Descriptive Statistics - Lecture Slides | BINF 702, Study notes of Bioinformatics

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         !"# !)!"!'- -)6""%-6%" 8 ,))(&!" '*%9 > negexpdata = -rexp(1000) > hist(negexpdata, nclass = 20) > points(mean(negexpdata), 0, pch = 'o') > points(median(negexpdata ), 0, pch = '*') Section 2.2 — Comparison of the Arithmetic Mean and the Median (All | Three Distributions) Histogram of symmdata Histogram of expdata Histogram of negexpdata 8 zo & o { a eS 2 4 0 1 97 3 4 ;° ° “ : 7 soe symmdata BINF702 - FALLO8- SOLKA - CHAPTER 2 Descriptive Statistics 
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         #> !)!!'- -) 6"8'!' *".9 Eq. 2.2 - If , 1, , then . i iy cx i n y cx = = =
> x = rnorm(1000) > mean(x) [1] 0.02741812 > mean(2*x) [1] 0.05483624
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2 1 2 a constant then . c y c x c= + > x = rnorm(1000) > mean(x) [1] 0.02741812 > mean(2*x+5) [1] 5.054836 2.4 — Measures of Spread = These two datasets have the same mean = c(rep(10, 10)) = C(rep(0,9),100) = Are they the same? BINF702 - FALLO8- SOLKA - CHAPTER 2 Descriptive Statistics 
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         #C 6&!' %8-;" "% "%%!"9 ( ) ( ) 2 2 1 2 1 Def. 2.7 - The sample variance, or variance , is defined as follows: 1 Def. 2.8 - The sample standard deviation, or standard deviation, is defined as follows: 1 N i I n i i x x S n x x s n = = − = − − = −


         #@ !)!!'-;""% "%%!"8'!' *".9 1 1 2 2 2 2 2 Eq. 2.6 Suppose there are two samples , , and y , , were , 1, , , 0 If the respective sample variances of the two samples are denoted by and Then ; n n i i x y y x y x x x y y cx i n c s s s c s s cs = = > = =



         #= -!'"!';!" Def. 2.9 The coefficient of variation (CV) is defined by 100%* s x      
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!"H*&*;'!(*0&-)&0+- -%'"!"!'2!!)+-(,# http://www.graphpad.com/articles/interpret/Analyzing_one_group/descr_stats.htm 2.6 — The Coefficient of Variation and R = There is no COV implemented in R but it would be trivial to implement one. BINF702 - FALLO8- SOLKA - CHAPTER 2 Descriptive Statistics 
         #:!&%"8-9  Arguments: x: a vector of values for which the histogram is desired. breaks: one of: * a vector giving the breakpoints between histogram cells, * a single number giving the number of cells for the histogram, * a character string naming an algorithm to compute the number of cells (see Details), * a function to compute the number of cells. In the last three cases the number is a suggestion only.
         #:!&%"8-9  freq: logical; if 'TRUE', the histogram graphic is a representation of frequencies, the 'counts' component of the result; if 'FALSE', probability densities, component 'density', are plotted (so that the histogram has a total area of one). Defaults to 'TRUE' _iff_ 'breaks' are equidistant (and 'probability' is not specified). probability: an _alias_ for '!freq', for S compatibility. include.lowest: logical; if 'TRUE', an 'x[i]' equal to the 'breaks' value will be included in the first (or last, for 'right = FALSE') bar. This will be ignored (with a warning) unless 'breaks' is a vector. right: logical; if 'TRUE', the histograms cells are right-closed (left open) intervals.
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         #:!&%"8-9 ; The definition of "histogram" differs by source (with country-specific biases). R's default with equi-spaced breaks (also the default) is to plot the counts in the cells defined by 'breaks'. Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area _provided_ the breaks are equally-spaced. The default with non-equi-spaced breaks is to give a plot of area one, in which the _area_ of the rectangles is the fraction of the data points falling in the cells. If 'right = TRUE' (default), the histogram cells are intervals of the form '(a, b]', i.e., they include their right-hand endpoint, but not their left one, with the exception of the first cell when 'include.lowest' is 'TRUE'.
         #:!&%"8-9 ; For 'right = FALSE', the intervals are of the form '[a, b)', and 'include.lowest' really has the meaning of "_include highest_". A numerical tolerance of 1e-7 times the median bin size is applied when counting entries on the edges of bins. The default for 'breaks' is '"Sturges"': see 'nclass.Sturges'. Other names for which algorithms are supplied are '"Scott"' and '"FD"' / '"Friedman-Diaconis"' (with corresponding functions 'nclass.scott' and 'nclass.FD'). Case is ignored and partial matching is used. Alternatively, a function can be supplied which will compute the intended number of breaks as a function of 'x'.
         #:!&%"8-9 K8*&9 an object of class '"histogram"' which is a list with components: breaks: the n+1 cell boundaries (= 'breaks' if that was a vector). counts: n integers; for each cell, the number of 'x[]' inside. density: values f^(x[i]), as estimated density values. If 'all(diff(breaks) == 1)', they are the relative frequencies 'counts/n' and in general satisfy sum[i; f^(x[i]) (b[i+1]-b[i])] = 1, where b[i] = 'breaks[i]'.
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