corrected for underscores

Underscores "_" in defunct equations were replaced by "\_" to make them render correctly in in-line math.

Author: JoramSoch

D/iass.md

@@ -33,7 +33,7 @@ $$ \label{eq:anova}
 y_{ijk} = \mu + \alpha_i + \beta_j + \gamma_{ij} + \varepsilon_{ijk}, \; \varepsilon_{ijk} \overset{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0, \sigma^2) \; .
 $$
 
-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:
+Then, the interaction sum of squares is defined as the [explained sum of squares](/D/ess) (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:
 
 $$ \label{eq:iass}
 \begin{split}
@@ -42,4 +42,4 @@ $$ \label{eq:iass}
 \end{split}
 $$
 
-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

@@ -33,10 +33,10 @@ $$ \label{eq:anova}
 y_{ij} = \mu + \delta_i + \varepsilon_{ij}, \; \varepsilon_{ij} \overset{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0, \sigma^2) \; .
 $$
 
-Then, the treatment sum of squares is defined as the [explained sum of squares] (ESS) for each main effect, i.e. as the sum of squared deviations of the average for each level of the factor, from the average across all observations:
+Then, the treatment sum of squares is defined as the [explained sum of squares](/D/ess) (ESS) for each main effect, i.e. as the sum of squared deviations of the average for each level of the factor, from the average across all observations:
 
 $$ \label{eq:trss}
 \mathrm{SS}_\mathrm{treat} = \sum_{i=1}^{k} \sum_{j=1}^{n_i} (\bar{y}_i - \bar{y})^2 \; .
 $$
 
-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/anova1-fols.md

@@ -46,7 +46,7 @@ $$ \label{eq:anova1-f}
 F = \frac{\frac{1}{k-1} \sum_{i=1}^{k} n_i (\bar{y}_i - \bar{y})^2}{\frac{1}{n-k} \sum_{i=1}^{k} \sum_{j=1}^{n_i} (y_{ij} - \bar{y}_i)^2}
 $$
 
-where $\bar{y} _i$ is the average of all values $y_{ij}$ from category $i$ and $\bar{y}$ is the grand mean of all values $y_{ij}$ from all categories $i = 1, \ldots, k$.
+where $\bar{y}\_i$ is the average of all values $y\_{ij}$ from category $i$ and $\bar{y}$ is the grand mean of all values $y\_{ij}$ from all categories $i = 1, \ldots, k$.
 
 1) The [ordinary least squares estimates for one-way ANOVA](/P/anova1-ols) are
 

P/anova2-pss.md

@@ -45,7 +45,7 @@ $$ \label{eq:anova2-pss}
 \mathrm{SS}_\mathrm{tot} = \mathrm{SS}_{A} + \mathrm{SS}_{B} + \mathrm{SS}_{A \times B} + \mathrm{SS}_\mathrm{res}
 $$
 
-where $\mathrm{SS} _\mathrm{tot}$ is the [total sum of squares](/D/tss), $\mathrm{SS} _{A}$, $\mathrm{SS} _{B}$ and $\mathrm{SS} _{A \times B}$ are [treatment](/D/trss) and [interaction sum of squares](/D/iass) (summing into the [explained sum of squares](/D/ess)) and $\mathrm{SS} _\mathrm{res}$ is the [residual sum of squares](/D/rss).
+where $\mathrm{SS}\_\mathrm{tot}$ is the [total sum of squares](/D/tss), $\mathrm{SS}\_{A}$, $\mathrm{SS}\_{B}$ and $\mathrm{SS}\_{A \times B}$ are [treatment](/D/trss) and [interaction sum of squares](/D/iass) (summing into the [explained sum of squares](/D/ess)) and $\mathrm{SS}\_\mathrm{res}$ is the [residual sum of squares](/D/rss).
 
 
 **Proof:** The [total sum of squares](/D/tss) for [two-way ANOVA](/D/anova2) is given by

P/bin-ent.md

@@ -87,4 +87,4 @@ $$ \label{eq:bin-ent-s4}
 \mathrm{H}(X) = n \cdot \mathrm{H}_\mathrm{bern}(p) - \mathrm{E}_\mathrm{lbc}(n,p) \; .
 $$
 
-Note that, because $0 \leq \mathrm{H}_\mathrm{bern}(p) \leq 1$, we have $0 \leq n \cdot \mathrm{H}_\mathrm{bern}(p) \leq n$, and because the [entropy is non-negative](/P/ent-nonneg), it must hold that $n \geq \mathrm{E}_\mathrm{lbc}(n,p) \geq 0$.
+Note that, because $0 \leq \mathrm{H}\_\mathrm{bern}(p) \leq 1$, we have $0 \leq n \cdot \mathrm{H}\_\mathrm{bern}(p) \leq n$, and because the [entropy is non-negative](/P/ent-nonneg), it must hold that $n \geq \mathrm{E}\_\mathrm{lbc}(n,p) \geq 0$.