Data analysis in MATLAB

Data analysis in MATLAB Christian Ruff

Why use MATLAB to analyse data? • One single programme can be used for: • importing single-subject data from any format • re-arranging for multi-subject analyses • statistical tests • plotting results  Errors are less likely  One single script for analysis and documentation  This can even be used by your experimental COGENT-script (online-analysis)  Ultimately, MATLAB is **much** more flexible than SPSS or EXCEL, especially for graphs • Nuisances: • some details of SPSS procedures not available (but on the web) • Use not as intuitive as SPSS buttons, but help<functionname> and doc <functionname>

Outline • How to: (1) Import single-subject data from any format (2) Inspect single-subject data for distribution / outliers etc. (3) Re-arrange data for multi-subject analyses (4) Perform statistical tests  all as steps in one single script

(1) Importing data: Reading in files • MATLAB can read in many different types of files, using different functions • These can be listed with help fileformats • Examples are: • xlsread:EXCEL data • dlmread:tab-delimited text (or any other form of delimited text, e.g., whitespace) • csvread: comma-separated numbers • textread: any mixture of text and numbers • importdata:any formatted data as a full file (looks for the most appropriate function to use) • fopen/fread: any formatted data by line, but need extensive user specification of format • help<functionname> and doc <functionname> give instructions and examples • MATLAB can also be used to save data in the corresponding formats (e.g., dlmwrite, csvwrite, fopen/fwrite/fprintf)

(1) Importing data: Types of variables • Data can be stored in files in very different formats (see e.g. different field-types in excel-sheets) • Three elementary formats are: • Strings: characters (such as letters), cannot be (sensibly) manipulated numerically e.g., variable names or condition descriptions example_string = ‘123.456’; • Double: used for numbers, can be numerically manipulated Doubles are not stored element-by-element, but as wholes example_number = 123.456; • Logicals: used for boolean logic, so can take only the value 0 (false) and 1 (true) can be numerically manipulated, but does not make sense often used for indexing example_logical = logical(123.456);

(1) Importing data: Variable conversion • Raw data files often contain mixtures of strings and numbers • Numerical values are often represented as strings in imported data • After importing data into a variable in MATLAB, the format of each variable can be seen by typing whos<variable_name> (<variable_name>), or tested with isnumeric,ischar, or islogical • The Matlab workspace contains an array editor that is similar to Excel • Strings can be converted into doubles by the commands double or str2num, thisturns numbers in “text format” into numbers that you can do computations with e.g. example_number = double(example_string); • Doubles can be converted into strings by the command char or num2str;this makes it possible to include numbers in text that you want to write into a file e.g. example_string = char(example_string);

(1) Importing data: Variable formats • Relevant variable formats include: • Matrices: - contain m( x n x o…) elements, can be accessed by row or column - all elements in a matrix are forced to be in the same format  matrices are well suited for storing numbers  matrices are not ideal for strings (of different lengths e.g. words) • Cells: - contain m( x n x o…) elements, can only be accessed element-by-element - each element can be of different format and length  well suited for storing string variables, and mixtures of variables  not ideal for storing only number variables that have to be accessed and manipulated as a group (e.g., by row and column)

(1) Importing data: Variable formats • Relevant variable formats include: • Structures: - contain m( x n x o…) elements that all have several fields - each field in any element can contain any variable (e.g., string, numerical) in any format (e.g., cell, matrices…) - the fields of different elements can easily be combined if they have the same format  well suited for different variables that are nevertheless linked (e.g., data from different subjects)  not ideal for storing only number variables that have to be accessed and manipulated as a group (e.g., by row and column)  easy to combine one field of different elements into a matrix (e.g., different trials)  see strucdem

(1) Importing data: Transforming variables • Arrays / cells / structures can easily be converted into each other: • Numerical array to cell: num2cell or mat2cell  cell2mat • String array to cell: cellstr  char • Structure to array: struct2array  struct • Structure to cell: struct2cell  cell2struct • Arrays / cells / structures can be appended or combined • Numerical arrays: [123;456] or cat • String array: strvcat or strcat • Cells: cat • Structures: cat  If the dimensions of the to-be-combined variables are known, then all of these operations can also be performed simply by indexing (e.g. num3(1,:) = num1; num3(2,:) = num2;)

(2) Inspecting data: Descriptive statistics • Descriptive statistics: mean, median, min, max, prctile,range, var, std, skewness, kurtosis, cdfplot - many of these also work for data with missing values, by appending “nan”(e.g., nanmean) • Visualisation of distribution: - Histogram: hist, also available with superimposed normal distribution: histfit - Test for normal distribution: - visually with normplot - statistically with lillietest (when testing for normality), kstest (when testing for any distribution) or kstest2 (when testing for identity of distributions of two or more variables) - Scatterplot of two variables: scatter, also available for several variables: plotmatrix - Lineplot of data against one dimension (e.g., time): plot, or two dimensions: plot3 - visual check for outliers: boxplot (or check for impact of outliers with trimmean)

(3) Transforming data for multi-subject analyses Matrices are by far the most convenient data format for statistical analyses: • Most descriptive-statistics commands work on dimensions of matrices e.g., mean(matrix,1)over rows, mean(matrix,2) over columns, etc. • Matrices can easily be indexed with logicals e.g., rows = (matrix(:,2)==1);data(:,1) = matrix(rows,:); • Condition indices can easily be created as matrices e.g., data(:,[2:3]) = fullfact([2 12]); • Matrices can be easily transformed with • Sort and sortrows  to sort data • flipud, fliplr, flipdim, rot90  to flip dimensions • reshape  to change dimensions • squeeze to remove dimensions • shiftdim, circshift to shift dimensions

(4) Statistics: mean comparison The MATLAB statistics toolbox contains functions for many (non-)parametric tests (help stats) These ask for data in different input formats (help <functionname> and doc <functionname> They give out all relevant statistics as variables, and/or as tables (if displayopt = ‘on’) • Comparing several independent measures:anova1, anova2, anovan, manova1, kruskalwallis • Comparing several dependent (or mixed) measures:rmaov1, rmaov2, bwoav2, rmaov31, rmaov32, rmaov33, friedman, epsGG, epsHF (all repeated measures ANOVAs from http://www.mathworks.com/matlabcentral/fileexchange) • Post-hoc contrasts: multcompare, grpstats • Comparing two independent measures: Comparing two dependent variables: ttest2, ranksum ttest, signtest, signrank

(4) Statistics: association/ dimension reduction • Bivariate associations: • correlation: corrcoef • linear regression: regress or robustfit(weighted to minimise impact of outliers) • nonlinear regression (e.g. logistic regression): nlinfit • Multivariate associations: • Canoncorr, manova1, mdscale, classify, cluster • Dimension reduction: • princomp, factoran • Bootstrapping is available: Bootstrp

(4) Statistics: many other useful things • The statistics toolbox contains functions for many statistical distributions (beta, binomial, exponential, gamma, poisson, weibull…): • Fits • Cumulative and probability density functions and their inverses • random number generation • Efficient design of factorial experiments (e.g. Fullfact; randn) • Advanced statistical methods are either implemented (e.g., hidden Markov Models, decision trees) or can be found on the web: • http://www.statsci.org/matlab • http://www.mathworks.com/matlabcentral/fileexchange • If you want to know more, look at the excellent MATLAB documentation at: • http://www.mathworks.com/access/helpdesk/help/techdoc/

Data analysis in MATLAB