class: middle, inverse, title-slide # Fundamentals of Statistical Testing ### Dr Milan Valášek ### 24 January 2022 --- ## Overview - Recap on distributions - More about the normal distribution - Sampling - Sampling distribution - Standard error - Central Limit Theorem --- ## Objectives After this lecture you will understand - that there exist mathematical functions that describe different distributions - what makes the normal distribution normal and what are its properties - how random fluctuations affect sampling and parameter estimates - the function of the sampling distribution and the standard error - the Central Limit Theorem &nbsp; .center[**With this knowledge you'll build a solid foundation for understanding all the statistics we will be learning in this programme!**] --- ## It's all Greek to me! - `\(\mu\)` is the *population* mean - `\(\bar{x}\)` is the *sample* mean - `\(\hat{\mu}\)` is the **estimate** of the *population* mean - Same with *SD*: `\(\sigma\)`, `\(s\)`, and `\(\hat{\sigma}\)` - Greek is for populations, Latin is for samples, hat is for population estimates --- ## Recap on distributions - Numerically speaking, the number of observations per each value of a variable - Which values occur more often and which less often - The shape formed by the bars of a bar chart/histogram .codePanel[ ```r df <- tibble(eye_col = sample(c("Brown", "Blue", "Green", "Gray"), 555, replace = T, prob = c(.55, .39, .04, .02)), age = rnorm(length(eye_col), 20, .65)) p1 <- df %>% ggplot(aes(x = eye_col)) + geom_bar(fill = c("skyblue4", "chocolate4", "slategray", "olivedrab"), colour=NA) + labs(x = "Eye colour", y = "Count") p2 <- df %>% ggplot(aes(x = age)) + geom_histogram() + stat_density(aes(y = ..density.. * 80), geom = "line", color = theme_col, lwd = 1) + labs(x = "Age (years)", y = "Count") plot_grid(p1, p2) ``` <!-- -->]