Correlation, Causation, Confounding, and Spurious Relationships

/**
 * Fintech Math Bootcamp · Lesson 085 of 120
 * Correlation, Causation, Confounding, and Spurious Relationships
 * Module 09: Dependence, Regression, and Model Foundations
 *
 * Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
 * Rule:     association ≠ effect of intervention
 *
 * Try it:   Does this grouped example prove a causal benefit from switching every case to B?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson085() {
  const a={easyRecovered:90,easy:100,hardRecovered:1,hard:10};
  const b={easyRecovered:19,easy:20,hardRecovered:20,hard:100};
  const result={pooledA:(a.easyRecovered+a.hardRecovered)/(a.easy+a.hard),
    pooledB:(b.easyRecovered+b.hardRecovered)/(b.easy+b.hard),
    easy:[a.easyRecovered/a.easy,b.easyRecovered/b.easy],
    hard:[a.hardRecovered/a.hard,b.hardRecovered/b.hard]};
  return result;
}

export const checkedResult = {"pooledA":0.8272727272727273,"pooledB":0.325,"easy":[0.9,0.95],"hard":[0.1,0.2]};

// Run this file directly: npx tsx lessons/09-dependence-regression-and-model-foundations/085-correlation-causation-confounding-and-spurious-relationships.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson085(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 085 of 120
Correlation, Causation, Confounding, and Spurious Relationships
Module 09: Dependence, Regression, and Model Foundations

Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
Rule:     association ≠ effect of intervention

Try it:   Does this grouped example prove a causal benefit from switching every case to B?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.
"""

import json


def lesson_085():
    a = {"easy_recovered": 90, "easy": 100, "hard_recovered": 1, "hard": 10}
    b = {"easy_recovered": 19, "easy": 20, "hard_recovered": 20, "hard": 100}
    return {
        "pooledA": (a["easy_recovered"] + a["hard_recovered"]) / (a["easy"] + a["hard"]),
        "pooledB": (b["easy_recovered"] + b["hard_recovered"]) / (b["easy"] + b["hard"]),
        "easy": [a["easy_recovered"] / a["easy"], b["easy_recovered"] / b["easy"]],
        "hard": [a["hard_recovered"] / a["hard"], b["hard_recovered"] / b["hard"]],
    }


if __name__ == "__main__":
    print(json.dumps(lesson_085(), indent=2))

// Fintech Math Bootcamp - Lesson 085 of 120
// Correlation, Causation, Confounding, and Spurious Relationships
// Module 09: Dependence, Regression, and Model Foundations
//
// Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
// Rule:     association != effect of intervention
//
// Try it:   Does this grouped example prove a causal benefit from switching every case to B?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;

public class Main {
    // Recovered and total case counts by difficulty.
    static final class Outcomes {
        final double easyRecovered, easy, hardRecovered, hard;

        Outcomes(double easyRecovered, double easy, double hardRecovered, double hard) {
            this.easyRecovered = easyRecovered;
            this.easy = easy;
            this.hardRecovered = hardRecovered;
            this.hard = hard;
        }
    }

    static Map<String, Object> lesson085() {
        Outcomes a = new Outcomes(90, 100, 1, 10);
        Outcomes b = new Outcomes(19, 20, 20, 100);
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("pooledA", (a.easyRecovered + a.hardRecovered) / (a.easy + a.hard));
        result.put("pooledB", (b.easyRecovered + b.hardRecovered) / (b.easy + b.hard));
        result.put("easy", new double[] {a.easyRecovered / a.easy, b.easyRecovered / b.easy});
        result.put("hard", new double[] {a.hardRecovered / a.hard, b.hardRecovered / b.hard});
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson085(), ""));
    }

