### Data analysis tools

- Basic statistics
- Averages and variability:

`x=randn(20,1);`

mean(x)

median(x)

mode(x)

std(x)

var(x)

- T-tests
- Paired:

`[h, p, ci, stats] = ttest(x – y) or ttest(x)`

- Unpaired:

`[h, p, ci, stats] = ttest2(x, y)`

- ANOVA
- One-way:

`[p, table, stats] = anova1(x)`

- Where x is a matrix with each column = a group

- Two-way:

`[p, table, stats] = anova2(x)`

- Where x is a matrix with each columns = factor1 and rows = factor2

- N-way:

`anovan.m`

- Repeated measures and mixed ANOVAs (not built in)

`RMAOV1.m, RMAOV2.m, RMAOV31.m, RMAOV32.m, RMAOV33.m, BWAOV2.m (between & within factors)`

- Correlations and regression
`[r p] = corr(x, y)`

(x and y must be column vectors)

`[b, bint, r, rint, stats] = regress(y, x)`

(y is a column vector and x is a matrix of column vectors = predictors)

`stepwise(x, y)`

produces an interactive figure for stepwise regression (x is a matrix of column vectors, y is a column vector)

`p = polyfit(x, y, n)`

where x and y are column vectors, n is the degree of polynomial (1=line); returns vector of coefficients corresponding to x^n, x^(n-1), …, x, 1.

### Additional analysis tools

- Principal components analysis

`[coeff, score, latent, tsquare] = princomp(x)`

### Basic plotting tools

- Scatterplots and line plots:

`x = rand(10,1); y = rand(size(x));`

plot(x, y);

plot(x, y, ‘g*-’, ‘linewidth’,4)

plot(x, y, ‘ro‘);

ye = .2*rand(size(x));

errorbar(x, y, ye, ‘.’)

- Bar graphs:

`bar(y)`

- 3D plots:

`x = rand(10,1); y = rand(size(x)); z = rand(size(x));`

plot3(x, y, z,’*’);

m = rand(5,5);

bar3(m)

- Adding text, titles, and labels:

`text(.3, .3, ‘Hello’, ‘fontsize’, 16);`

xlabel(‘Whatever’);

ylabel(‘Something else’)

title(‘Anything’,’fontsize’,20)

- Modifying axis properties:

`errorbar(x, y, ye, ‘.’)`

axis([-1 3 -1 3]);

axis equal

axis off

box off

set(gca, ‘xtick’, [.1:.2:30])

set(gca,’xticklabel’, [1:6:400])