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    Factors in R

    What is a Factor?

    A factor is R's way of representing categorical data - variables that represent categories or groups rather than continuous measurements. In scientific research, factors are essential for representing experimental treatments, species classifications, measurement scales, or any variable with a fixed set of possible values.

    Key characteristics:

    • Categorical data: Represents discrete categories, not continuous values
    • Limited levels: Has a predefined set of possible values called "levels"
    • Internal storage: Stored internally as integers with text labels
    • Statistical importance: Essential for statistical modeling and analysis
    • Memory efficient: Stores repeated category names efficiently

    Why factors matter in science:

    • Experimental design: Treatment groups, control vs. experimental conditions
    • Classification: Species, genera, taxonomic groups
    • Ordinal data: Rating scales, severity levels, developmental stages
    • Grouping variables: Site locations, sampling methods, instrument types

    Creating Factors

    Basic factor creation:

    r
    # Experimental treatments
treatment <- factor(c("Control", "Low_dose", "High_dose", "Control", "Low_dose", "High_dose"))
treatment
[1] Control   Low_dose  High_dose Control   Low_dose  High_dose
Levels: Control High_dose Low_dose

# Species identification
species <- factor(c("Quercus_alba", "Pinus_strobus", "Acer_rubrum", "Quercus_alba", "Pinus_strobus"))
species
[1] Quercus_alba  Pinus_strobus Acer_rubrum   Quercus_alba  Pinus_strobus
Levels: Acer_rubrum Pinus_strobus Quercus_alba

# Soil types in ecological study
soil_type <- factor(c("Clay", "Sand", "Loam", "Clay", "Sand", "Clay", "Loam"))
soil_type
[1] Clay Sand Loam Clay Sand Clay Loam
Levels: Clay Loam Sand

    Factors with specified levels:

    r
    # Specify all possible levels (even if not all are present in data)
treatment_levels <- factor(c("Control", "Low_dose", "High_dose"), 
                          levels = c("Control", "Low_dose", "Medium_dose", "High_dose"))
treatment_levels
[1] Control   Low_dose  High_dose
Levels: Control Low_dose Medium_dose High_dose

# pH categories with logical order
ph_category <- factor(c("Acidic", "Neutral", "Basic", "Acidic", "Basic"),
                     levels = c("Acidic", "Neutral", "Basic"))
ph_category
[1] Acidic  Neutral Basic   Acidic  Basic  
Levels: Acidic Neutral Basic

    Ordered factors (ordinal data):

    r
    # Severity scale (has natural order)
disease_severity <- factor(c("Mild", "Severe", "Moderate", "Mild", "Severe"),
                          levels = c("Mild", "Moderate", "Severe"),
                          ordered = TRUE)
disease_severity
[1] Mild     Severe   Moderate Mild     Severe  
Levels: Mild < Moderate < Severe

# Developmental stages
plant_stage <- factor(c("Seedling", "Juvenile", "Adult", "Seedling", "Adult"),
                     levels = c("Seedling", "Juvenile", "Adult"),
                     ordered = TRUE)
plant_stage
[1] Seedling Juvenile Adult    Seedling Adult   
Levels: Seedling < Juvenile < Adult

# Likert scale responses
agreement <- factor(c("Strongly Disagree", "Agree", "Neutral", "Strongly Agree"),
                   levels = c("Strongly Disagree", "Disagree", "Neutral", "Agree", "Strongly Agree"),
                   ordered = TRUE)
agreement
[1] Strongly Disagree Agree             Neutral           Strongly Agree   
Levels: Strongly Disagree < Disagree < Neutral < Agree < Strongly Agree

    Understanding Factor Structure

    Examining factors:

    r
    treatment <- factor(c("Control", "Treated", "Control", "Treated", "Control"))

