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Working with Tables Introduction to Tables in R In R, tables are a way to summarize categorical data. They are often created from factors or categorical variables to provide counts or frequencies. Tables can be very useful for understanding the distribution of categorical data and for exploratory data analysis. Creating Tables Using table() The table() function is the most common way to create a frequency table from a vector or data frame. Basic Usage:  # Create a vector of categorical data categories <- c(“A”, “B”, “A”, “C”, “B”, “A”, “C”, “C”, “B”) # Create a frequency table freq_table <- table(categories) print(freq_table) # Output: # categories # A B C # 3 3 3 This table shows the count of each category in the categories vector Using table() with Multiple Factors You can create a contingency table (cross-tabulation) for two or more factors. This table shows the count of each combination of gender and age_group. Manipulating Tables  # Create vectors for two factors gender <- c(“Male”, “Female”, “Female”, “Male”, “Male”, “Female”) age_group <- c(“Young”, “Old”, “Young”, “Young”, “Old”, “Old”) # Create a contingency table contingency_table <- table(gender, age_group) print(contingency_table) # Output: #         age_group # gender   Old Young #   Female   2    1 #   Male     2    2 Accessing Table Elements You can access specific elements of a table using indexing.  # Access the count of Females in the Old age group count_female_old <- contingency_table[“Female”, “Old”] print(count_female_old) # Output: # [1] 2 Adding and Removing Table Elements You can modify tables by adding or removing elements.  # Add a new level to the ‘age_group’ factor age_group <- factor(age_group, levels = c(“Young”, “Old”, “Middle-aged”)) # Create a new contingency table with the additional level contingency_table_updated <- table(gender, age_group) print(contingency_table_updated) # Output: #          age_group # gender   Young Old Middle-aged #   Female    1   2          0 #   Male      2   2          0 Converting Tables to Data Frames You can convert a table to a data frame for easier manipulation and analysis.  # Convert the contingency table to a data frame df_from_table <- as.data.frame(contingency_table) print(df_from_table) # Output: #    gender age_group Freq # 1 Female       Old    2 # 2 Female     Young    1 # 3   Male       Old    2 # 4   Male     Young    2 Analyzing Tables Computing Proportions You can compute proportions from a frequency table to understand the relative distribution.  # Compute proportions prop_table <- prop.table(freq_table) print(prop_table) # Output: # categories #          A          B          C # 0.3333333  0.3333333  0.3333333 Aggregating Data You can use aggregate() with tables to summarize data across different dimensions.  # Aggregate data by gender and age group to compute the total counts agg_table <- aggregate(Freq ~ gender + age_group, data = df_from_table, sum) print(agg_table) # Output: #  gender age_group Freq # 1 Female     Old    2 # 2 Female   Young    1 # 3   Male     Old    2 # 4   Male   Young    2 Marginal Tables You can compute marginal totals for rows or columns.  # Compute row-wise marginal totals row_totals <- margin.table(contingency_table, 1) print(row_totals) # Compute column-wise marginal totals col_totals <- margin.table(contingency_table, 2) print(col_totals) # Output: # Row totals: # Female   Male #      3      4 # Column totals: # Young Old #    3   4 Extended Examples Example: Creating and Analyzing a Multi-Dimensional Table Suppose we have a data frame with more complex categorical data.  # Create a more complex data frame data <- data.frame(   region = factor(c(“North”, “South”, “East”, “West”, “North”, “East”)),   outcome = factor(c(“Success”, “Failure”, “Success”, “Success”, “Failure”, “Failure”)) ) # Create a multi-dimensional table multi_table <- table(data$region, data$outcome) print(multi_table) # Output: #         outcome # region Failure Success #   East        1        1 #   North       1        1 #   South       1        0 #   West        0        1 In this table, we see the counts of Failure and Success outcomes for each region. Example: Visualizing Tables You can visualize tables using bar plots.  # Create a bar plot of the frequency table barplot(freq_table, main = “Frequency of Categories”, xlab = “Categories”, ylab = “Frequency”) This will create a bar plot showing the frequency of each category. Summary Tables in R are a powerful way to summarize and analyze categorical data. Using functions like table(), you can create frequency tables, contingency tables, and more. Manipulating and analyzing these tables involves accessing elements, converting to data frames, computing proportions, and aggregating data. Visualizing tables through plots can also provide valuable insights.

The by() Function Introduction to by() The by() function in R is used to apply a function to each subset of data defined by a factor or a list of factors. It is particularly useful for performing calculations or transformations on groups of data within data frames or lists. Syntax of by() The general syntax of by() is:  by(data, INDICES, FUN, …) data: The object to which the function will be applied (typically a data frame or a list). INDICES: A factor or a list of factors defining the subsets. FUN: The function to apply to each subset. …: Additional arguments passed to the function. Basic Example Let’s start with a simple example where we apply a function to subsets of a data frame.  # Create a data frame df <- data.frame(   id = 1:6,   value = c(10, 20, 15, 25, 30, 35),   group = factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) ) # Apply the mean() function to each group defined by ‘group’ result <- by(df$value, df$group, mean) print(result) # Output: # df$group: A # [1] 18.33333 # df$group: B # [1] 26.66667 In this example, by() calculates the mean of the value column in df for each level of the group factor. Advanced Examples Applying More Complex Functions You can apply more complex functions to each subset. For example, let’s calculate the variance for each group.  # Apply the var() function to calculate the variance within each group variance_by_group <- by(df$value, df$group, var) print(variance_by_group) # Output: # df$group: A # [1]  97.5 # df$group: B # [1]  97.5 Applying a Custom Function You can also apply a custom function to each group. Suppose we want to create a function that returns the minimum and maximum of each subset.  # Custom function to calculate minimum and maximum min_max <- function(x) {   return(c(min = min(x), max = max(x))) } # Apply the custom function min_max_by_group <- by(df$value, df$group, min_max) print(min_max_by_group) # Output: # df$group: A # min max # 10  30 # df$group: B # min max # 20  35 Using by() with Data Frames by() can be used to apply functions to entire data frames.  # Create a more complex data frame df2 <- data.frame(   id = 1:6,   value1 = c(10, 20, 15, 25, 30, 35),   value2 = c(5, 15, 10, 20, 25, 30),   group = factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) ) # Calculate the mean of columns ‘value1’ and ‘value2’ for each group mean_by_group <- by(df2[, c(“value1”, “value2”)], df2$group, colMeans) print(mean_by_group) # Output: # df2$group: A # value1 value2 #  18.33333  10.00000 # df2$group: B # value1 value2 # 26.66667  22.50000 Using by() with a List of Factors You can also use by() with a list of factors for more complex grouping.  # Additional factor vector subgroup <- factor(c(“X”, “Y”, “X”, “Y”, “X”, “Y”)) # Apply the mean() function to each combination of ‘group’ and ‘subgroup’ mean_by_groups <- by(df$value, list(df$group, subgroup), mean) print(mean_by_groups) # Output: # df$group: A df$subgroup: X # [1] 20 # df$group: A df$subgroup: Y # [1] 15 # df$group: B df$subgroup: X # [1] 20 # df$group: B df$subgroup: Y # [1] 25 Summary The by() function in R is a powerful tool for applying functions to subsets of data defined by factors. It is especially useful for performing calculations or transformations on data frames or lists, allowing for flexible and efficient data manipulation. Mastering the use of by() can greatly enhance your ability to analyze grouped data in R.

The split() Function Introduction to split() The split() function in R is used to divide data into groups based on a factor or a list of factors. It splits a vector, data frame, or list into subsets according to the values of a factor or factors. Syntax of split() The general syntax of split() is:  split(x, f, drop = FALSE, …) x: The object to be split (usually a vector, data frame, or list). f: A factor or a list of factors that define the grouping. drop: A logical value indicating whether levels that do not occur should be dropped from the result. …: Additional arguments to pass to methods. Basic Example Let’s start with a simple example where we split a vector based on a factor.  # Numeric vector values <- c(10, 20, 15, 25, 30, 35) # Factor vector defining groups groups <- factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) # Split the vector based on the factor split_values <- split(values, groups) print(split_values) # Output: # $A # [1] 10 15 30 # $B # [1] 20 25 35 In this example, split() divides the values vector into two components: one for each level of groups (A and B). Advanced Examples Splitting a Data Frame You can use split() to divide a data frame into a list of data frames based on a factor.  # Create a data frame df <- data.frame(   id = 1:6,   value = c(10, 20, 15, 25, 30, 35),   group = factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) ) # Split the data frame by the ‘group’ column split_df <- split(df, df$group) print(split_df) # Output: # $A #   id value group # 1  1    10     A # 3  3    15     A # 5  5    30     A # $B #   id value group # 2  2    20     B # 4  4    25     B # 6  6    35     B Splitting by Multiple Factors You can split data by multiple factors by providing a list of factors.  # Additional factor vector subgroups <- factor(c(“X”, “Y”, “X”, “Y”, “X”, “Y”)) # Split the data frame by both ‘group’ and ‘subgroup’ split_df_multiple <- split(df, list(df$group, df$subgroup)) print(split_df_multiple) # Output: # $`A.X` #   id value group subgroup # 1  1    10     A        X # 5  5    30     A        X # $`A.Y` #   id value group subgroup # 3  3    15     A        Y # $`B.X` #   id value group subgroup # 2  2    20     B        X # $`B.Y` #   id value group subgroup # 4  4    25     B        Y # 6  6    35     B        Y Dropping Unused Levels You can use the drop argument to control whether unused levels are included in the result.  # Factor vector with levels not in data f <- factor(c(“A”, “B”, “A”, “B”, “A”, “C”), levels = c(“A”, “B”, “C”, “D”)) # Split with unused levels split_values_with_levels <- split(values, f) print(split_values_with_levels) # Output: # $A # [1] 10 15 30 # $B # [1] 20 25 35 # $C # NULL # $D # NULL Here, split() includes the levels “C” and “D” even though they are not present in the data. If you set drop = TRUE, those levels would be omitted. Applying Functions to Split Data You can use lapply() in conjunction with split() to apply functions to each subset.  # Calculate the mean for each subset mean_by_group <- lapply(split(df$value, df$group), mean) print(mean_by_group) # Output: # $A # [1] 18.33333 # $B # [1] 26.66667 In this example, lapply() applies the mean function to each subset of df$value created by split(). Summary The split() function in R is a versatile tool for dividing data into subsets based on one or more factors. It can be used with vectors, data frames, and lists, and is often combined with other functions to perform more complex data manipulations and analyses. Understanding how to effectively use split() can greatly enhance your ability to handle and analyze grouped data in R.

The tapply() Function Introduction to tapply() The tapply() function in R is used to apply a function to subsets of a vector, where the subsets are defined by a factor or factors. It is particularly useful for performing aggregate calculations (like means, sums, etc.) on subsets of data. Syntax of tapply() The general syntax of tapply() is:  tapply(X, INDEX, FUN, …) X: The vector on which you want to apply a function. INDEX: A factor or a list of factors defining the subsets of X. FUN: The function to apply to each subset. …: Additional arguments passed to the function. Basic Example Consider a simple example where we have a numeric vector and a factor vector defining groups.  # Numeric vector values <- c(10, 20, 15, 25, 30, 35) # Factor vector defining groups groups <- factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) # Calculate the mean of values for each group mean_by_group <- tapply(values, groups, mean) print(mean_by_group) # Output: #  A  B # 25  30 In this example, tapply() calculates the mean of values for each level of groups (A and B). Advanced Examples Calculating Sum You can use tapply() to calculate other statistics, such as the sum.  # Calculate the sum of values for each group sum_by_group <- tapply(values, groups, sum) print(sum_by_group) # Output: #  A  B # 60  80 Applying a Custom Function You can also apply a custom function to each group.  # Custom function: standard deviation std_dev_by_group <- tapply(values, groups, sd) print(std_dev_by_group) # Output: #  A  B # 10  10 Using Multiple Factors INDEX can be a vector or a list of factors, allowing for more complex aggregations.  # Additional factor vectors groups1 <- factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) groups2 <- factor(c(“X”, “Y”, “X”, “Y”, “X”, “Y”)) # Calculate the mean of values for each combination of groups mean_by_groups <- tapply(values, list(groups1, groups2), mean) print(mean_by_groups) # Output: #     groups2 # groups1  X  Y #      A 20 30 #      B 25 35 In this example, tapply() calculates the mean of values for each combination of the levels of groups1 and groups2. Handling Missing Values If you have missing values (NA) in your data, tapply() ignores them by default, but you can control this behavior using additional arguments.  # Numeric vector with NAs values_with_na <- c(10, 20, NA, 25, NA, 35) # Calculate the mean, ignoring NA values mean_with_na <- tapply(values_with_na, groups, mean, na.rm = TRUE) print(mean_with_na) # Output: # A  B # 25  30 Summary The tapply() function is a powerful tool for performing aggregate operations on subsets of data defined by factors. It allows you to calculate descriptive statistics, apply custom functions, and handle data grouped by one or more factors. By using tapply(), you can efficiently summarize and analyze grouped data.

