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 (and export it as well)
(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)
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
(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)
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
(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
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
(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
(all repeated measures ANOVAs from http://www.mathworks.com/matlabcentral/fileexchange)
•
Post-hoc contrasts: multcompare, grpstats
•
Comparing two independent measures:
ttest2, ranksum
Comparing two dependent variables:
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 from many distributions
•
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/