Laboratory in Oceanography: Data and Methods. Intro to the Statistics Toolbox. MAR599, Spring 2009 Miles A. Sundermeyer. Intro to Statistics Toolbox Statistics Toolbox/Descriptive Statistics. Measures of Central Tendency Geometric Mean: Harmonic Mean:. Intro to Statistics Toolbox
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Intro to the Statistics Toolbox
MAR599, Spring 2009
Miles A. Sundermeyer
Statistics Toolbox/Descriptive Statistics
Statistics Toolbox/Descriptive Statistics
Statistics Toolbox/Descriptive Statistics
Examples of Skewness & Kurtosis:
Statistics Toolbox/Descriptive Statistics
Statistics Toolbox/Descriptive Statistics
Example:
Bootstrap Method for estimating uncertainty on Lagrangian Integral Time Scale (from Sundermeyer and Price, 1998)
“Integrating the LACFs using 100 days as the upper limit of the integral of Rii(t) in (12) gives the integral timescales I(11,22) = (10.6 ± 4.8, 5.4 ± 2.8) days for the (zonal, meridional) components, where uncertainties represent 95% confidence limits estimated using a bootstrap method [e.g., Press et al., 1986].”
Statistics Toolbox/Statistical Visualization
>> x = exprnd(10,100,1);
>> normplot(x)
Statistics Toolbox/Statistical Visualization
>> x = normrnd(5,1,100,1);
>> y = wblrnd(2,0.5,100,1);
>> qqplot(x,y);
Statistics Toolbox/Statistical Visualization
Statistics Toolbox/Probability Distributions/Supported Distributions
Statistics Toolbox/Probability Distributions/Supported Distributions
Supported distributions (cont’d)
Statistics Toolbox/Probability Distributions/Supported Distributions
Supported statistics
Statistics Toolbox/Hypothesis Tests
Statistics Toolbox/Hypothesis Tests
http://www.stats4students.com/Essentials/StandardScore/Overview.phphttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Intro to Statistics Toolbox
Statistics Toolbox/Hypothesis Tests
http://www.stats4students.com/Essentials/StandardScore/Overview.phphttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Intro to Statistics Toolbox
Statistics Toolbox/Hypothesis Tests
http://www.socialresearchmethods.net/kb/stat_t.phphttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Intro to Statistics Toolbox
Statistics Toolbox/Hypothesis Tests
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Hypothesis Tests
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Twoway ANOVA
Example: Determine effect of car model and factory on the mileage rating of cars.
There are three models (columns) and two factories (rows). Data from first factory is in first three rows, data from second factory is in last three rows. Do some cars have different mileage than others?
>> load mileage
mileage =
33.3000 34.5000 37.4000
33.4000 34.8000 36.8000
32.9000 33.8000 37.6000
32.6000 33.4000 36.6000
32.5000 33.7000 37.0000
33.0000 33.9000 36.7000
>> cars = 3;
>> [p,tbl,stats] = anova2(mileage,cars);[p,tbl,stats] = anova1(hogg);
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Analysis of Variance
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Regression Analysis
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Regression Analysis
Example (system of equations):
Suppose we have a series of measurements of stream discharge and stage, measured at n different times.
time (day) = [0 14 28 42 56 70]
stage (m) = [0.612 0.647 0.580 0.629 0.688 0.583]
discharge (m3/s) = [0.330 0.395 0.241 0.338 0.531 0.279]
Suppose we now wish to fit a rating curve to these measurements. Let x = stage, y = discharge, then we can write this series of measurements as:
yi = mxi + b, with i = 1:n.
This in turn can be written as: y = Xb, or:
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Regression Analysis
yi = mxi + b
y = Xb
Intro to Statistics Toolboxhttp://www.stats4students.com/Essentials/StandardScore/Overview.php
Statistics Toolbox/Regression Analysis
Note: Tidal Harmonics can cause tidal cycle to appear asymmetric.
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1
40

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100
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10
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24
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m
e
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h
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1
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40
PSD (cm s–1)2
0.1
80
0.01
0.001
0.0001
1
10
100
1000
cycles day1
www.soes.soton.ac.uk/teaching/courses/oa311/tides_3.ppt
Intro to Statistics Toolbox
Statistics Toolbox/Regression Analysis
Example: Harmonic analysis (cont’d)
Southampton Surface Currents:
Harmonic analysis for M2, M4=2xM2, M6=3xM2 ...
Intro to Statistics Toolbox asymmetric.
Statistics Toolbox/Regression Analysis
Data Handling Matlab asymmetric.
Useful Tidbits …