Slide Análise de Variância-2021 2

❯◆■❉❆❉❊ ■■■ ▼❆❚ ✵✷✸ ✲ ❊st❛tíst✐❝❛ ■■ ❆ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ ❇❛❤✐❛ ✷✵✷✶✳✷ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶ ✴ ✸✶ ❆◆❖❱❆ ❆◆❖❱❆ ❆♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛ ❱✐♠♦s ♦ ♣r♦❝❡ss♦ ♣❛r❛ t❡st❛r ❛ ❤✐♣ót❡s❡ ❞❡ ✐❣✉❛❧❞❛❞❡ ❞❛s ♠é❞✐❛s ❞❡ ❞✉❛s ♣♦♣✉❧❛çõ❡s✳ ❆❣♦r❛✱ ✈❡r❡♠♦s ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ t❡st❛r ❛ ✐❣✉❛❧❞❛❞❡ ❞❛s ♠é❞✐❛s ❞❡ três ♦✉ ♠❛✐s ♣♦♣✉❧❛çõ❡s✱ ❜❛s❡❛❞♦ ♥❛ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛s ❛♠♦str❛✐s✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷ ✴ ✸✶ ❆◆❖❱❆ ❆◆❖❱❆ ❆♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛ ❆ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛ t❛♠❜é♠ é út✐❧ ♣❛r❛ ✈❡r✐✜❝❛r s❡ ♦s ❢❛t♦r❡s ❡①❡r✲ ❝❡♠ ✐♥✢✉ê♥❝✐❛ ❡♠ ❛❧❣✉♠❛ ✈❛r✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡✳ ❖s ❢❛t♦r❡s ♣r♦♣♦st♦s ♣♦❞❡♠ s❡r ❞❡ ♦r✐❣❡♠ q✉❛❧✐t❛t✐✈❛ ♦✉ q✉❛♥t✐t❛t✐✈❛✱ ♠❛s ❛ ✈❛r✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ❞❡✈❡rá s❡r ❝♦♥tí♥✉❛✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✸ ✴ ✸✶ ❆◆❖❱❆ ❊①❡♠♣❧♦ ❊①❡♠♣❧♦ ❯♠❛ ❝♦♠♣❛♥❤✐❛ ♣r♦❞✉③ ✐♠♣r❡ss♦r❛s ❡ ♠áq✉✐♥❛s ❞❡ ❢❛① ❡♠ s✉❛s ❢á✲ ❜r✐❝❛s ❧♦❝❛❧✐③❛❞❛s ❡♠ três ❡st❛❞♦s ❆✱ ❇ ❡ ❈✳ P❛r❛ ♠❡❞✐r q✉❛♥t♦ ♦s ❡♠♣r❡❣❛❞♦s ❞❡ss❛s ❢á❜r✐❝❛s s❛❜❡♠ s♦❜r❡ ❣❡r❡♥❝✐❛♠❡♥t♦ ❞❛ q✉❛❧✐❞❛❞❡ t♦t❛❧✱ ✉♠❛ ❛♠♦str❛ ❛❧❡❛tór✐❛ ❞❡ s❡✐s ❡♠♣r❡❣❛❞♦s ❞❡ ❝❛❞❛ ❢á❜r✐❝❛ ❢♦✐ s❡❧❡❝✐♦♥❛❞❛ ❡ s❡✉s ✐♥t❡❣r❛♥t❡s ❢♦r❛♠ s✉❜♠❡t✐❞♦s ❛ ✉♠ ❡①❛♠❡ ❞❡ s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s s♦❜r❡ ❛ q✉❛❧✐❞❛❞❡✱ ❧♦❣♦ ✉♠ t♦t❛❧ ❞❡ ✶✽ ❡♠♣r❡❣❛❞♦s ❢♦r❛♠ ❛✈❛❧✐❛❞♦s✳ ❖s ❣❡r❡♥t❡s q✉❡r❡♠ ✉s❛r ❡ss❡s ❞❛❞♦s ♣❛r❛ t❡st❛r ❛ ❤✐♣ót❡s❡ ❞❡ q✉❡ ❛ ♠é❞✐❛ ❞❛s ♥♦t❛s ❞❡ ❡①❛♠❡ é ❛ ♠❡s♠❛ ♣❛r❛ t♦❞❛s ❛s três ❢á❜r✐❝❛s✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✹ ✴ ✸✶ ❆◆❖❱❆ ❊①❡♠♣❧♦ ◆♦t❛çã♦ ❉❡✜♥✐r❡♠♦s ❛ ♣♦♣✉❧❛çã♦ ✶ ❝♦♠♦ t♦❞♦s ♦s ❡♠♣r❡❣❛❞♦s ❞❛ ❢á❜r✐❝❛ ❆✱ ❛ ♣♦♣✉❧❛çã♦ ✷ ❝♦♠♦ t♦❞♦s ♦s ❡♠♣r❡❣❛❞♦s ❞❛ ❢á❜r✐❝❛ ❇ ❡ ❛ ♣♦♣✉❧❛çã♦ ✸ ❝♦♠♦ t♦❞♦s ♦s ❡♠♣r❡❣❛❞♦s ❞❛ ❢á❜r✐❝❛ ❈✳ ❆❞♠✐t❛♠♦s q✉❡✿ µ✶ = ♠é❞✐❛ ❞❛s ♥♦t❛s ❞❡ ❡①❛♠❡ ❞❛ ♣♦♣✉❧❛çã♦ ✶ µ✷ = ♠é❞✐❛ ❞❛s ♥♦t❛s ❞❡ ❡①❛♠❡ ❞❛ ♣♦♣✉❧❛çã♦ ✷ µ✸ = ♠é❞✐❛ ❞❛s ♥♦t❛s ❞❡ ❡①❛♠❡ ❞❛ ♣♦♣✉❧❛çã♦ ✸ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✺ ✴ ✸✶ ❆◆❖❱❆ ❊①❡♠♣❧♦ ❍✐♣ót❡s❡s ❊♠❜♦r❛ ❥❛♠❛✐s s❛✐❜❛♠♦s ♦s ✈❛❧♦r❡s r❡❛✐s ❞❡ µ✶✱ µ✷ ❡ µ✸✱ q✉❡r❡♠♦s ✉s❛r ♦s r❡s✉❧t❛❞♦s ❛♠♦str❛✐s ♣❛r❛ t❡st❛r ❛s s❡❣✉✐♥t❡s ❤✐♣ót❡s❡s✿ ❍✵ : µ✶ = µ✷ = µ✸ ❍✶ : P❡❧♦ ♠❡♥♦s ✉♠❛ ❞❛s ♠é❞✐❛s é ❞✐❢❡r❡♥t❡ ❈♦♠ ❛ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛ ♣♦❞❡♠♦s ❞❡t❡r♠✐♥❛r s❡ ❛s ❞✐❢❡r❡♥ç❛s ♦❜✲ s❡r✈❛❞❛s ♥❛s três ♠é❞✐❛s ❛♠♦str❛✐s sã♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ❣r❛♥❞❡s ♣❛r❛ r❡❥❡✐t❛r♠♦s ❍✵✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✻ ✴ ✸✶ ❆◆❖❱❆ ❈♦♥❝❡✐t♦s ❆❧❣✉♥s ❝♦♥❝❡✐t♦s ❆ ❛♥á❧✐s❡ ