introduction to past statistcs

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


http://folk.uio.no/ohammer/past/index.htmlor Google: PAST Hammer


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Statistics - Definition


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


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


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


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


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


http://www.statistics4u.info/fundstat_eng/cc_kurtosis.html

y > 0

y < 0

normal distribution y = 0


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Summary Statistics


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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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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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


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



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PAST Univariate Statistics


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2

3


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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

17.10.201224.10.2012

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

introduction to past statistcs

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