Data Type

name description
factor Factor or Quanlitative data
numeric Quantatitive data. descrete or continuous.

Basic

  • Assignment

      x <- c(1, 2, 3, 4, 5)

Term

  • statistic: a number that is a property of the sample.
  • parameter: a number that is a property of all data
  • average: mean
  • proportion: a ratio of the observations in the specific category by all the number of data

Useful functions

  • table(x)
  • summary(x)
  • names(x): show column names
  • sd(x): standard derivation
  • var(x): variance
  • mean(x): mean
  • median(x): median
  • IQR(x): width of interquartile range
  • quantile(x): shows quantiles
  • sum
    • sum(x): calculate total of elements in x
    • cumsum(x): cumulative summation.
  • length(x): the number of elements in x
  • data.frame(x): creates data frames
  • rounding
    • round(x, d): round values. second parameter represents decimal point.
    • ceiling(x): round up values
    • floor(x): round down valoues
  • calculation
    • sqrt(x): square

Calculate relative frequency

freq <- table(x)
freq / sum(freq)

Read csv

  • read.csv(path) 
      x <- read.csv(path)

Directory operation

  • dir(): show directory contents
  • setwd(path): set working directory
  • getwd(): get working directory

Dataframe operation

  • dataframe$column: data of the column

Graph

  • plot(x)

      plot(table(x)
  • boxplot(x)
  • hist(x): histogram

Boxplot

  • Quartiles: numbers that separate the data into quarters.
    • Q1 - 1st quartile: middle value of the lower half of the data
    • Q2 - 2nd quartile (median): if there are even number of observations, median is the average of the central 2 observations.
    • Q3 - 3rd quartile: middle value of the upper half of the data
    • Q1 < Q2 < Q3
  • Inter-Quartile Range: [ Q1 - IQR * 1.5, Q3 + IQR * 1.5 ] ([ 2.5 Q1 - 1.5 Q3, 2.5 Q3 - 1.5 Q1 ])
    • IQR = Q3 - Q1

Utility functions

T value calculation from samples

  • x: vector of observations
  • target: mean value
# calculate T value
tv <- function (x, target=0) {
  (mean(x) - target) / sqrt(var(x) / length(x))
}

Mean Squared Error

  • x: vector of observations
  • population
mse <- function (x, population) {
  var(x) + (mean(x) - population)^2
}

degree of freedom

dfv <- function (v_a, n_a, v_b, n_b) {
  (v_a + v_b) ^ 2 / (v_a ^ 2 / (n_1 - 1) + v_b ^ 2 / (n_2 - 1))
}

dfs <- function (s_a, n_a, s_b, n_b) {
  dfv(s_a ^ 2, n_a, s_b ^ 2, n_b)
}

ttmv <- function (m_a, v_a, n_a, m_b, v_b, n_b) {
  (m_a - m_b) / sqrt(v_a / n_a + v_b / n_b)
}

ttms <- function (m_a, s_a, n_a, m_b, s_b, n_b) {
  ttmv(m_a, s_a ^ 2, n_a, m_b, s_b ^ 2, n_b)
}

Confidence interval

  • m: sample mean
  • s: sample standard derivation
  • n: the number of samples
  • significance_level
confint_ns <- function (m, s, n, significance_level = 0.95) {
  m + qnorm(c(0, 1) + c(1, -1) * (1 - significance_level) / 2) * s / sqrt(n)
}

confing_nv <- function (m, v, n, significance_level = 0.95) {
  confint_ns(m, sqrt(v), n, significance_level)
}

confint_nx <- function (x, significance_level = 0.95) {
  confint_ns(mean(x, na.rm=TRUE), sd(x, na.rm=TRUE), sum(!is.na(x)), significance_level)
}

confint_p <- function (p, n, significance_level = 0.95) {
  p + qnorm(c(0, 1) + c(1, -1) * (1 - significance_level) / 2) * sqrt(p * (1 - p) / n)
}

confint_px <- function (x, n, significance_level = 0.95) {
  confint_p(x / n, n, significance_level)
}

confint_t <- function (df, significance_level = 0.95) {
  qt(c(0, 1) + c(1, -1) * (1 - significance_level) / 2, df)
}

confint_ms <- function (m, s, n, significance_level = 0.95) {
  m + confint_t(n - 1, significance_level) * s / sqrt(n)
}

confint_mv <- function (m, v, n, significance_level = 0.95) {
  confint_ms(m, sqrt(v), n, significance_level)
}

confint_vs <- function (s, n, significance_level = 0.95) {
  confint_vv(s ^ 2, n, significance_level)
}

confint_vv <- function (v, n, significance_level = 0.95) {
  (n - 1) * v / qchisq(c(1, 0) + c(-1, 1) * (1 - significance_level) / 2, n - 1)
}

Required Sample Size calculation

  • p: estimaterd proportion.
  • diff: permitted proportion difference
  • confidence_level
sample_size <- function (p, diff, confidence_level = 0.95) {
  (qnorm(1 - (1 - confidence_level) / 2) * sqrt(p * (1 - p)) / diff)^2
}

Outlier

# Function to calculate outlier
#
# Example
#   > x <- c(1, 7, 3, 9, 0, 6, 43, 42, 3, 8, 5, 9, 1, 0)
#   > outlier(x)
#   [1] 43 42
# 
outlier <- function (x) {
  q1 <- quantile(x, 0.25)
  q3 <- quantile(x, 0.75)
  iqr <- IQR(x)
  
  low <- q1 - 1.5 * iqr
  high <- q3 + 1.5 * iqr
  x[x < low | high < x] 
}