Research Methodology and Statistic Chapter 9: Data processing (Scilab) Dr. Supakit Nootyaskool IT-KMITL

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1 9 Research Methodology and Statistic Chapter 9: Data processing (Scilab) Dr. Supakit Nootyaskool IT-KMITL

2 Topics Introducing Scilab variables, vector, matrix arithmetic and logic operator comparators and condition loops simple plot graph simple statistic writing Scilab script

3 What is Scilab Open source (GPL) Cross-platform (Mac/Win) computational package Numerically oriented programming language It can be used for Image/signal processing Statistical analysis Numerical optimization It can run on Matlab code

4 Download:

5 Select full installation

6 Update module & Convert M-File to Scilab

7 Console Variable Command history

8 1. Variable, Vector, Matrix 1x1 [10] 1x3 [ ] 3x x [10; 20; 30] [ ; ]

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10 2. access elements in a matrix or a vector -->a = [1 2 3; 4 5 6; 7 8 9] a =

11 Some variable beep() %pi %inf //produce a beep sound //floating point number of pi //infinity

12 3. Arithmetic operations -->a+3 ans = >a-2 -->a*2 -->a/2 -->a.^2 -->a^2 -->a*a -->a.^2 ans = >a^2 ans =

13 -->a -->a' ans = >a = [1 2 3; 4 5 6; 7 8 9] -->b = [1 1 1; 2 2 2; 3 3 3] -->a*b -->a.*b

14 4. Help (F1)

15 --> [t,a] = meshgrid(0.1:.01:2, 0.1:0.5:7); -->f=2; -->pi = %pi -->Z = 10.*exp(-a.*0.4).*sin(2*pi.*t.*f); -->surf(z);

16 5. Clearing variable All variable clearing ---> clear Individual variable clearing ---> a = > b = > clear a Command console clearing ---> clc Graph clearing ---> clf

17 6. Display or Not display data After typing some command without putting ; (semicolon), the program will display output immediately. ---> a = 10; ---> a = 10 a = 10

18 7. Loop Loop uses : operator to define sequence of number generating Example Create 1 to 10 increasing 1 ---> 1:10 Create 1 to 10 increasing 2 ---> 1:2:10 Crate to 1000 increasing 0.5 and assign to A ---> a = -1000:0.5:1000;

19 Loop: For for commands statements end; Example: Display hello world 10 times ---> for n=1:10 ---> disp( hello world ); ---> end;

20 Loop: While while condition statements end; The condition being true will be stop the loop. Example: Display hello world 10 times n=0; while n<10 disp( hello world ); n=n+1; end;

21 8. Comparison operators == Equal <> Different (Not equal) < Less then > Greater than &T True &F False & And Or ~ Not <= Less or equal >= Grate or equal

22 Example Comparison between X and Y ---> x = [1 2 3 ] ---> y = [3 4 3] ---> x == y Ans = F F T

23 Condition: If if condition Statements then Statements end; Example: Display hello world 10 times ---> if x(1) == y(1) ---> disp( SameValue ); ---> else ---> disp( NotSameValue ); ---> end;

24 9. 2-D and 3-D plots Line color decide by using r =red, g =green, c =cyan, m =magenta, y =yellow, w =white Plot styles., +, o, x, * Example: plot(x,y, option) ---> plot(1,2, xr )

25 Do you know number of row or column in the variable? ---> size(a) //return No.row x No.col Ans > size(a,'r') //return number of row ---> size(a,'c') //return number of column ---> size(a') Ans 30 1

26 Example: Graph plotting ---> plot([1,3], [2,5], r ) Clear graph ---> clf

27 Statistic Measures of central tendency Measures of variation Type of distributions Z-Score T-Score Measure of relationship

28 Statistic Measures of central tendency Z-Score Measures of variation Mean Median Mode Measure of relationship Type of distributions

29 10. Mean mean(var, option) option: r = row, c =column ---> a = [ ; ; ]; ---> mean(a); ---> mean(a, r ); ---> mean(a, c ); Excel: average (cell)

30 11. Median median(var, option) option: r = row, c =column ---> a = [ ; ; ]; ---> median(a); ---> median(a, r ); ---> median(a, c ); Excel: median(cell)

31 12. Mode f = nfreq(var) [num,i] = max( f(:,2) ) // num=maxvalue, i=position modev = f(i,1) ---> a = [ ]; --->f = nfreq(a); ---> [m,n] = max(a, r ); ---> median(a, c ); Excel: median(cell) Matlab mode(a)

32 -->a = [ ]; -->f = nfreq(a) f = -->modev= f(n,1) modev = >[num,i]= max(f(:,2)) i = 4. num = Observing Number of value 7. Mode value 5.

