Introduction to PAST Statistcs
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Transcript of Introduction to PAST Statistcs
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8/13/2019 Introduction to PAST Statistcs
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Structure
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 2
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 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
17.10.201224.10.201231.10.2012
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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PAST Software
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 3
http://folk.uio.no/ohammer/past/index.htmlor Google: PAST Hammer
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Statistics - Definition
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 4
Statistics is the science of making effective use of numerical data relatingto groups of individuals or experiments. It deals with all aspects of this,including not only the collection, analysis and interpretation of such data,
but also the planning of the collection of data, in terms of the design ofsurveys and experiments. Classical statistical methods are methodswhich are concerned with the analysis of empirical (i.e. observed,measured) data.(Dodge 2003: The Oxford Dictionary of Statistical Terms)
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Statistics Definition II
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 5
We use Statistics to draw conclusions about very large groups of individuals(animate or inanimate) when we can only study small samples of them!
The questions we are trying to answer:
1. If I assume that the sample of individuals I have studied is representativeof the group they come from, what can I tell about the group as a whole?
2. How confident can I be that the sample of individuals I have studied was
like the group as a whole?
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Measures of Location: Mean - Median - Mode
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 8Davis (2002)
The mode is the value that occurswith the greatest frequency.
The median is the value midwayin the frequency distribution.
The mean is another word for thearithmetic average
What is a typical member of a population?
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Measures of Location: Mean Median - Mode
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 9
Mean:
Median:
Mode:
Data values: 8-12-10-7-7-11-8
Sum: 63
Mean: 63/7 = 9
n: 7
Data values: 7-7-8-8-10-11-12
Sum: 63
Median = 8
n: 7
The mode is the value that occurs with the greatest frequency.
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Measures of Spread:
Variance Standard deviation
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 10Davis (2002)
How spread out are the values around the typical member of a population?
Texas oil field
Oklahomaoil field
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Measures of shape: coefficient of variation
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 12
The dispersion in a variable is sometimes given by the coefficientof variation (CV), which is a dimensionless measure of variability
expressed as a fraction of the mean.
CV =standard deviation
mean
Example:Ants standard deviation = 3 mm, mean length = 10 mm
Dogs standard deviation = 20 cm, mean length = 100 cm
Are ants or dogs more variable in their length?
CVants = 3/10 = 0.3 = 30% CVdogs = 20/100 = 0.2 = 20%
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Measures of shape: coefficient of skewness
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 13
http://www.statistics4u.info/fundstat_eng/cc_skewness.html
positively skewed:long tail of high values
to the right
negatively skewed:long tail of small values
to the left
skewness close to zero:histogram is approximately
symmetric
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Measures of shape: Kurtosis
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 14
http://www.statistics4u.info/fundstat_eng/cc_kurtosis.html
y > 0
y < 0
normal distribution y = 0
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Summary Statistics
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 15
Measures of location:
Measures of spread:
Measures of shape:
MeanMedian
Mode
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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Standard error and 95% confidence interval
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 17Townend (2002)
Temperature interval: 14.5 16 C
Population mean: 15.2 C
Margin of error: 16 - 15.2 C= 0.8 C
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Standard error and 95% confidence interval
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 18Townend (2002)
s.d. standard deviation
frequency distributionfor a population
frequency distributionfor the means of samples
of 5 individuals
frequency distributionfor the means of samples
of 10 individuals
standard deviation of sample means standard error
standarderror
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Standard error and 95% confidence interval
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 19
Example:
There is approximately a 68% change that the true population mean lies in the range9.0 +/- 0.76 = between 8.24 and 9.76
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Difference between
standard deviationand standard error
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 20
Standard deviation:Standard deviation is a measure of how much deviation there is betweenindividuals in a population.
Standard error:Standard error is a measure of the margin of error involved in estimatingthe mean of a population.
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PAST
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 21
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PAST Univariate Statistics
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 22
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3
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Next week
15. Oktober 2012 | Fachbereich 11 | Angewandte Geowissenschaften | Dr. Olaf Lenz | 23
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
17.10.201224.10.2012
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