# Check if it's a factor
is.factor(treatment)
[1] TRUE

# Get the levels
levels(treatment)
[1] "Control" "Treated"

# Number of levels
nlevels(treatment)
[1] 2

# See the internal structure
str(treatment)
 Factor w/ 2 levels "Control","Treated": 1 2 1 2 1

# Convert to character to see underlying integers
as.numeric(treatment)
[1] 1 2 1 2 1

# Table of frequencies
table(treatment)
treatment
Control Treated 
      3       2

    Factor information:

    r
    # Create a research dataset
research_data <- data.frame(
  subject_id = 1:12,
  species = factor(rep(c("Mouse", "Rat", "Rabbit"), each = 4)),
  treatment = factor(rep(c("Control", "Drug_A", "Drug_B", "Placebo"), 3)),
  sex = factor(rep(c("Male", "Female"), 6)),
  response = c(23, 45, 67, 12, 34, 56, 78, 21, 43, 65, 87, 32)
)

str(research_data)
'data.frame':	12 obs. of  5 variables:
 $ subject_id: int  1 2 3 4 5 6 7 8 9 10 ...
 $ species   : Factor w/ 3 levels "Mouse","Rabbit",..: 1 1 1 1 3 3 3 3 2 2 ...
 $ treatment : Factor w/ 4 levels "Control","Drug_A",..: 1 2 3 4 1 2 3 4 1 2 ...
 $ sex       : Factor w/ 2 levels "Female","Male": 2 1 2 1 2 1 2 1 2 1 ...
 $ response  : num  23 45 67 12 34 56 78 21 43 65 ...

# Summary shows factor level counts
summary(research_data)
   subject_id       species    treatment      sex       response    
 Min.   : 1.00   Mouse :4    Control:3     Female:6   Min.   :12.00  
 1st Qu.: 3.75   Rabbit:4    Drug_A :3     Male  :6   1st Qu.:26.25  
 Median : 6.50   Rat   :4    Drug_B :3                Median :42.00  
 Mean   : 6.50               Placebo:3                Mean   :44.42  
 3rd Qu.: 9.25                                        3rd Qu.:63.50  
 Max.   :12.00                                        Max.   :87.00

    Working with Factor Levels

    Changing level names:

    r
    # Original factor
habitat <- factor(c("F", "G", "W", "F", "G", "W"))
habitat
[1] F G W F G W
Levels: F G W

# Rename levels to be more descriptive
levels(habitat) <- c("Forest", "Grassland", "Wetland")
habitat
[1] Forest     Grassland  Wetland    Forest     Grassland  Wetland   
Levels: Forest Grassland Wetland

# Alternative method using labels during creation
habitat2 <- factor(c("F", "G", "W", "F", "G", "W"),
                  levels = c("F", "G", "W"),
                  labels = c("Forest", "Grassland", "Wetland"))
habitat2
[1] Forest     Grassland  Wetland    Forest     Grassland  Wetland   
Levels: Forest Grassland Wetland

    Reordering levels:

    r
    # Default alphabetical order
size <- factor(c("Large", "Small", "Medium", "Large", "Small"))
size
[1] Large  Small  Medium Large  Small 
Levels: Large Medium Small

# Reorder to logical size order
size_ordered <- factor(size, levels = c("Small", "Medium", "Large"))
size_ordered
[1] Large  Small  Medium Large  Small 
Levels: Small Medium Large

# Or make it an ordered factor
size_ordinal <- factor(size, levels = c("Small", "Medium", "Large"), ordered = TRUE)
size_ordinal
[1] Large  Small  Medium Large  Small 
Levels: Small < Medium < Large

    Adding and dropping levels:

    r
    # Original factor
season <- factor(c("Spring", "Summer", "Fall", "Spring", "Summer"))
levels(season)
[1] "Fall"   "Spring" "Summer"

# Add new level
levels(season) <- c(levels(season), "Winter")
levels(season)
[1] "Fall"   "Spring" "Summer" "Winter"

# Drop unused levels
season_used <- season[1:3]  # Only first 3 elements
season_used
[1] Spring Summer Fall  
Levels: Fall Spring Summer Winter

droplevels(season_used)  # Remove unused "Winter" level
[1] Spring Summer Fall  
Levels: Fall Spring Summer

