Update the notes

index.html

@@ -11,7 +11,7 @@
 
 <meta name="author" content="Brad Duthie" />
 
-<meta name="date" content="2023-09-13" />
+<meta name="date" content="2023-09-18" />
 
 <title>On the equivalence of t-tests, anovas, and linear models</title>
 
@@ -359,7 +359,7 @@
 <h1 class="title toc-ignore">On the equivalence of t-tests, anovas, and
 linear models</h1>
 <h4 class="author">Brad Duthie</h4>
-<h4 class="date">13 September 2023</h4>
+<h4 class="date">18 September 2023</h4>
 
 </div>
 

notes.Rmd

@@ -1,11 +1,11 @@
 ---
 title: "On the equivalence of t-tests, anovas, and linear models"
 author: "Brad Duthie"
-date: "13 September 2023"
+date: "18 September 2023"
 output:
   word_document: default
-  pdf_document: default
   html_document: default
+  pdf_document: default
 linkcolor: blue
 ---
 

scratch.R

@@ -1,4 +1,3 @@
-
 plant_data <- read.csv(file = "two_discrete_x_values.csv");
 
 species_1 <- plant_data$height[plant_data$species_ID == "species_1"];
@@ -7,60 +6,39 @@ hist(species_1, breaks = 10, col = "blue", xlim = c(0, 300),
      main = "", xlab = "Plant height", cex.lab = 1.25, 
      ylim = c(0, 15));
 hist(species_2, breaks = 10, col = "red", add = TRUE)
-legend(x = 0, y = 15, fill = c("red", "blue"), 
-       legend = c("species_2", "species_1"));
-
+#legend(x = 0, y = 15, fill = c("red", "blue"), 
+#       legend = c("species_2", "species_1"));
 
 
+n1     <- length(species_1);
+n2     <- length(species_2);
+var_y1 <- var(species_1);
+var_y2 <- var(species_2);
+s_p    <- sqrt(((n1 - 1)*var_y1 + (n2 - 1)*var_y2)/(n1 + n2 - 2));
+SEybar <- s_p * sqrt((n1 + n2) / (n1*n2));
+tval   <- (mean(species_1) - mean(species_2)) / SEybar;
 
-
-#################
 #################
 #################  Using the t-test function in R and lm
 #################
-#################
-t.test(species_1, species_2, var.equal = TRUE);
+t.test(species_1, species_2, var.equal = FALSE);
+
+# Use a linear model instead to get the same numbers
 lmod1 <- lm(height ~ 1 + species_ID, data = plant_data);
-lmod1 <- lm(height ~ species_ID, data = plant_data);
 summary(lmod1);
 
 
-
-
-
-
-
-
-
-#################
 #################
 #################  How R sees the linear model and t-test
 #################
-#################
 is_species_2 <- as.numeric(plant_data$species_ID == "species_2");
 plant_height <- plant_data$height;
 lm_table_eg  <- data.frame(plant_height, is_species_2);
 
 
-
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-#################
 #################
 #################  Thinking about this in a plot
 #################
-#################
 plot(x = lm_table_eg$is_species_2, y = lm_table_eg$plant_height, 
      ylim = c(0, 275), pch = 20, cex.axis = 1.25, cex.lab = 1.25, 
      ylab = "Plant height", xlab = "Is species 2: Yes (1) or no (0)", 
@@ -75,106 +53,36 @@ points(x = 1, y = summary(lmod1)$coefficients[1,1] +
          summary(lmod1)$coefficients[2,1], pch = 18, col = "orange", cex = 3);
 
 
-
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-#################
 #################
 #################  Analysis of variance with two categories
 #################
-#################
 aov_1 <- aov(height ~ species_ID, data = plant_data);
 summary(aov_1);
 
 
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-#################
 #################
 #################  What happens when we have three categories? ANOVA
 #################
-#################
 plant_data <- read.csv(file = "three_discrete_x_values.csv");
 aov_2 <- aov(height ~ species_ID, data = plant_data);
 summary(aov_2);
 
 
 
-
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-
-#################
 #################
 #################  Three categories with a linear model
 #################
-#################
 lmod2 <- lm(height ~ 1 + species_ID, data = plant_data);
 summary(lmod2);
 
 # Can we check out the mean values?
 tapply(X = plant_data$height, INDEX = plant_data$species_ID, 
        FUN = mean);
 
-
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-#################
 #################
 #################  What's really going on with 3 groups?
 #################
-#################
 the_intercept <- rep(x = 1, length = length(plant_data$height));
 is_species_2  <- as.numeric(plant_data$species_ID == "species_2");
 is_species_3  <- as.numeric(plant_data$species_ID == "species_3");
@@ -188,24 +96,9 @@ head(lm_table_eg);
 
 
 
-
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-#################
 #################
 #################  Even more elegant, using matrices!
 #################
-#################
 Y <- as.matrix(lm_table_eg[,1]);
 X <- as.matrix(lm_table_eg[,2:4]);
 

slides.Rmd

@@ -0,0 +1,28 @@
+---
+title: "Mendelian genetics"
+output:
+  beamer_presentation:
+    theme: "default"
+    colortheme: "default"
+    fonttheme: "default"
+  ioslides_presentation: default
+  slidy_presentation: default
+header-includes:
+- \usepackage{hyperref}
+- \usepackage{caption}
+- \usepackage[normalem]{ulem}
+- \definecolor{links}{HTML}{2A1B81}
+- \hypersetup{colorlinks,linkcolor=,urlcolor=links}
+colorlinks: true
+linkcolor: blue
+urlcolor: blue
+---
+
+```{r, echo = FALSE}
+library(knitr);
+opts_chunk$set(echo = FALSE);
+```
+
+
+## How is variation inherited from parent to offspring?
+