2. Análisis de Scott-Knott
El procedimiento de Scott y Knott (1974) es una técnica que utiliza la prueba de la razón de verosimilitud para agrupar n tratamientos en k grupos.
Ejemplo 1:
Aplicaremos el análisis de Scott-Knott para agrupar los tratamientos del cuadro siguiente en grupos similares.
| N | P | K | BLK | Y |
|---|---|---|---|---|
| n0 | p0 | k0 | 1 | 1.32 |
| n0 | p0 | k0 | 2 | 2.12 |
| n0 | p0 | k0 | 3 | 1.75 |
| n0 | p0 | k0 | 4 | 2.35 |
| n0 | p0 | k1 | 1 | 2.58 |
| n0 | p0 | k1 | 2 | 3.56 |
| n0 | p0 | k1 | 3 | 2.86 |
| n0 | p0 | k1 | 4 | 2.75 |
| n0 | p1 | k0 | 1 | 1.66 |
| n0 | p1 | k0 | 2 | 2.66 |
| n0 | p1 | k0 | 3 | 1.73 |
| n0 | p1 | k0 | 4 | 2.58 |
| n0 | p1 | k1 | 1 | 2.26 |
| n0 | p1 | k1 | 2 | 2.08 |
| n0 | p1 | k1 | 3 | 1.95 |
| n0 | p1 | k1 | 4 | 2.7 |
| n1 | p0 | k0 | 1 | 1.8 |
| n1 | p0 | k0 | 2 | 2.2 |
| n1 | p0 | k0 | 3 | 2.95 |
| n1 | p0 | k0 | 4 | 2.96 |
| n1 | p0 | k1 | 1 | 2.72 |
| n1 | p0 | k1 | 2 | 3.2 |
| n1 | p0 | k1 | 3 | 2.25 |
| n1 | p0 | k1 | 4 | 2.75 |
| n1 | p1 | k0 | 1 | 1.72 |
| n1 | p1 | k0 | 2 | 3.85 |
| n1 | p1 | k0 | 3 | 2.62 |
| n1 | p1 | k0 | 4 | 3 |
| n1 | p1 | k1 | 1 | 2.95 |
| n1 | p1 | k1 | 2 | 3.28 |
| n1 | p1 | k1 | 3 | 2.4 |
| n1 | p1 | k1 | 4 | 3.35 |
Subiremos los datos al sistema.
El análisis de Scott-Knott se realizará con la configuración que se muestra en la siguiente figura.
Clicando en calcular obtenemos los resultados. También se puede descargar los resultados en un archivo en formato Word.
Los resultados son:
Agrupación (algoritmo de Scott-Knott)
| Grupos | Media | Scott-Knott | Media+Error Estándar | Media - Error Estándar |
|---|---|---|---|---|
| n1 | 2.750 | a | 2.607 | 2.893 |
| n0 | 2.307 | b | 2.166 | 2.448 |
Ejemplo 2:
Los datos del siguiente cuadro se refieren a 45 tipos diferentes de tratamientos (columna X) con 4 réplicas cada uno (columna R). Las respuestas se midieron en la columna “Y”. Apliquemos el análisis de Scott-Knott para agrupar estos tratamientos en grupos similares.