33 Creating my_mode function 1) Open scinote selecting from menu Applications->SciNotes 2) Writing code from this example function [modev,num] = my_mode(arr) f = nfreq(arr) //freq [num,i] = max( f(:,2) ) // num=maxvalue, i=position modev = f(i,1) endfunction 3) Save to a directory in the name of myfunc.sci 4) Run command exec( myfunc.sci ); 5) Test function a = [ ]; [x,y] = my_mode(a);

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35 Statistic Measures of central tendency Measures of variation Type of distributions Z-Score T-Score Measure of relationship Range Standard derivation

36 Measure of variation? A measure of variation indicates the degree to which scores are either cluster or spread out in distribution. For example Class A=[0, 50, 100] mean(a) = 50 Class B = [45, 50, 50] mean(b) = 50 Both of the A and B, the mean value showed the same distribution.

37 13. Range r = max(arr) min(arr) ---> a = [ ]; --->r = max(a) min(a) Excel: max(cell)-min(cell) Matlab range(a)

38 14. Average Deviation (AD) u=mean(x) sum( abs(x-u) ) / length(x) ---> X = [ ]; ---> u = mean(x) --->s = sum(abs(x-u)) --->s/length(x) Excel: -- Matlab --

39 15. Standard Deviation (SD) stdev(arr) ---> X = [ ]; ---> u = mean(x) --->s = sum((x-u)^2) --->sqrt(s/ length(x)) Excel: stdev(cell) Matlab stdev(a)

40 Statistic Measures of central tendency Measures of variation Type of distributions T-Score Z-Score Z-Score Measure of relationship

41 Distribution graphs Uniform distribution The graph show the constant value by each data same height. Normal distribution (Gaussian distribution) left side and right side are equally Sum of mean, median and mode value are closely. Lepokuritc distribution Specific of graph is very tall The most data close at the mean Patykurtic distribution Specific at top of graph small curve The data are distributed

42 Skewed distribution Example of score from student examination The positive skewed distribution Most student have high score. The negative skewed distribution A few student people have high score.

43 Z-score & T-Score Z = (x-x )/sd Summarize all data Mean = 0 SD = 1 Below mean Over mean T = 10Z + 50 Summarize all data Mean = 50 SD = 10

44 Calculate Z-score and T-score x = [ ]; xbar = mean(x); z_score = (x-xbar)/stdev(x); t_score = 10*z + 50

45 Histogram plotting Plotting histogram from example data by cutting 10 sections w = [ ] histplot(10,w,normalization=%f)

46 Measures of central tendency Statistic Pearson correlation Spearman correlation Relationship graphs Measures of variation Type of distributions Z-Score T-Score Measure of relationship

47 16.Pearson correlation Pearson-Moment correlation coefficient used measuring correlation of two variables. Example comparison between height and weight data.

48 --->h = [ ] ---> w = [ ] ---> plot(w,h, x )

49 16. Pearson Correlation No small setting correlation function in SciLab However, we can create from basic commands Excel: correl(cell1,cell2) Matlab corr2(x,y)

50 Code: Pearson correlation ' Pearson Correlation function r = my_corr (x,y) xbar = mean(x); ybar = mean(y); xx = x-xbar; yy = y-ybar; sxx = sum(xx^2); syy = sum(yy^2); sxy = sum(xx.* yy); r = sxy/sqrt(sxx*syy); endfunction

51 Spearman Correlation x y Rank1 Rank

52 Spearman Correlation x y Rank1 Rank If two or more data is the same value, apply the mean value X Rank Example 2+3/2 =

53 Spearman Correlation x y Rank1 Rank

54 Spearman Correlation x y Rank1 Rank2 D R1-R2} D^ Sum of D^2 = = 6 Calculate = -0.5

55 Code: Spearman correlation function r = my_spearman(x,y) [ix,kx] = gsort(x); [iy,ky] = gsort(y); d = abs(kx-ky); s = sum(d^2); n = length(x) r = 1 - ( (6*s)/(n*(n^2-1))) endfunction

56 Summary