8 = 18.375) median: (7+8)/2 = 7.5

2 3 6 7 8 9 12 100


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Exercise 2


Person Income ($)

Sam 4 785 320

Harvey 32 190Fred 31 870

Jill 26 500

Adrienne 24 200

Mean

Median

980 016

31 870

Exercise 2: Given are the incomes of five people in a small village. Calculate the mean and the median.Which measure is better? Why?

The median is better, because the mean is quite sensitive to erratic high values or outliers


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Exercise 3


Exercise 3: Given are the results of 31 vocabulary tests.20 23 28 30 32 35 22 23 27

30 33 36 23

31 30 30 33 36 23 24 26 3134 23 20 25

33 32 30 37 23

mean: (883/31 = 28.48)

median: 30

mode: 23

mode median

mean


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Exercise 4


Exercise 4: Suppose that the following scores were obtained on administering an English language test to tennon-native speakers who had undergone before a language course for brushing-up their knowledge, and tenotherwise similar people who had not undergone a language course:

mean: 37.8 mean: 42.7

standard dev.: 22.63 standard dev.: 11.36


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Data Presentation


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Introduction on data presentation


Graphs help to verify that it is valid to use a particular test

Graphs may reveal unexpected patterns in the data

Graphs quickly reveal any mistakes in our data

exploratory data analysis

antipollution

treatment

insects

0 mg 100

1 mg 1202 mg 140

3 mg 2500

Does adding the antipollution treatment

lead to an increase in invertebrates?


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Column graphs (bar graphs)

22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 10Townend (2002)


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PAST column graph


1

2


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PAST histogram


1

2


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Line graph


Changes in mean stomatal conductance of two tree species over the course of a day

Townend (2002)


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Line graph


Mean concentrations of insecticide at different distances from fish cages at a fish farm

Townend (2002)


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PAST Line graph


1

2


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Scatter graph


Relationship between the mean mass per seed and the number of seeds produced, for a range of plantspecimens collected on Mossely Heath. The circled point appears to be an unusual observation, which

could warrant further investigation

Townend (2002)


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Scatter graph: Independent/dependent variable


Example: How fast individual lions can run might be controlled by how long their legs are, butthe length of their legs is not controlled by how fast they run.

Controlling (independent) variable:leg length

Response (dependent) variable:running speed

X-axis

Y-axis


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Scatter graph



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PAST Scatter graph


1

2


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Ternary plot

22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 22source: wikipedia


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PAST Ternary plot


1) A: 10; B: 80; C: 10

2) A: 30; B: 60; C: 103) A: 40; B: 40; C: 20

1

23

10% C

10% A

80% B

1

2


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Tables


When it is important that the reader can obtain the values in your results accurately orif readers are likely to want to use or compare your actual figures elsewhere, ratherthan just to compare with other populations in your experiment or survey.

When you need to present a lot of data and this appears messy when you try to drawa graph of them.

When data can be presented a lot more compactly in a table.

There are sometimes situations where a table might be better than a graph


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Standard error and error bars in graphs


Tree

height(m)

Townend (2002)


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Standard error and error bars in tables



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PAST error bars



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PAST error bars



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Box-and-whisker plot


Histogram

Box-and-whisker plots

Davis (2002)


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PAST Box-and-whisker plot


Outlier


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Next week


Basics (3 lectures with exercises)Introduction on StatisticsData Presentation

Requirements of Data for Statistical Analysis

Elementary Statistics (6 lectures with exercises)t-tests and F-testsAnalysis of VarianceCorrelation and RegressionChi-square TestsNon-parametric TestsMultivariate ANOVA/Repeated Measures

Analysis of Multivariate Data (3 lectures with exercises)Cluster-AnalysisPrincipal Component Analysis

(Detrended) Correspondence Analysis

Time Series Analysis (1 lecture with exercises)Analysis of stationary data: Spectral AnalysisAnalysis of non-stationary data: Wavelet Analysis

Final exam

17.10.2012

24.10.2012

31.10.2012

07.11.201214.11.201221.11.201228.11.201205.12.201212.12.2012

16.01.201323.01.2013

30.01.2013

06.02.2013

13.02.2013

Statistical Data Presentation

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