| X | R | Y |
|---|---|---|
| tr-1 | 1 | 303.71 |
| tr-1 | 2 | 387.48 |
| tr-1 | 3 | 243.12 |
| tr-1 | 4 | 244.41 |
| tr-2 | 1 | 243.27 |
| tr-2 | 2 | 308.71 |
| tr-2 | 3 | 379.08 |
| tr-2 | 4 | 466.34 |
| tr-3 | 1 | 353.43 |
| tr-3 | 2 | 430.22 |
| tr-3 | 3 | 389.47 |
| tr-3 | 4 | 395.17 |
| tr-4 | 1 | 432.32 |
| tr-4 | 2 | 451.5 |
| tr-4 | 3 | 449.89 |
| tr-4 | 4 | 422.23 |
| tr-5 | 1 | 461.81 |
| tr-5 | 2 | 460.31 |
| tr-5 | 3 | 450.64 |
| tr-5 | 4 | 452.64 |
| tr-6 | 1 | 343.64 |
| tr-6 | 2 | 360.03 |
| tr-6 | 3 | 424.08 |
| tr-6 | 4 | 389.52 |
| tr-7 | 1 | 353.85 |
| tr-7 | 2 | 505.1 |
| tr-7 | 3 | 347.18 |
| tr-7 | 4 | 409.39 |
| tr-8 | 1 | 376.46 |
| tr-8 | 2 | 383.6 |
| tr-8 | 3 | 368.52 |
| tr-8 | 4 | 379.59 |
| tr-9 | 1 | 397.32 |
| tr-9 | 2 | 382.49 |
| tr-9 | 3 | 372.34 |
| tr-9 | 4 | 395.65 |
| tr-10 | 1 | 402.68 |
| tr-10 | 2 | 388.91 |
| tr-10 | 3 | 377.91 |
| tr-10 | 4 | 391.31 |
| tr-11 | 1 | 370.65 |
| tr-11 | 2 | 381.84 |
| tr-11 | 3 | 378.9 |
| tr-11 | 4 | 390.16 |
| tr-12 | 1 | 387.94 |
| tr-12 | 2 | 401.63 |
| tr-12 | 3 | 398.43 |
| tr-12 | 4 | 393.95 |
| tr-13 | 1 | 405.28 |
| tr-13 | 2 | 388.02 |
| tr-13 | 3 | 375.33 |
| tr-13 | 4 | 421.38 |
| tr-14 | 1 | 389.74 |
| tr-14 | 2 | 394.8 |
| tr-14 | 3 | 379.14 |
| tr-14 | 4 | 370.75 |
| tr-15 | 1 | 383.01 |
| tr-15 | 2 | 378.22 |
| tr-15 | 3 | 392.4 |
| tr-15 | 4 | 391.19 |
| tr-16 | 1 | 306.69 |
| tr-16 | 2 | 386.29 |
| tr-16 | 3 | 249.55 |
| tr-16 | 4 | 243.92 |
| tr-17 | 1 | 256.87 |
| tr-17 | 2 | 312.19 |
| tr-17 | 3 | 378.55 |
| tr-17 | 4 | 467 |
| tr-18 | 1 | 356.05 |
| tr-18 | 2 | 443.09 |
| tr-18 | 3 | 391.43 |
| tr-18 | 4 | 386.47 |
| tr-19 | 1 | 421.96 |
| tr-19 | 2 | 453.42 |
| tr-19 | 3 | 461.09 |
| tr-19 | 4 | 423.83 |
| tr-20 | 1 | 463.66 |
| tr-20 | 2 | 462.27 |
| tr-20 | 3 | 451.75 |
| tr-20 | 4 | 456.44 |
| tr-21 | 1 | 348.77 |
| tr-21 | 2 | 362.53 |
| tr-21 | 3 | 429.85 |
| tr-21 | 4 | 391.1 |
| tr-22 | 1 | 354.74 |
| tr-22 | 2 | 519.12 |
| tr-22 | 3 | 349.15 |
| tr-22 | 4 | 420.63 |
| tr-23 | 1 | 378.47 |
| tr-23 | 2 | 385.42 |
| tr-23 | 3 | 371.61 |
| tr-23 | 4 | 371.75 |
| tr-24 | 1 | 389.87 |
| tr-24 | 2 | 392.98 |
| tr-24 | 3 | 371.85 |
| tr-24 | 4 | 394.08 |
| tr-25 | 1 | 420.47 |
| tr-25 | 2 | 390.08 |
| tr-25 | 3 | 378.94 |
| tr-25 | 4 | 380.15 |
| tr-26 | 1 | 372.57 |
| tr-26 | 2 | 384.68 |
| tr-26 | 3 | 383.08 |
| tr-26 | 4 | 397.54 |
| tr-27 | 1 | 385.02 |
| tr-27 | 2 | 389.89 |
| tr-27 | 3 | 399.57 |
| tr-27 | 4 | 398.8 |
| tr-28 | 1 | 410.15 |
| tr-28 | 2 | 387.02 |
| tr-28 | 3 | 378.37 |
| tr-28 | 4 | 423.13 |
| tr-29 | 1 | 390.52 |
| tr-29 | 2 | 399.14 |
| tr-29 | 3 | 380.5 |
| tr-29 | 4 | 382.63 |
| tr-30 | 1 | 388.67 |
| tr-30 | 2 | 388.44 |
| tr-30 | 3 | 392.69 |
| tr-30 | 4 | 393.38 |
| tr-31 | 1 | 325.99 |
| tr-31 | 2 | 381.41 |
| tr-31 | 3 | 273.55 |
