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Laboratory in Oceanography: Data and Methods

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min, max - absolute minimum and maximum values of data (see also nanmin, nanmax) mean ... Noteworthy features of Gaussian distributions. symmetry about its mean ... – PowerPoint PPT presentation

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Title: Laboratory in Oceanography: Data and Methods


1
Laboratory in Oceanography Data and Methods
Computing Basic Statistics
  • MAR599, Spring 2009
  • Miles A. Sundermeyer

2
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
3
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
4
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
  • Basic Statistics
  • Let
  • min, max - absolute minimum and maximum values of
    data
  • (see also nanmin, nanmax)
  • mean -
  • median - the value separating the higher half of
    a sample population, or
  • probability distribution, and the lower
    half
  • mode - the value that has the largest number of
    observations
  • Note The mode function is most useful with
    discrete or coarsely rounded data. The mode for
    a continuous probability distribution is defined
    as the peak of its density function. Application
    to a sample from such a distribution is unlikely
    to provide a good estimate of the peak it would
    be better to compute a histogram or density
    estimate and calculate the peak of that estimate.
    Also, the mode function is not suitable for
    finding peaks in distributions with multiple
    modes.

5
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
6
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
7
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
  • Variance and Standard Deviation
  • var - variance of a
  • Note The above calculation of variance is
    biased low for unbiased variance, must normalize
    by (n-1). By default, Matlab computes the
    unbiased variance, i.e.,
  • std - standard deviation of a sqrt(var(a))

8
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
9
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
  • Percentiles
  • prctile - Percentile (or centile) is the value of
    a variable below which a certain percent of
    observations fall e.g., the 20th percentile is
    the value (or score) below which 20 percent
    of the observations may be found.
  • cdfplot - Plots the cumulative distribution
    function (CDF) of the observations in the
    data sample vector.

10
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
11
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
12
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
  • Normality
  • Gaussian - Gaussian or Normal distribution is the
    probability distribution function given by
  • Noteworthy features of Gaussian distributions
  • symmetry about its mean
  • the mode and median both equal the mean
  • the inflection points of the distribution curve
    occur one standard deviation away from the mean,
    i.e. at (x - s) and (x  s)
  • Exist numerous tests for normality, e.g.,
    Lilliefors, Kolmogorov-Smirnov, Jarque-Bera, and
    others. Also many more general tests for
    comparing distributions.

13
Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
14
Computing Basic Statistics Useful Tidbits
  • Useful Tidbits
  • if ltexpressiongt statements
  • elseif ltexpressiongt
  • statements
  • else
  • statements
  • end

e.g., nrand(1) if (ngt0.5) disp('heads') else
if (nlt0.5) disp('tails') else disp('neither!'
) end
15
Computing Basic Statistics Useful Tidbits
  • Useful Tidbits
  • while ltexpressiongt statements
  • end

e.g., nrand(1) while ngt0.5 if
(ngt0.5) disp('heads') elseif
(nlt0.5) disp('tails') else disp('neither!'
) break end nrand(1) end
16
Computing Basic Statistics Useful Tidbits
Gaussian Distribution
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