Laboratory in Oceanography: Data and Methods

1. Laboratory in Oceanography: Data and Methods Computing Basic Statistics MAR550, Spring 2013 Miles A. Sundermeyer

2. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/stats/

3. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/stats/

4. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/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/toolbox/stats/

6. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/stats/

7. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/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/toolbox/stats/

9. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/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/toolbox/stats/

11. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/stats/

12. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/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 − σ) and (x + σ) • 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/toolbox/stats/

14. Computing Basic Statistics see also: http://www.mathworks.com/access/helpdesk/help/toolbox/stats/

15. Computing Basic Statistics Useful Tidbits … • Useful Tidbits • if <expression> statements • elseif <expression> • statements • else • statements • end e.g., n=rand(1) if (n>0.5) disp('heads') elseif (n<0.5) disp('tails') else disp('neither!') end

16. Computing Basic Statistics Useful Tidbits … • Useful Tidbits • while <expression> statements • end e.g., n=rand(1) while n>0.5 if (n>0.5) disp('heads') elseif (n<0.5) disp('tails') else disp('neither!') break end n=rand(1) end

17. Computing Basic Statistics Useful Tidbits … Gaussian Distribution

18. Computing Basic Statistics Useful Tidbits … Random Walk in 2-D