## ----message=FALSE, warning=FALSE, include=FALSE------------------------- library(knitr) options(knitr.kable.NA = '') knitr::opts_chunk$set(comment=">") options(digits=2) set.seed(333) ## ----message=FALSE, warning=FALSE, echo=FALSE, fig.cap="Correlation between the frequentist p-value and the probability of direction (pd)", fig.align='center'---- library(dplyr) library(tidyr) library(ggplot2) library(see) read.csv("https://raw.github.com/easystats/easystats/master/publications/makowski_2019_bayesian/data/data.csv") %>% mutate(effect_existence = ifelse(true_effect == 1, "Presence of true effect", "Absence of true effect"), p_direction = p_direction * 100) %>% ggplot(aes(x=p_direction, y=p_value, color=effect_existence)) + geom_point2(alpha=0.1) + geom_segment(aes(x=95, y=Inf, xend=95, yend=0.1), color="black", linetype="longdash") + geom_segment(aes(x=-Inf, y=0.1, xend=95, yend=0.1), color="black", linetype="longdash") + geom_segment(aes(x=97.5, y=Inf, xend=97.5, yend=0.05), color="black", linetype="dashed") + geom_segment(aes(x=-Inf, y=0.05, xend=97.5, yend=0.05), color="black", linetype="dashed") + theme_modern() + scale_y_reverse(breaks = c(0.05, round(seq(0, 1, length.out = 11), digits=2))) + scale_x_continuous(breaks = c(95, 97.5, round(seq(50, 100, length.out = 6)))) + scale_color_manual(values=c("Presence of true effect"="green", "Absence of true effect"="red")) + theme(legend.title = element_blank()) + guides(colour = guide_legend(override.aes = list(alpha = 1))) + xlab("Probability of Direction (pd)") + ylab("Frequentist p-value") ## ----message=FALSE, warning=FALSE, fig.align='center'-------------------- library(bayestestR) library(logspline) library(KernSmooth) # Compute the correlations data <- data.frame() for(the_mean in runif(25, 0, 4)){ for(the_sd in runif(25, 0.5, 4)){ x <- rnorm(100, the_mean, abs(the_sd)) data <- rbind(data, data.frame("direct" = pd(x), "kernel" = pd(x, method="kernel"), "logspline" = pd(x, method="logspline"), "KernSmooth" = pd(x, method="KernSmooth") )) } } data <- as.data.frame(sapply(data, as.numeric)) # Visualize the correlations library(ggplot2) library(GGally) GGally::ggpairs(data) + theme_classic() ## ----message=FALSE, warning=FALSE---------------------------------------- data <- data.frame() for(i in 1:25){ the_mean <- runif(1, 0, 4) the_sd <- abs(runif(1, 0.5, 4)) parent_distribution <- rnorm(100000, the_mean, the_sd) true_pd <- pd(parent_distribution) for(j in 1:25){ sample_size <- round(runif(1, 25, 5000)) subsample <- sample(parent_distribution, sample_size) data <- rbind(data, data.frame("sample_size" = sample_size, "true" = true_pd, "direct" = pd(subsample) - true_pd, "kernel" = pd(subsample, method="kernel")- true_pd, "logspline" = pd(subsample, method="logspline") - true_pd, "KernSmooth" = pd(subsample, method="KernSmooth") - true_pd )) } } data <- as.data.frame(sapply(data, as.numeric)) ## ----message=FALSE, warning=FALSE, fig.align='center'-------------------- library(tidyr) library(dplyr) data %>% tidyr::gather(Method, Distance, -sample_size, -true) %>% ggplot(aes(x=sample_size, y = Distance, color = Method, fill= Method)) + geom_point(alpha=0.3, stroke=0, shape=16) + geom_smooth(alpha=0.2) + geom_hline(yintercept=0) + theme_classic() + xlab("\nDistribution Size")