corrected some pages

Several small mistakes/errors were corrected in several proofs/definitions.

Author: JoramSoch

D/iass.md

@@ -35,11 +35,11 @@ $$
 
 Then, the interaction sum of squares is defined as the [explained sum of squares] (ESS) for each interaction, i.e. as the sum of squared deviations of the average for each cell from the average across all observations, controlling for the [treatment sums of squares](/D/trss) of the corresponding factors:
 
-\begin{equation} \label{eq:iass}
+$$ \label{eq:iass}
 \begin{split}
 \mathrm{SS}_\mathrm{A \times B} &= \sum_{i=1}^{a} \sum_{j=1}^{b} \sum_{k=1}^{n_{ij}} ([\bar{y}_{i j \bullet} - \bar{y}_{\bullet \bullet \bullet}] - [\bar{y}_{i \bullet \bullet} - \bar{y}_{\bullet \bullet \bullet}] - [\bar{y}_{\bullet j \bullet} - \bar{y}_{\bullet \bullet \bullet}])^2 \\
 &= \sum_{i=1}^{a} \sum_{j=1}^{b} \sum_{k=1}^{n_{ij}} (\bar{y}_{i j \bullet} - \bar{y}_{i \bullet \bullet} - \bar{y}_{\bullet j \bullet} + \bar{y}_{\bullet \bullet \bullet})^2 \; .
 \end{split}
-\end{equation}
+$$
 
-Here, $\bar{y} _{i j \bullet}$ is the mean for the $(i,j)$-th cell (out of $a \times b$ cells), computed from $n_{ij}$ values $y_{ijk}$, $\bar{y} _{i \bullet \bullet}$ and $\bar{y} _{\bullet j \bullet}$ are the level means for the two factors and and $\bar{y} _{\bullet \bullet \bullet}$ is the mean across all values $y_{ijk}$.
+Here, $\bar{y}_{i j \bullet}$ is the mean for the $(i,j)$-th cell (out of $a \times b$ cells), computed from $n_{ij}$ values $y_{ijk}$, $\bar{y}_{i \bullet \bullet}$ and $\bar{y}_{\bullet j \bullet}$ are the level means for the two factors and and $\bar{y}_{\bullet \bullet \bullet}$ is the mean across all values $y_{ijk}$.

D/trss.md

@@ -39,4 +39,4 @@ $$ \label{eq:trss}
 \mathrm{SS}_\mathrm{treat} = \sum_{i=1}^{k} \sum_{j=1}^{n_i} (\bar{y}_i - \bar{y})^2 \; .
 $$
 
-Here, $\bar{y}_i$ is the mean for the $i$-th level of the factor (out of $k$ levels), computed from $n_i$ values $y_{ij}$, and $\bar{y}$ is the mean across all values $y_{ij}$.
+Here, $\bar{y} _i$ is the mean for the $i$-th level of the factor (out of $k$ levels), computed from $n_i$ values $y_{ij}$, and $\bar{y}$ is the mean across all values $y_{ij}$.

P/anova2-pss.md

@@ -54,7 +54,7 @@ $$ \label{eq:anova2-tss}
 \mathrm{SS}_\mathrm{tot} = \sum_{i=1}^{a} \sum_{j=1}^{b} \sum_{k=1}^{n_{ij}} (y_{ijk} - \bar{y}_{\bullet \bullet \bullet})^2
 $$
 
-where $\bar{y} _{\bullet \bullet \bullet}$ is the mean across all values $y_{ijk}$. This can be rewritten as
+where $\bar{y}_{\bullet \bullet \bullet}$ is the mean across all values $y_{ijk}$. This can be rewritten as
 
 $$ \label{eq:anova2-pss-s1}
 \begin{split}

P/bin-post.md

@@ -66,7 +66,7 @@ Combining the likelihood function \eqref{eq:Bin-LF} with the prior distribution
 $$ \label{eq:Bin-JL}
 \begin{split}
 \mathrm{p}(y,p) &= \mathrm{p}(y|p) \, \mathrm{p}(p) \\
-&= {n \choose y} \, p^y \, (1-p)^{n-y} \cdot frac{1}{B(\alpha_0,\beta_0)} \, p^{\alpha_0-1} \, (1-p)^{\beta_0-1} \\
+&= {n \choose y} \, p^y \, (1-p)^{n-y} \cdot \frac{1}{B(\alpha_0,\beta_0)} \, p^{\alpha_0-1} \, (1-p)^{\beta_0-1} \\
 &= \frac{1}{B(\alpha_0,\beta_0)} {n \choose y} \, p^{\alpha_0+y-1} \, (1-p)^{\beta_0+(n-y)-1} \; .
 \end{split}
 $$