if (condition) {
# Action if condition is true
}1 Conditional Statements for Statistical Analysis
Within this chapter, we’ll focus on different statistical use cases for selection control. Selection control refers to a program control structure that allows for conditional execution of code. We’ll cover the following topics:
- if statements;
- if-else statements;
- if-elseif-else statements;
- vectorized ifelse statements; and,
- switch statements in R.
We’ll explore how to use these conditional statements for tasks like applying classifications based on thresholds and discretizing continuous values into bins.
1.1 if Statements
We make choices based on conditions every day. For example:
- If the alarm rings, we get up
- If a plant looks dry, we water it
- If it’s raining, we take an umbrella
These are conditional decisions: we act only when a specific condition is met.
In R, we use if statements to make these kinds of decisions. This structure tells R to perform an action only when the condition is true. The basic structure of an if statement is given in Listing 1.1.
graph TD
A([Start]) --> B{Condition}
B -->|"<condition> is FALSE"| E([End])
B -->|"<condition> is TRUE"| C[Execute if block]
C --> E
style A fill:#f9f,stroke:#333,stroke-width:2px
style B fill:#bbf,stroke:#333,stroke-width:2px
style C fill:#dfd,stroke:#333,stroke-width:2px
style E fill:#f9f,stroke:#333,stroke-width:2px
1.1.1 Control Flow Diagrams
We can visualize the flow of an if statement using a control flow diagram. Alongside the if statement structure in Listing 1.1, we also included a control flow diagram in Figure 1.1. By following the arrows in the diagram from the start to the end of the process we can see a step-by-step breakdown of the process involved in executing an if statement.
The control flow diagram for the if statement consists of five steps:
- Start: Begin the process
- Condition: Check if the condition is true or false
-
If true: Execute the code in the
ifblock -
If false: Skip the
ifblock and continue to the end - End: Finish the process
For each step, the diagram uses color-coding and shapes for clarity. We’ve created a key in Figure 1.2 to explain the symbols used in the flow chart.
graph LR
A([Start/End]) --- A1([Oval: Indicates the start or end of a process])
style A fill:#f9f,stroke:#333,stroke-width:2px
style A1 fill:#fff,stroke:#fff,stroke-width:0px
B{Decision} --- B1[Diamond: Represents a decision or branching point]
style B fill:#bbf,stroke:#333,stroke-width:2px
style B1 fill:#fff,stroke:#fff,stroke-width:0px
C[Process] --- C1[Rectangle: Represents a process or action step]
style C fill:#dfd,stroke:#333,stroke-width:2px
style C1 fill:#fff,stroke:#fff,stroke-width:0px
D((Connector)) --- D1[Circle: Used as a connector between flow lines]
style D fill:#fff,stroke:#333,stroke-width:2px
style D1 fill:#fff,stroke:#fff,stroke-width:0px
E[/Input/Output/] --- E1[Parallelogram: Represents input or output operations]
style E fill:#ffd,stroke:#333,stroke-width:2px
style E1 fill:#fff,stroke:#fff,stroke-width:0px
linkStyle 0 stroke-width:0px
linkStyle 1 stroke-width:0px
linkStyle 2 stroke-width:0px
linkStyle 3 stroke-width:0px
linkStyle 4 stroke-width:0px
We’ll frequently use these diagrams to illustrate the flow of control structures.
1.1.2 Example: Classifying a Value Based on a Threshold
Let’s consider an example of threshold-based classification, a fundamental concept in statistics often used for decision-making. In this scenario, we evaluate a value against a predetermined threshold to categorize it accordingly. Usually, we will estimate the value of a variable and compare it to a pre-set threshold.
For instance, if we have a test score and want to determine if it meets the passing threshold, we can use an if statement. Suppose we have a score of 75 and a passing threshold of 80, we can use the following code:
value <- 75
threshold <- 80
if (value >= threshold) {
print("Pass")
}graph LR
A([Start]) --> B["value = 75<br>threshold = 80"]
B --> C{"value ≥ threshold"}
C -->|TRUE| D["Print 'Pass'"]
C -->|FALSE| F([End])
D --> F
style A fill:#f9f,stroke:#333,stroke-width:2px
style B fill:#dfd,stroke:#333,stroke-width:2px
style C fill:#bbf,stroke:#333,stroke-width:2px
style F fill:#f9f,stroke:#333,stroke-width:2px
In this example, the program checks if the score meets or exceeds the threshold. If it does, it prints "Pass". In this case, since 75 is less than 80, the condition value >= threshold is FALSE. Therefore, the code inside the if block (printing "Pass") is not executed.