    Factors in Data Analysis

    Cross-tabulation:

    r
    # Create experimental data
experiment <- data.frame(
  genotype = factor(rep(c("Wild_type", "Mutant_A", "Mutant_B"), each = 20)),
  condition = factor(rep(rep(c("Control", "Stress"), each = 10), 3)),
  survival = factor(c(rep(c("Alive", "Dead"), c(9, 1)),      # Wild_type Control
                     rep(c("Alive", "Dead"), c(7, 3)),       # Wild_type Stress  
                     rep(c("Alive", "Dead"), c(8, 2)),       # Mutant_A Control
                     rep(c("Alive", "Dead"), c(4, 6)),       # Mutant_A Stress
                     rep(c("Alive", "Dead"), c(6, 4)),       # Mutant_B Control
                     rep(c("Alive", "Dead"), c(3, 7))))      # Mutant_B Stress

# Cross-tabulation
table(experiment$genotype, experiment$condition)
           
            Control Stress
  Mutant_A       10     10
  Mutant_B       10     10
  Wild_type      10     10

# Three-way table
table(experiment$genotype, experiment$condition, experiment$survival)
, , survival = Alive

           condition
genotype    Control Stress
  Mutant_A        8      4
  Mutant_B        6      3
  Wild_type       9      7

, , survival = Dead

           condition
genotype    Control Stress
  Mutant_A        2      6
  Mutant_B        4      7
  Wild_type       1      3

    Factors in statistical analysis:

    r
    # ANOVA example with factors
plant_growth <- data.frame(
  treatment = factor(rep(c("Control", "Fertilizer_A", "Fertilizer_B"), each = 8)),
  growth_rate = c(12, 14, 13, 15, 11, 16, 12, 14,     # Control
                 18, 20, 19, 22, 17, 21, 18, 20,      # Fertilizer_A  
                 25, 27, 24, 28, 23, 29, 25, 26)      # Fertilizer_B
)

# Boxplot by treatment group
boxplot(growth_rate ~ treatment, data = plant_growth,
        main = "Plant Growth by Treatment",
        xlab = "Treatment", ylab = "Growth Rate (cm/week)")

# ANOVA
growth_anova <- aov(growth_rate ~ treatment, data = plant_growth)
summary(growth_anova)
            Df Sum Sq Mean Sq F value   Pr(>F)    
treatment    2  672.3   336.1   134.4 1.18e-11 ***
Residuals   21   52.5     2.5                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Post-hoc comparisons
TukeyHSD(growth_anova)

    Factors vs. character variables:

    r
    # Character variable
char_treatment <- c("Control", "Treated", "Control", "Treated")
class(char_treatment)
[1] "character"

# Factor variable
factor_treatment <- factor(c("Control", "Treated", "Control", "Treated"))
class(factor_treatment)
[1] "factor"

# Statistical functions behave differently
# This won't work properly with character:
# aov(response ~ char_treatment, data = mydata)  # May cause issues

# This works correctly with factor:
# aov(response ~ factor_treatment, data = mydata)  # Proper statistical analysis

    Common Factor Operations

    Converting between data types:

    r
    # Character to factor
species_char <- c("Oak", "Pine", "Maple", "Oak", "Pine")
species_factor <- factor(species_char)
species_factor
[1] Oak   Pine  Maple Oak   Pine 
Levels: Maple Oak Pine

# Factor to character
as.character(species_factor)
[1] "Oak"   "Pine"  "Maple" "Oak"   "Pine"

# Factor to numeric (gets internal codes)
as.numeric(species_factor)
[1] 2 3 1 2 3

# Proper way to convert factor of numbers to numeric
numeric_factor <- factor(c("10", "20", "15", "10", "25"))
as.numeric(numeric_factor)  # Wrong! Gets 1, 2, 3, 1, 4
[1] 1 2 3 1 4

as.numeric(as.character(numeric_factor))  # Correct!
[1] 10 20 15 10 25

    Combining factors:

    r
    # Two separate factors
site1_species <- factor(c("Oak", "Pine", "Maple"))
site2_species <- factor(c("Oak", "Birch", "Pine"))