    // Minimal JSON writer: two-space indent, whole numbers without a decimal point, NaN as null.
    static String toJson(Object value, String indent) {
        if (value == null) return "null";
        if (value instanceof Boolean) return value.toString();
        if (value instanceof Number) return formatNumber(((Number) value).doubleValue());
        if (value instanceof String) return quote((String) value);
        if (value instanceof double[]) {
            List<Object> boxed = new ArrayList<Object>();
            for (double d : (double[]) value) boxed.add(d);
            return toJson(boxed, indent);
        }
        if (value instanceof Object[]) return toJson(Arrays.asList((Object[]) value), indent);
        String inner = indent + "  ";
        StringBuilder out = new StringBuilder();
        if (value instanceof Map) {
            Map<?, ?> map = (Map<?, ?>) value;
            if (map.isEmpty()) return "{}";
            out.append("{\n");
            int i = 0;
            for (Map.Entry<?, ?> entry : map.entrySet()) {
                out.append(inner).append(quote(entry.getKey().toString())).append(": ")
                   .append(toJson(entry.getValue(), inner));
                out.append(++i < map.size() ? ",\n" : "\n");
            }
            return out.append(indent).append("}").toString();
        }
        List<?> list = (List<?>) value;
        if (list.isEmpty()) return "[]";
        out.append("[\n");
        for (int i = 0; i < list.size(); i++) {
            out.append(inner).append(toJson(list.get(i), inner));
            out.append(i + 1 < list.size() ? ",\n" : "\n");
        }
        return out.append(indent).append("]").toString();
    }

    static String formatNumber(double x) {
        if (Double.isNaN(x) || Double.isInfinite(x)) return "null";
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return Long.toString((long) x);
        return Double.toString(x);
    }

    static String quote(String s) {
        StringBuilder out = new StringBuilder("\"");
        for (char c : s.toCharArray()) {
            if (c == '"' || c == '\\') out.append('\\').append(c);
            else if (c == '\n') out.append("\\n");
            else if (c < 0x20) out.append(String.format("\\u%04x", (int) c));
            else out.append(c);
        }
        return out.append('"').toString();
    }
}

// Fintech Math Bootcamp · Lesson 085 of 120
// Correlation, Causation, Confounding, and Spurious Relationships
// Module 09: Dependence, Regression, and Model Foundations
//
// Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
// Rule:     association ≠ effect of intervention
//
// Try it:   Does this grouped example prove a causal benefit from switching every case to B?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
package main

import (
	"encoding/json"
	"fmt"
)

type Lesson085Result struct {
	PooledA float64   `json:"pooledA"`
	PooledB float64   `json:"pooledB"`
	Easy    []float64 `json:"easy"`
	Hard    []float64 `json:"hard"`
}

// Outcomes holds recovered and total case counts by difficulty.
type Outcomes struct {
	EasyRecovered, Easy, HardRecovered, Hard float64
}

func lesson085() Lesson085Result {
	a := Outcomes{EasyRecovered: 90, Easy: 100, HardRecovered: 1, Hard: 10}
	b := Outcomes{EasyRecovered: 19, Easy: 20, HardRecovered: 20, Hard: 100}
	return Lesson085Result{
		PooledA: (a.EasyRecovered + a.HardRecovered) / (a.Easy + a.Hard),
		PooledB: (b.EasyRecovered + b.HardRecovered) / (b.Easy + b.Hard),
		Easy:    []float64{a.EasyRecovered / a.Easy, b.EasyRecovered / b.Easy},
		Hard:    []float64{a.HardRecovered / a.Hard, b.HardRecovered / b.Hard},
	}
}

func main() {
	out, err := json.MarshalIndent(lesson085(), "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

// Fintech Math Bootcamp · Lesson 085 of 120
// Correlation, Causation, Confounding, and Spurious Relationships
// Module 09: Dependence, Regression, and Model Foundations
//
// Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
// Rule:     association ≠ effect of intervention
//
// Try it:   Does this grouped example prove a causal benefit from switching every case to B?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <optional>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>

// A minimal JSON value, enough to print this lesson's result.
struct Json {
    enum class Kind { Null, Bool, Number, String, Array, Object };
    Kind kind = Kind::Null;
    bool flag = false;
    double number = 0.0;
    std::string text;
    std::vector<std::string> keys;  // object keys, parallel to items
    std::vector<Json> items;        // array elements or object values