Common Functions Used with Factors levels() The levels() function is used to get or set the levels of a factor. Levels are the distinct categories that a factor can take. Getting Levels  # Create a factor data <- factor(c(“High”, “Low”, “Medium”, “Medium”, “High”, “Low”)) # Get the levels of the factor levels(data) # Output: # [1] “High”   “Low”    “Medium” Setting Levels You can set the levels of a factor to a new set of values. # Set new levels for the factor levels(data) <- c(“Low”, “Medium”, “High”, “Very High”) # Print the factor with updated levels print(data) # Output: # [1] High   Low    Medium Medium High   Low Levels: Low Medium High Very High nlevels() The nlevels() function returns the number of levels in a factor.  # Number of levels in the factor nlevels(data) # Output: # [1] 4 as.factor() The as.factor() function converts a vector into a factor. This is useful when you want to convert a character vector or numeric vector into a factor.  # Convert a character vector to a factor char_vector <- c(“Red”, “Green”, “Blue”, “Green”, “Red”) factor_char_vector <- as.factor(char_vector) # Print the factor print(factor_char_vector) # Output: # [1] Red   Green Blue  Green Red  Levels: Blue Green Red summary() The summary() function provides a summary of a factor, showing the frequency of each level.  # Summary of the factor summary(factor_char_vector) # Output: # Blue  Green    Red #   1      2      2 table() The table() function creates a frequency table of the factor levels. This function is useful for seeing how many observations fall into each category.  # Frequency table of the factor freq_table <- table(factor_char_vector) print(freq_table) # Output: # factor_char_vector # Blue Green   Red #    1     2     2 relevel() The relevel() function changes the reference level of a factor. This is useful in modeling when you want to change which level is used as the baseline.  # Relevel the factor to set “Blue” as the reference level relevel_factor <- relevel(factor_char_vector, ref = “Blue”) # Print the relevel factor print(relevel_factor) # Output: # [1] Blue  Green Red   Green Red  Levels: Blue Green Red fct_reorder() From the forcats package, fct_reorder() reorders the levels of a factor based on another variable. This is useful when you want to order levels by some numeric summary.  # Install and load the forcats package if not already installed # install.packages(“forcats”) library(forcats) # Create a data frame df <- data.frame(   category = factor(c(“A”, “B”, “C”, “B”, “A”, “C”)),   value = c(10, 20, 30, 40, 50, 60) ) # Reorder levels of ‘category’ based on the mean of ‘value’ df$category <- fct_reorder(df$category, df$value, .fun = mean) # Print the reordered factor print(df$category) # Output: # [1] A B C B A C Levels: A B C fct_recode() Also from the forcats package, fct_recode() allows you to rename the levels of a factor.  # Recode the levels of a factor df$category <- fct_recode(df$category,                           “Group 1” = “A”,                           “Group 2” = “B”,                           “Group 3” = “C”) # Print the recoded factor print(df$category) # Output: # [1] Group 1 Group 2 Group 3 Group 2 Group 1 Group 3  Levels: Group 1 Group 2 Group 3 fct_collapse() fct_collapse() is another function from the forcats package that allows you to combine levels into broader categories.  # Collapse the levels of the factor df$category <- fct_collapse(df$category,                             “Group A” = c(“A”, “B”),                             “Group B” = “C”) # Print the collapsed factor print(df$category) # Output: # [1] Group A Group A Group B Group A Group A Group B Levels: Group A Group B fct_expand() fct_expand() ensures that all levels specified are included in the factor, even if they are not present in the data.  # Expand the factor to include all specified levels df$category <- fct_expand(df$category, “Group A”, “Group B”, “Group C”) # Print the expanded factor print(df$category) # Output: # [1] Group A Group A Group B Group A Group A Group B  Levels: Group A Group B Group C