| tr-31 | 4 | 248.53 |
| tr-32 | 1 | 253.63 |
| tr-32 | 2 | 314.45 |
| tr-32 | 3 | 379.23 |
| tr-32 | 4 | 467.72 |
| tr-33 | 1 | 375.61 |
| tr-33 | 2 | 434.47 |
| tr-33 | 3 | 380.64 |
| tr-33 | 4 | 396.86 |
| tr-34 | 1 | 434.89 |
| tr-34 | 2 | 455.26 |
| tr-34 | 3 | 438.48 |
| tr-34 | 4 | 425.06 |
| tr-35 | 1 | 462.11 |
| tr-35 | 2 | 451.76 |
| tr-35 | 3 | 470.8 |
| tr-35 | 4 | 451.99 |
| tr-36 | 1 | 345.65 |
| tr-36 | 2 | 361.05 |
| tr-36 | 3 | 426.21 |
| tr-36 | 4 | 390.07 |
| tr-37 | 1 | 354.8 |
| tr-37 | 2 | 496.63 |
| tr-37 | 3 | 348.22 |
| tr-37 | 4 | 410.72 |
| tr-38 | 1 | 387.07 |
| tr-38 | 2 | 365.21 |
| tr-38 | 3 | 372.14 |
| tr-38 | 4 | 384.97 |
| tr-39 | 1 | 410.36 |
| tr-39 | 2 | 386.29 |
| tr-39 | 3 | 376.62 |
| tr-39 | 4 | 398.01 |
| tr-40 | 1 | 384.49 |
| tr-40 | 2 | 369.99 |
| tr-40 | 3 | 384.72 |
| tr-40 | 4 | 375.07 |
| tr-41 | 1 | 383.9 |
| tr-41 | 2 | 393.21 |
| tr-41 | 3 | 371.61 |
| tr-41 | 4 | 391.21 |
| tr-42 | 1 | 388.59 |
| tr-42 | 2 | 401.63 |
| tr-42 | 3 | 400.36 |
| tr-42 | 4 | 388.48 |
| tr-43 | 1 | 405.39 |
| tr-43 | 2 | 389.75 |
| tr-43 | 3 | 376.22 |
| tr-43 | 4 | 419.04 |
| tr-44 | 1 | 391.31 |
| tr-44 | 2 | 389.96 |
| tr-44 | 3 | 389.71 |
| tr-44 | 4 | 372.49 |
| tr-45 | 1 | 387.07 |
| tr-45 | 2 | 380.8 |
| tr-45 | 3 | 392.53 |
| tr-45 | 4 | 380.93 |
Subiremos los datos al sistema.
El análisis de Scott-Knott se realizará con la configuración que se muestra en la siguiente figura.
Clicando en calcular obtenemos los resultados. También se puede descargar los resultados en un archivo en formato Word.
Los resultados son:
Agrupación (algoritmo de Scott-Knott)
| Grupos | Media | Scott-Knott | Media + Error Estándar | Media - Error |
|---|---|---|---|---|
| tr-35 | 459.165 | a | 454.597 | 463.733 |
| tr-20 | 458.530 | a | 455.782 | 461.278 |
| tr-5 | 456.350 | a | 453.583 | 459.117 |
| tr-19 | 440.075 | a | 430.026 | 450.124 |
| tr-4 | 438.985 | a | 431.910 | 446.060 |
| tr-34 | 438.423 | a | 432.134 | 444.711 |
| tr-22 | 410.910 | b | 371.357 | 450.463 |
| tr-7 | 403.880 | b | 367.372 | 440.388 |
| tr-37 | 402.593 | b | 368.254 | 436.931 |
| tr-28 | 399.668 | b | 389.364 | 409.971 |
| tr-43 | 397.600 | b | 388.295 | 406.905 |
| tr-13 | 397.502 | b | 387.452 | 407.553 |
| tr-33 | 396.895 | b | 383.575 | 410.215 |
| tr-12 | 395.488 | b | 392.519 | 398.456 |
| tr-42 | 394.765 | b | 391.159 | 398.371 |
| tr-18 | 394.260 | b | 376.202 | 412.318 |
| tr-27 | 393.320 | b | 389.787 | 396.853 |
| tr-39 | 392.820 | b | 385.519 | 400.121 |
| tr-25 | 392.410 | b | 382.730 | 402.090 |
| tr-3 | 392.072 | b | 376.354 | 407.791 |
| tr-30 | 390.795 | b | 389.493 | 392.097 |
| tr-10 | 390.202 | b | 385.122 | 395.283 |
| tr-29 | 388.197 | b | 383.961 | 392.434 |
| tr-24 | 387.195 | b | 382.003 | 392.387 |
| tr-9 | 386.950 | b | 381.058 | 392.842 |