    Json() = default;
    Json(bool value) : kind(Kind::Bool), flag(value) {}
    Json(int value) : kind(Kind::Number), number(value) {}
    Json(double value) : kind(Kind::Number), number(value) {}
    Json(const char* value) : kind(Kind::String), text(value) {}
    Json(const std::string& value) : kind(Kind::String), text(value) {}
    Json(const std::vector<double>& values) : kind(Kind::Array) {
        for (double v : values) items.push_back(Json(v));
    }
};

Json jsonArray(const std::vector<Json>& values) {
    Json array;
    array.kind = Json::Kind::Array;
    array.items = values;
    return array;
}

Json jsonObject(const std::vector<std::pair<std::string, Json>>& fields) {
    Json object;
    object.kind = Json::Kind::Object;
    for (const auto& field : fields) {
        object.keys.push_back(field.first);
        object.items.push_back(field.second);
    }
    return object;
}

// Shortest decimal form that reads back as the same double.
std::string formatNumber(double x) {
    if (!std::isfinite(x)) return "null";
    char buffer[32];
    if (x == std::floor(x) && std::fabs(x) < 1e15) {
        std::snprintf(buffer, sizeof buffer, "%.0f", x);
        return buffer;
    }
    for (int precision = 1; precision <= 17; ++precision) {
        std::snprintf(buffer, sizeof buffer, "%.*g", precision, x);
        if (std::strtod(buffer, nullptr) == x) break;
    }
    return buffer;
}

std::string quote(const std::string& s) {
    std::string out = "\"";
    for (char c : s) {
        if (c == '"' || c == '\\') { out += '\\'; out += c; }
        else if (c == '\n') out += "\\n";
        else out += c;
    }
    return out + "\"";
}

std::string toJson(const Json& value, const std::string& indent = "") {
    switch (value.kind) {
        case Json::Kind::Null: return "null";
        case Json::Kind::Bool: return value.flag ? "true" : "false";
        case Json::Kind::Number: return formatNumber(value.number);
        case Json::Kind::String: return quote(value.text);
        default: break;
    }
    const bool isObject = value.kind == Json::Kind::Object;
    if (value.items.empty()) return isObject ? "{}" : "[]";
    const std::string inner = indent + "  ";
    std::string out = isObject ? "{\n" : "[\n";
    for (std::size_t i = 0; i < value.items.size(); ++i) {
        out += inner;
        if (isObject) out += quote(value.keys[i]) + ": ";
        out += toJson(value.items[i], inner);
        out += i + 1 < value.items.size() ? ",\n" : "\n";
    }
    return out + indent + (isObject ? "}" : "]");
}

// Recovered and total case counts by difficulty.
struct Outcomes {
    double easyRecovered, easy, hardRecovered, hard;
};

Json lesson085() {
    const Outcomes a{90, 100, 1, 10};
    const Outcomes b{19, 20, 20, 100};
    return jsonObject({
        {"pooledA", (a.easyRecovered + a.hardRecovered) / (a.easy + a.hard)},
        {"pooledB", (b.easyRecovered + b.hardRecovered) / (b.easy + b.hard)},
        {"easy", std::vector<double>{a.easyRecovered / a.easy, b.easyRecovered / b.easy}},
        {"hard", std::vector<double>{a.hardRecovered / a.hard, b.hardRecovered / b.hard}},
    });
}

int main() {
    std::cout << toJson(lesson085()) << '\n';
    return 0;
}

// Fintech Math Bootcamp · Lesson 085 of 120
// Correlation, Causation, Confounding, and Spurious Relationships
// Module 09: Dependence, Regression, and Model Foundations
//
// Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
// Rule:     association ≠ effect of intervention
//
// Try it:   Does this grouped example prove a causal benefit from switching every case to B?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

/// A minimal JSON value, enough to print this lesson's result.
#[allow(dead_code)]
enum Json {
    Null,
    Bool(bool),
    Num(f64),
    Str(String),
    Arr(Vec<Json>),
    Obj(Vec<(String, Json)>),
}

