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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 2
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 3
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 4
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 5
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 6
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 7
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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22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 8
Data Presentation
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Introduction on data presentation
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 9
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 13
1
2
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PAST histogram
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 14
1
2
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Line graph
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 15
Changes in mean stomatal conductance of two tree species over the course of a day
Townend (2002)
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Line graph
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 16
Mean concentrations of insecticide at different distances from fish cages at a fish farm
Townend (2002)
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PAST Line graph
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 17
1
2
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Scatter graph
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 18
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 19
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 20Townend (2002)
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PAST Scatter graph
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 21
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 23
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 24
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
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 25
Tree
height(m)
Townend (2002)
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Standard error and error bars in tables
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 26Townend (2002)
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PAST error bars
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 27
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PAST error bars
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 28
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Box-and-whisker plot
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 29
Histogram
Box-and-whisker plots
Davis (2002)
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PAST Box-and-whisker plot
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 30
Outlier
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Next week
22. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 31
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