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Concepto y Fundamentos; La Variable Confusora; Ejemplos Clásicos y Reales; Impacto en Decisiones y Políticas; Estrategias de Detección y Control

La Paradoja de Simpson

Ciencias Ambientales

La Paradoja de Simpson

Cuando la intuición estadística falla.

Índice

• Concepto y Fundamentos

• La Variable Confusora

• Ejemplos Clásicos y Reales

• Impacto en Decisiones y Políticas

• Estrategias de Detección y Control

Introducción a la Paradoja de Simpson

La Paradoja de Simpson es un fenómeno estadístico donde una tendencia observada en grupos de datos individuales se invierte o desaparece al combinar esos grupos. Este efecto desafía nuestra intuición lógica, mostrando cómo las conclusiones sobre subgrupos pueden ser opuestas a las del total.

Análisis de gráficos de líneas y barras para tendencias de datos.

Datos Agregados vs. Desagregados

Los datos agregados combinan toda la información; los desagregados la dividen en subgrupos. La paradoja surge al comparar promedios generales con los de subgrupos, revelando conclusiones opuestas. Analizar ambos es crucial.

Gráficos: elija la representación adecuada para sus datos.

Alfabetización gráfica en combinatoria: distribuciones y datos.

El Corazón de la Paradoja: La Variable Confusora

• Causa principal de la Paradoja de Simpson.

• Una tercera variable no considerada inicialmente.

• Influye tanto en la causa como en el efecto.

• Distorsiona la relación observada al principio.

Ejemplo Clásico: Eficacia de Tratamientos Médicos

Analicemos dos tratamientos para cálculos renales. En general, el Tratamiento A parece mejor. Pero, al separar por tamaño de cálculo, el Tratamiento B es superior en ambos casos.

Caso Real: Admisiones Universitarias en Berkeley (1973)

En 1973, la Universidad de Berkeley fue acusada de discriminar a mujeres en admisiones. Los datos agregados lo sugerían. Sin embargo, al analizar por departamento, se reveló que las mujeres postulaban a carreras más competitivas, revirtiendo la conclusión.

Campus de conocimiento: Admisiones universitarias en Berkeley.

Deportes: El Rendimiento de Jugadores de Béisbol

Un jugador puede batear mejor en cada temporada individual que otro. Sin embargo, al combinar ambas temporadas, su promedio total puede ser inferior. Esto ocurre si la cantidad de turnos al bate varía significativamente.

Aceleración instantánea en el béisbol: el momento del impacto.

Salud Pública: Vacunas y Datos de COVID-19

En datos agregados de COVID-19, los vacunados podrían parecer más afectados. Esto es un artefacto de la Paradoja de Simpson. La edad o comorbilidades no controladas distorsionan la interpretación real.

Profesional de salud administra vacuna para prevenir enfermedades.

Profesional de salud analiza datos con probabilidad condicional.

Mecanismos: Sesgo de Selección y Distribución Desigual

• No siempre es sesgo intencional.

• Variable confusora distribuida desigualmente.

• Pacientes graves reciben tratamientos novedosos.

• Crea correlación engañosa (espuria).

La Paradoja de Simpson

Concepto y Fundamentos; La Variable Confusora; Ejemplos Clásicos y Reales; Impacto en Decisiones y Políticas; Estrategias de Detección y Control

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