Laboratory in Oceanography: Data and Methods

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Laboratory in Oceanography Data and Methods
Computing Basic Statistics

• MAR599, Spring 2009
• Miles A. Sundermeyer

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Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
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Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
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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/
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Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
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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))

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Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
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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/
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Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
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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.

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Computing Basic Statistics see also
http//www.mathworks.com/access/helpdesk/help/tool
box/stats/
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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
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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
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Computing Basic Statistics Useful Tidbits
Gaussian Distribution