| tr-15 | 386.205 | b | 382.824 | 389.586 |
| tr-44 | 385.868 | b | 381.395 | 390.340 |
| tr-45 | 385.332 | b | 382.523 | 388.142 |
| tr-41 | 384.982 | b | 380.097 | 389.868 |
| tr-26 | 384.467 | b | 379.349 | 389.586 |
| tr-14 | 383.608 | b | 378.221 | 388.994 |
| tr-21 | 383.062 | b | 365.148 | 400.977 |
| tr-36 | 380.745 | b | 363.012 | 398.478 |
| tr-11 | 380.387 | b | 376.360 | 384.415 |
| tr-6 | 379.317 | b | 361.634 | 397.001 |
| tr-40 | 378.567 | b | 374.930 | 382.205 |
| tr-38 | 377.347 | b | 372.127 | 382.568 |
| tr-8 | 377.043 | b | 373.848 | 380.237 |
| tr-23 | 376.812 | b | 373.527 | 380.098 |
| tr-32 | 353.757 | c | 307.925 | 399.590 |
| tr-17 | 353.653 | c | 308.418 | 398.887 |
| tr-2 | 349.350 | c | 301.500 | 397.200 |
| tr-31 | 307.370 | d | 277.882 | 336.858 |
| tr-16 | 296.613 | d | 263.528 | 329.697 |
| tr-1 | 294.680 | d | 260.672 | 328.688 |
Según el análisis de Scott-Knott con un nivel de confianza del 95%, todos 45 tratamientos se pueden dividir en 4 grupos distintos,como se muestra en Gráfico de Scott-Knott en la figura anterior.
Ejemplo 3:
Los datos de la tabla tienen cinco tipos de tratamientos (A, B, C, D y E). Apliquemos el método de Scott-Knott para agrupar estos tratamientos.
| Tratamiento | Filas | Columnas | Y |
|---|---|---|---|
| A | 1 | 2 | 52.61 |
| A | 2 | 3 | 54.18 |
| A | 3 | 5 | 40.32 |
| A | 4 | 4 | 46.21 |
| A | 5 | 1 | 50.97 |
| B | 1 | 3 | 45.91 |
| B | 2 | 4 | 56.98 |
| B | 3 | 2 | 39.04 |
| B | 4 | 1 | 48.53 |
| B | 5 | 5 | 30.62 |
| C | 1 | 4 | 58.97 |
| C | 2 | 1 | 73.07 |
| C | 3 | 3 | 56.12 |
| C | 4 | 5 | 50.2 |
| C | 5 | 2 | 66.19 |
| D | 1 | 1 | 43.93 |
| D | 2 | 5 | 40.81 |
| D | 3 | 4 | 31.01 |
| D | 4 | 2 | 50.74 |
| D | 5 | 3 | 41.94 |
| E | 1 | 5 | 31.94 |
| E | 2 | 2 | 47.83 |
| E | 3 | 1 | 46.26 |
| E | 4 | 3 | 31.32 |
| E | 5 | 4 | 38.95 |
Subiremos los datos al sistema.
El análisis de Scott-Knott se realizará con la configuración que se muestra en la siguiente figura.
Pulsando en calcular obtenemos los resultados. También se puede descargar los resultados en un archivo en formato word.
Los resultados son:
Agrupamiento (Scott-Knott Algorithm)
| Grupos | Media | Scott-Knott | Media + Error Estándar | Media - Error Estándar |
|---|---|---|---|---|
| C | 60.910 | a | 52.006 | 69.814 |
| A | 48.858 | b | 43.2284 | 54.4876 |
| B | 44.216 | b | 34.266 | 54.166 |
| D | 41.686 | b | 34.583 | 48.789 |
| E | 39.26 | b | 31.5275 | 46.992 |
Del análisis Scott-Knott se puede ver que los cinco tratamientos pueden ser agrupados en solo dos grupos. Un grupo que contiene solo el tratamiento C y el otro que contiene los tratamientos A.B.D y E.
El nivel de confianza puede cambiar directamente los resultados del análisis.
Sugerencia: Repite el procedimiento anterior cambiando el nivel de confianza al 75% (0.75) para ver la diferencia.