# Combine factors (may create unexpected levels)
combined_simple <- c(site1_species, site2_species)
combined_simple  # Character vector, not factor!
[1] "Oak"   "Pine"  "Maple" "Oak"   "Birch" "Pine"

# Proper way to combine factors
combined_factor <- factor(c(as.character(site1_species), as.character(site2_species)))
combined_factor
[1] Oak   Pine  Maple Oak   Birch Pine 
Levels: Birch Maple Oak Pine

    Recoding factors:

    r
    # Original factor
original_treatment <- factor(c("T1", "T2", "T3", "T1", "T2", "T3"))

# Recode to meaningful names
recoded_treatment <- factor(original_treatment,
                           levels = c("T1", "T2", "T3"),
                           labels = c("Control", "Low_Nutrient", "High_Nutrient"))
recoded_treatment
[1] Control      Low_Nutrient  High_Nutrient Control      Low_Nutrient  High_Nutrient
Levels: Control Low_Nutrient High_Nutrient

# Conditional recoding
ph_values <- factor(c("Low", "Medium", "High", "Low", "Medium", "High"))
ph_binary <- ifelse(ph_values == "High", "Basic", "Not_Basic")
ph_binary <- factor(ph_binary)
ph_binary
[1] Not_Basic Not_Basic Basic     Not_Basic Not_Basic Basic    
Levels: Basic Not_Basic

    Factors in Real Scientific Examples

    Ecological field study:

    r
    # Bird survey data
bird_survey <- data.frame(
  site_id = 1:24,
  habitat = factor(rep(c("Forest", "Grassland", "Wetland", "Urban"), each = 6)),
  season = factor(rep(c("Spring", "Summer", "Fall"), 8)),
  species = factor(c("Robin", "Sparrow", "Duck", "Pigeon", "Hawk", "Owl",
                    "Robin", "Sparrow", "Duck", "Pigeon", "Hawk", "Owl",
                    "Robin", "Sparrow", "Duck", "Pigeon", "Hawk", "Owl",
                    "Robin", "Sparrow", "Duck", "Pigeon", "Hawk", "Owl")),
  abundance = c(12, 8, 5, 15, 2, 3, 18, 12, 8, 20, 4, 5, 
               6, 4, 15, 8, 1, 7, 25, 18, 3, 35, 8, 12)
)

# Analysis by habitat type
aggregate(abundance ~ habitat, data = bird_survey, mean)
    habitat abundance
1    Forest  8.500000
2 Grassland 10.000000
3      Urban 18.333333
4   Wetland  8.666667

# Two-way analysis
aggregate(abundance ~ habitat + season, data = bird_survey, sum)
    habitat  season abundance
1    Forest    Fall        32
2 Grassland    Fall        32
3      Urban    Fall        75
4   Wetland    Fall        40
5    Forest  Spring        43
6 Grassland  Spring        38
7      Urban  Spring        61
8   Wetland  Spring        32
9    Forest  Summer        36
10Grassland  Summer        50
11     Urban  Summer        74
12   Wetland  Summer        38

    Clinical trial analysis:

    r
    # Medical research data
clinical_data <- data.frame(
  patient_id = 1:60,
  treatment = factor(rep(c("Placebo", "Drug_Low", "Drug_High"), each = 20)),
  age_group = factor(rep(c("Young", "Middle", "Old"), 20),
                    levels = c("Young", "Middle", "Old"), ordered = TRUE),
  response = factor(c(
    rep(c("None", "Mild", "Strong"), c(12, 6, 2)),      # Placebo
    rep(c("None", "Mild", "Strong"), c(8, 8, 4)),       # Drug_Low
    rep(c("None", "Mild", "Strong"), c(3, 7, 10))       # Drug_High
  ), levels = c("None", "Mild", "Strong"), ordered = TRUE)
)