Factors and Levels in R Introduction to Factors In R, a factor is a data type used for categorical data. Factors are variables that can take on a limited number of distinct values, called levels. They are particularly useful for representing categorical variables like gender, blood type, or product category. Creating Factors Creating Simple Factors To create a factor in R, you use the factor() function. Here’s how you can create a factor from a character vector:  # Character vector data <- c(“High”, “Low”, “Medium”, “Medium”, “High”, “Low”) # Convert to factor factor_data <- factor(data) # Print the factor print(factor_data) Specifying Levels You can specify the order of levels when creating a factor. This is useful when there is a natural order in the categories (e.g., levels of satisfaction).  # Specify the order of levels ordered_factor <- factor(data, levels = c(“Low”, “Medium”, “High”), ordered = TRUE) # Print the ordered factor print(ordered_factor) Examining Levels Getting Levels You can use the levels() function to retrieve the levels of a factor.  # Get the levels print(levels(factor_data)) Modifying Levels You can also modify the levels of a factor after it has been created.  # Modify the levels levels(factor_data) <- c(“Low”, “Medium”, “High”) # Print the factor with modified levels print(factor_data) Characteristics of Factors Underlying Numeric Representation Factors are stored as integers with a corresponding set of levels. Each level corresponds to an integer, and the factor itself is essentially a vector of these integers.  # Display the underlying integer values as.integer(factor_data) Using Factors in Models Factors are used in statistical models to represent categorical variables. For example, in a linear regression model, factors are automatically treated as independent variables.  # Create a dataframe df <- data.frame(   response = c(10, 20, 15, 25, 30),   category = factor(c(“A”, “B”, “A”, “B”, “A”)) ) # Fit a linear model model <- lm(response ~ category, data = df) # Model summary summary(model) Manipulating Factors Converting Between Factors and Characters You can convert a factor to a character vector and vice versa.  # Convert a factor to characters char_vector <- as.character(factor_data) print(char_vector) # Convert a character vector to a factor new_factor <- as.factor(char_vector) print(new_factor) Recoding Levels You can recode the levels of factors to rename or group them.  # Recoding levels factor_data <- factor(data, levels = c(“Low”, “Medium”, “High”), labels = c(“Low”, “Medium”, “High”)) print(factor_data) Advanced Examples Factors with Missing Levels Factors can have levels that are not present in the data. This is useful for maintaining the structure of your data when some categories are missing.  # Create a factor with missing levels factor_with_missing <- factor(data, levels = c(“Low”, “Medium”, “High”, “Very High”)) # Print the factor print(factor_with_missing) Using Factors in Frequency Tables Factors are often used to create frequency tables, which are useful for summarizing categorical data.  # Create a frequency table frequency_table <- table(factor_data) print(frequency_table) Using Factors for Grouping Factors are also used for grouping data in analyses, such as with tapply() and aggregate() functions.  # Create some data values <- c(10, 20, 30, 40, 50, 60) groups <- factor(c(“A”, “B”, “A”, “B”, “A”, “B”)) # Calculate the mean by group mean_by_group <- tapply(values, groups, mean) print(mean_by_group) Summary Factors in R are powerful tools for working with categorical data. They allow you to manage and analyze qualitative variables with defined levels and are integrated into various aspects of data analysis in R, from descriptive statistics to statistical modeling. Understanding and manipulating factors is essential for effective analysis of categorical data.