#[allow(dead_code)]
impl Json {
    fn obj(fields: Vec<(&str, Json)>) -> Json {
        Json::Obj(fields.into_iter().map(|(k, v)| (k.to_string(), v)).collect())
    }

    fn nums(values: &[f64]) -> Json {
        Json::Arr(values.iter().map(|&v| Json::Num(v)).collect())
    }

    /// Pretty-prints with two-space indentation.
    fn pretty(&self, indent: &str) -> String {
        let inner = format!("{}  ", indent);
        match self {
            Json::Null => "null".to_string(),
            Json::Bool(b) => b.to_string(),
            Json::Num(x) => format_number(*x),
            Json::Str(s) => quote(s),
            Json::Arr(items) if items.is_empty() => "[]".to_string(),
            Json::Obj(fields) if fields.is_empty() => "{}".to_string(),
            Json::Arr(items) => {
                let body: Vec<String> = items
                    .iter()
                    .map(|v| format!("{}{}", inner, v.pretty(&inner)))
                    .collect();
                format!("[\n{}\n{}]", body.join(",\n"), indent)
            }
            Json::Obj(fields) => {
                let body: Vec<String> = fields
                    .iter()
                    .map(|(k, v)| format!("{}{}: {}", inner, quote(k), v.pretty(&inner)))
                    .collect();
                format!("{{\n{}\n{}}}", body.join(",\n"), indent)
            }
        }
    }
}

fn format_number(x: f64) -> String {
    if !x.is_finite() {
        "null".to_string()
    } else if x == x.trunc() && x.abs() < 1e15 {
        format!("{}", x as i64)
    } else {
        format!("{}", x)
    }
}

fn quote(s: &str) -> String {
    let mut out = String::from("\"");
    for c in s.chars() {
        match c {
            '"' => out.push_str("\\\""),
            '\\' => out.push_str("\\\\"),
            '\n' => out.push_str("\\n"),
            c => out.push(c),
        }
    }
    out.push('"');
    out
}

/// Recovered and total case counts by difficulty.
struct Outcomes {
    easy_recovered: f64,
    easy: f64,
    hard_recovered: f64,
    hard: f64,
}

fn lesson_085() -> Json {
    let a = Outcomes { easy_recovered: 90.0, easy: 100.0, hard_recovered: 1.0, hard: 10.0 };
    let b = Outcomes { easy_recovered: 19.0, easy: 20.0, hard_recovered: 20.0, hard: 100.0 };
    Json::obj(vec![
        ("pooledA", Json::Num((a.easy_recovered + a.hard_recovered) / (a.easy + a.hard))),
        ("pooledB", Json::Num((b.easy_recovered + b.hard_recovered) / (b.easy + b.hard))),
        ("easy", Json::nums(&[a.easy_recovered / a.easy, b.easy_recovered / b.easy])),
        ("hard", Json::nums(&[a.hard_recovered / a.hard, b.hard_recovered / b.hard])),
    ])
}

fn main() {
    println!("{}", lesson_085().pretty(""));
}

// Fintech Math Bootcamp · Lesson 085 of 120
// Correlation, Causation, Confounding, and Spurious Relationships
// Module 09: Dependence, Regression, and Model Foundations
//
// Scenario: A pooled recovery-rate comparison that reverses within difficulty groups
// Rule:     association ≠ effect of intervention
//
// Try it:   Does this grouped example prove a causal benefit from switching every case to B?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true };
Console.WriteLine(JsonSerializer.Serialize(Lesson085(), options));

static object Lesson085()
{
    var a = new { easyRecovered = 90.0, easy = 100.0, hardRecovered = 1.0, hard = 10.0 };
    var b = new { easyRecovered = 19.0, easy = 20.0, hardRecovered = 20.0, hard = 100.0 };
    return new
    {
        pooledA = (a.easyRecovered + a.hardRecovered) / (a.easy + a.hard),
        pooledB = (b.easyRecovered + b.hardRecovered) / (b.easy + b.hard),
        easy = new[] { a.easyRecovered / a.easy, b.easyRecovered / b.easy },
        hard = new[] { a.hardRecovered / a.hard, b.hardRecovered / b.hard },
    };
}