# Response by treatment
response_table <- table(clinical_data$treatment, clinical_data$response)
response_table
          
           None Mild Strong
  Drug_High   3    7     10
  Drug_Low    8    8      4
  Placebo    12    6      2

# Proportion table
prop.table(response_table, margin = 1)  # Proportions by treatment
          
               None  Mild Strong
  Drug_High 0.15 0.35  0.50
  Drug_Low  0.40 0.40  0.20
  Placebo   0.60 0.30  0.10

    Agricultural experiment:

    r
    # Crop yield study
crop_study <- data.frame(
  plot = 1:48,
  variety = factor(rep(c("Variety_A", "Variety_B", "Variety_C", "Variety_D"), each = 12)),
  irrigation = factor(rep(c("Low", "Medium", "High"), 16)),
  fertilizer = factor(rep(rep(c("None", "Organic", "Synthetic", "Both"), each = 3), 4)),
  yield_kg = runif(48, 800, 1200)  # Simulated yield data
)

# Multi-factor ANOVA
yield_model <- aov(yield_kg ~ variety + irrigation + fertilizer, data = crop_study)
summary(yield_model)

# Interaction effects
interaction_model <- aov(yield_kg ~ variety * irrigation, data = crop_study)
summary(interaction_model)

    Common Pitfalls and Solutions

    Problem 1: Unwanted factor conversion

    r
    # Reading data - strings become factors by default (older R versions)
# Solution: Use stringsAsFactors = FALSE or read with readr package
data <- read.csv("file.csv", stringsAsFactors = FALSE)

# Or convert after reading
data$treatment <- factor(data$treatment)

    Problem 2: Factor level order

    r
    # Default alphabetical order may not be logical
size <- factor(c("Large", "Small", "Medium"))
levels(size)
[1] "Large"  "Medium" "Small"   # Alphabetical, not logical

# Solution: Specify levels explicitly
size_correct <- factor(size, levels = c("Small", "Medium", "Large"))
levels(size_correct)
[1] "Small"  "Medium" "Large"   # Logical order

    Problem 3: Converting factors to numeric

    r
    # Wrong way
numeric_factor <- factor(c("10", "20", "30"))
as.numeric(numeric_factor)  # Gets 1, 2, 3 (internal codes)
[1] 1 2 3

# Right way
as.numeric(as.character(numeric_factor))  # Gets 10, 20, 30
[1] 10 20 30

    Problem 4: Unused levels

    r
    # After subsetting, unused levels remain
full_data <- factor(c("A", "B", "C", "D", "E"))
subset_data <- full_data[1:3]
levels(subset_data)
[1] "A" "B" "C" "D" "E"  # D and E still there

# Solution: Drop unused levels
clean_data <- droplevels(subset_data)
levels(clean_data)
[1] "A" "B" "C"  # Only used levels remain

    Key Points to Remember

    1. Use factors for categorical data - treatments, species, classifications
    2. Specify level order - don't rely on alphabetical ordering for ordinal data
    3. Ordered factors for rankings - use ordered = TRUE for scales and rankings
    4. Memory efficiency - factors are more efficient than character vectors for repeated values
    5. Statistical modeling - factors are essential for proper statistical analysis
    6. Level management - add, drop, and rename levels as needed
    7. Conversion pitfalls - be careful converting between factors, characters, and numbers
    8. Cross-tabulation power - use table() for frequency analysis
    9. Meaningful names - use descriptive level names, not codes
    10. Data import - check if categorical variables were imported as factors

    Factors are fundamental for statistical analysis in R and essential for properly handling categorical variables in scientific research. They ensure that statistical functions interpret your categorical data correctly and enable proper group comparisons and modeling.

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