## 1 Stats Intro

```%Creating a probability distribution
m=linspace(-5,10,50);
Mu=2
Sigma=1.5
p=normpdf(m,Mu,Sigma)
plot(p)

%Creating a cumulative probability distribution
P=normcdf(m,Mu,Sigma)
plot(P)

%Random values from multivariate normal distribution
Mu=[0 0]
Sigma=[1  0; ...
0  1];
[p]=mvnrand(Mu,Sigma)
p=mvnrnd(Mu,Sigma,10000);
plot(p(:,1),p(:,2),'+')

%Multivariate normal pdf
m=linspace(-5,5,50);
nM=length(m);
[M1,M2]=meshgrid(m);
p=mvnpdf([M1(:) M2(:)],Mu,Sigma);
p=reshape(p,nM,nM);

figure(938)
subplot(1,2,1)
imagesc(p)
axis square

subplot(1,2,2)
surf(p)
colormap summer
```

## 2 Statistics

### 2.1 Basic

zscore sampsizepwer

### 2.2 Hypothesis testing

#### 2.2.1 chi-GOF

hypothesis: data fits a normal distribution (nothing known) Is a normal distribution a good model for my data to begin with?

chigof

#### 2.2.2 z-test

ztest hypothesis: sample comes from a normal distribution known mean and variance

#### 2.2.3 T-test

ttest hypothesis: sample comes from a normal distribution known mean

ttest2 hypothesis: two samples are normal and have same means (nothing known)

#### 2.2.4 Non-normal (Wilcoxon)

signrank hypothesis: sample comes from some distribution known median

ranksum hypothesis: two samples have the same medians (nothing known)

#### 2.2.5 Chi-var-test

vartest hypothesis: sample comes from a normal distribution known variance

#### 2.2.6 F-test

vartest2 hypothesis: two samples have the same variance (nothing known)

vartestn: n samples

#### 2.2.7 ANOVA

hypothesis: samples come from the same populations with same means hypothesis: differences between group1 and group2 have impact on observations

anova1 1 factor

anova2: 2 factor anovan: n factors

#### 2.2.8 ANOCOVA

Just do regression

### 2.3 Correlation

corr xcorr xcorr2 xcorr2n cov partialcorr

### 2.4 Linear Regression

regress mvregress fitlm fitrlinear lasso ridge plsregress LinearModel

### 2.7 Machine learning

kmeans

Created: 2020-07-25 Sat 14:04