selection-control.qmd

# 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.

## 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 @lst-if-bare-bones. 

:::{.columns}


:::{.column}
```{r}
#| eval: false
#| lst-label: lst-if-bare-bones
#| lst-cap: if Statement Structure
if (condition) {
  # Action if condition is true
}
```
:::

:::{.column}
```{mermaid}
%%| echo: false
%%| label: fig-if-bare-bones
%%| fig-cap: Visual flow of an if statement.
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
```
:::


:::




### Control Flow Diagrams

We can visualize the flow of an `if` statement using a control flow diagram.
Alongside the `if` statement structure in @lst-if-bare-bones, we also included
a control flow diagram in @fig-if-bare-bones. 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:

1. **Start**: Begin the process
2. **Condition**: Check if the condition is true or false
3. **If true**: Execute the code in the `if` block
4. **If false**: Skip the `if` block and continue to the end
5. **End**: Finish the process

For each step, the diagram uses color-coding and shapes for clarity. We've 
created a key in @fig-flow-chart-key to explain the symbols used in the flow chart. 

```{mermaid}
%%| label: fig-flow-chart-key
%%| fig-cap: Symbols used in constructing the flow chart diagram for control flow.
%%| echo: false
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.


### 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:

```r
value <- 75
threshold <- 80

if (value >= threshold) {
  print("Pass")
}
```

```{mermaid}
%%| label: fig-if-threshold-example
%%| fig-cap: Visual representation of the if statement with a threshold.
%%| echo: false
graph LR
    A([Start]) --> B["value = 75<br>threshold = 80"]
    B --> C{"value &ge; 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.


## 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 @lst-if-else-bare-bones
and @fig-if-else-bare-bones, respectively.

:::{.columns}


:::{.column}
```{r}
#| eval: false
#| lst-label: lst-if-else-bare-bones
#| lst-cap: if-else Statement Structure
if (condition) {
  # code to execute if condition is TRUE
} else {
  # code to execute if condition is FALSE
}
```
:::

:::{.column}
```{mermaid}
%%| echo: false
%%| label: fig-if-else-bare-bones
%%| fig-cap: Visual representation of the if-else statement.
graph TD
    A([Start])  --> B{Condition}
    B -->|"&lt;condition&gt; is TRUE"| C[Execute if block]
    B -->|"&lt;condition&gt; 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
```
:::


:::


### 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. 

```{r}
value <- 75
threshold <- 80

if (value >= threshold) {
  print("Pass")
} else {
  print("Fail")
}
```


```{mermaid}
%%| label: fig-if-else-threshold-example
%%| fig-cap: Visual representation of the if-else statement with a threshold.
%%| echo: false
graph LR
    A([Start]) --> B["`value = 75
    threshold = 80`"]
    B --> C{"value &ge; 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
```

### 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"`.


```{r}
# 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.")
}
```


```{mermaid}
%%| label: fig-if-else-p-value-example
%%| fig-cap: Visual representation of the if-else statement applied to significance testing
%%| echo: false
graph LR
    A([Start]) --> B["`*p*-value = 0.03
    alpha = 0.05`"]
    B --> C{"value &ge; 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
```