This page includes statistics formulas in raw LaTex code. It is painful sometimes to write a complex formula and thus I hope this page is useful for those need to write them. In case you need to find symbols in LaTex, this linked pdf could be useful.

## Latex Code for Correlation Formula

The following are the sample correlation formula and its raw LaTex code.

\[r_{xy}=\frac{\sum_{i=1}^{n}((x_i-\bar{x})(y_i-\bar{y}))}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}}\]

r_{xy}=\frac{\sum_{i=1}^{n}((x_i-\bar{x})(y_i-\bar{y}))}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}}

## Latex Code for One-Way ANOVA Formula

The following are one-way ANOVA formulas and their raw LaTex code.

ANOVA is about partitioning the variance into different parts. `Sum of Square Total (SSB) `

is the total variance of all the observations. SSB can be separated into `Sum of Squares Between (SSB)`

and `Sum of squares Error (SSE)`

.

\[SST=SSB+SSE\]

The formulas of `SSB and SSE`

are as follows.

\[SSB=\sum_{i=1}^kn_i(\bar{x_i}-\bar{x})^2\]

\[SSE=\sum_{i=1}^{k}\sum_{j=1}^{n_i}(x_{ij}-\bar{x_i})^2\]

SSB=\sum_{i=1}^kn_i(\bar{x_i}-\bar{x})^2 SSE=\sum_{i=1}^{k}\sum_{j=1}^{n_i}(x_{ij}-\bar{x_i})^2

We also need to consider the degree of freedom, which leads to mean squares, namely `Mean Square Between (MSB)`

and `Mean Square Error (MSE)`

.

\[MSB=\frac{SSB}{k-1}\]

\[MSE=\frac{SSE}{n-k}\]

MSB=\frac{SSB}{k-1} MSE=\frac{SSE}{n-k}

Finally, the F value is the ratio of `MSB`

and `MSE`

.

\[F(k-1,n-k)=\frac{MSB}{MSE}=\frac{\frac{SSB}{k-1}}{\frac{SSE}{n-k}}=\frac{\frac{\sum_{i=1}^kn_i(\bar{x_i}-\bar{x})^2}{k-1}}{\frac{\sum_{i=1}^{k}\sum_{j=1}^{n_i}(x_{ij}-\bar{x_i})^2}{n-k}}\]

F(k-1,n-k)=\frac{MSB}{MSE}=\frac{\frac{SSB}{k-1}}{\frac{SSE}{n-k}}=\frac{\frac{\sum_{i=1}^kn_i(\bar{x_i}-\bar{x})^2}{k-1}}{\frac{\sum_{i=1}^{k}\sum_{j=1}^{n_i}(x_{ij}-\bar{x_i})^2}{n-k}}