R Language Using Built In Statistical Functions Complete Guide

R Language Using Built-in Statistical Functions

Mean Calculation: mean()

• Syntax: mean(x, trim = 0, na.rm = FALSE)
• Description: Computes the arithmetic mean of a numeric vector.
• Parameters:
  • x: Numeric vector.
  • trim: Fraction (0 to 0.5) of observations to drop from each end of x before computing the mean.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
• Example:

  data <- c(2, 4, 6, 8, 10)
  mean(data)  # Returns 6
  

Summation: sum()

• Syntax: sum(..., na.rm = FALSE)
• Description: Returns the sum of all the values present in its arguments.
• Parameters:
  • ...: One or more numeric arguments.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
• Example:

  data <- c(1, 3, 5, 7, 9)
  sum(data)  # Returns 25
  

Median Calculation: median()

• Syntax: median(x, na.rm = FALSE)
• Description: Provides the median value of a numeric vector.
• Parameters:
  • x: Numeric vector.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
• Example:

  data <- c(2, 4, 6, 8, 10, 12)
  median(data)  # Returns 7
  

Variance Calculation: var()

• Syntax: var(x, y = NULL, na.rm = FALSE, use)
• Description: Calculates the variance of the input data.
• Parameters:
  • x: Numeric vector.
  • y: An optional numeric vector of data for the second variable.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
  • use: A character string that specifies how to handle missing values.
• Example:

  data <- c(1, 2, 3, 4, 5)
  var(data)  # Returns 2
  

Standard Deviation: sd()

• Syntax: sd(x, na.rm = FALSE)
• Description: Returns the standard deviation of a numeric vector.
• Parameters:
  • x: Numeric vector.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
• Example:

  data <- c(1, 2, 3, 4, 5)
  sd(data)  # Returns 1.581139
  

Correlation: cor()

• Syntax: cor(x, y = NULL, use = ..., method = ...)
• Description: Computes the correlation coefficient between two or more numeric vectors.
• Parameters:
  • x: Numeric vector or matrix.
  • y: An optional numeric vector.
  • use: Indicates which pairs of values will be used to compute the correlation. Possible values are "all.obs", "complete.obs", "pairwise.complete.obs".
  • method: A character string indicating which correlation coefficient (or covariance) is to be computed. One of "pearson", "kendall", or "spearman".
• Example:

  data1 <- c(1, 2, 3, 4, 5)
  data2 <- c(2, 4, 6, 8, 10)
  cor(data1, data2, method = "pearson")  # Returns 1
  

Covariance: cov()

• Syntax: cov(x, y = NULL, use = ..., method = ...)
• Description: Calculates the covariance between two numeric vectors or a matrix.
• Parameters:
  • x: Numeric vector or matrix.
  • y: An optional numeric vector or matrix.
  • use: Indicates which pairs of values will be used to compute the covariance.
  • method: Matrix method used to compute covariances. The default is "p" for covariance matrix.
• Example:

  data1 <- c(1, 2, 3, 4, 5)
  data2 <- c(2, 4, 6, 8, 10)
  cov(data1, data2)  # Returns 4
  

Quantiles: quantile()

• Syntax: quantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE, names = TRUE, type = 7)
• Description: Produces sample quantiles corresponding to the given probabilities.
• Parameters:
  • x: Numeric vector.
  • probs: Numeric vector of probabilities with values in ([0,1]).
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
  • names: Logical value indicating whether the result should have a names attribute.
  • type: An integer between 1 and 9 selecting one of nine quantile algorithms.
• Example:

  data <- c(1, 2, 3, 4, 5)
  quantile(data, probs = c(0, 0.25, 0.5, 0.75, 1))  # Returns quantiles
  

Maximum and Minimum: max() and min()

• Syntax: max(..., na.rm = FALSE)
• Description: max() returns the maximum value in a numeric vector, and min() returns the minimum value.
• Parameters:
  • ...: One or more numeric vectors.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
• Example:

  data <- c(1, 2, 3, 4, 5)
  max(data)  # Returns 5
  min(data)  # Returns 1
  

Range Calculation: range()

• Syntax: range(..., na.rm = FALSE)
• Description: Returns a vector containing the minimum and maximum of all the given arguments.
• Parameters:
  • ...: One or more numeric vectors.
  • na.rm: Logical value indicating whether to remove NA values before the computation proceeds.
• Example:

  data <- c(1, 2, 3, 4, 5)
  range(data)   # Returns c(1, 5)
  

Distribution Functions

• Normal Distribution:
  • dnorm(x, mean = 0, sd = 1, log = FALSE): Probability density function (PDF).
  • pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE): Cumulative distribution function (CDF).
  • qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE): Quantile function.
  • rnorm(n, mean = 0, sd = 1): Generates random deviates.

Example of Normal Distribution Functions:

• dnorm():

  x <- seq(-3, 3, by = 0.1)
  plot(x, dnorm(x), type = "l", main = "Normal Distribution PDF")
  

• pnorm():

  pnorm(1.96)  # Returns 0.975
  

• qnorm():

  qnorm(0.975)  # Returns 1.96
  

• rnorm():

  set.seed(42)
  random_data <- rnorm(10, mean = 0, sd = 1)
  

Conclusion

Built-in statistical functions in R streamline data analysis, providing quick and reliable methods to calculate mean, median, variance, standard deviation, correlation, covariance, quantiles, and other statistical measures. Utilizing these functions enhances the efficiency and accuracy of your statistical computations. By delving into these functions in detail, you empower yourself with robust statistical tools to tackle complex analytical challenges with ease.

Key Takeaways:

-掌握 core statistical functions (mean(), sum(), etc.) for efficient data analysis.

• Utilize cor() and cov() for measuring relationships between variables.
• Leverage quantile(), max(), min(), and range() for distribution insights.
• Explore dnorm(), pnorm(), qnorm(), and rnorm() for normal distribution operations.
• Always handle missing data (NA) appropriately using parameters like na.rm.