In the next section, we’ll explore the if-else statement, which allows us to specify an alternative action if the condition is not met.
1.2 if-else Statements
In real life, we often have backup plans when making decisions. For example:
- if it’s raining, take an umbrella; otherwise, bring sunglasses.
- if the traffic is heavy, take a different route; otherwise, stay on the same route.
- if you’re hungry, eat a snack; otherwise, wait for the next meal.
These scenarios illustrate conditional decisions with both primary and secondary actions. In programming, we use similar logic to control program flow. The if-else statement in R allows us to execute one block of code if a condition is true and another different block of code if it’s false. The structure of an if-else statement and its control flow diagram are shown in Listing 1.2 and Figure 1.4, respectively.
if (condition) {
# code to execute if condition is TRUE
} else {
# code to execute if condition is FALSE
}graph TD
A([Start]) --> B{Condition}
B -->|"<condition> is TRUE"| C[Execute if block]
B -->|"<condition> is FALSE"| D[Execute else block]
C --> E([End])
D --> E
style A fill:#f9f,stroke:#333,stroke-width:2px
style B fill:#bbf,stroke:#333,stroke-width:2px
style C fill:#dfd,stroke:#333,stroke-width:2px
style D fill:#dfd,stroke:#333,stroke-width:2px
style E fill:#f9f,stroke:#333,stroke-width:2px
1.2.1 Example: Revisiting Classifying a value based on a threshold
Let’s revisit the example of classifying a value based on a threshold. In this case, we’ll use an if-else statement to provide outcomes for both scenarios. Just as before, we’ll print "Pass" if the value is greater than or equal to the threshold. With the addition of the else clause, we’ll print "Fail" if the value is less than the threshold.
[1] "Fail"graph LR
A([Start]) --> B["`value = 75
threshold = 80`"]
B --> C{"value ≥ threshold"}
C -->|TRUE| D["Print 'Pass'"]
C -->|FALSE| E["Print 'Fail'"]
D --> F([End])
E --> F
style A fill:#f9f,stroke:#333,stroke-width:2px
style B fill:#dfd,stroke:#333,stroke-width:2px
style C fill:#bbf,stroke:#333,stroke-width:2px
style F fill:#f9f,stroke:#333,stroke-width:2px
1.2.2 Example: Significance Testing
In statistical analysis, we often use p-values to determine the significance of results. A \(p\)-value is a measure of the strength of evidence against the null hypothesis. If the \(p\)-value is less than a pre-set significance level (usually \(\alpha = 0.05\)), we reject the null hypothesis. We can use an if-else statement to determine the significance of a \(p\)-value.
In the following example, we’ll check if a p-value is less than the significance level of 0.05. If it is, we’ll print "Reject the null hypothesis."; otherwise, we’ll print "Do not reject the null hypothesis".
# Sample p-value from a statistical test
p_value <- 0.03 # Example p-value
# Significance level
alpha <- 0.05
# Check the significance of the p-value
if (p_value < alpha) {
print("Reject the null hypothesis.")
} else {
print("Do not reject the null hypothesis.")
}[1] "Reject the null hypothesis."graph LR
A([Start]) --> B["`*p*-value = 0.03
alpha = 0.05`"]
B --> C{"value ≥ threshold"}
C -->|TRUE| D["Print 'Reject the null hypothesis'"]
C -->|FALSE| E["Print 'Do not reject the null hypothesis.'"]
D --> F([End])
E --> F
style A fill:#f9f,stroke:#333,stroke-width:2px
style B fill:#dfd,stroke:#333,stroke-width:2px
style C fill:#bbf,stroke:#333,stroke-width:2px
style F fill:#f9f,stroke:#333,stroke-width:2px
style E fill:#dfd,stroke:#333,stroke-width:2px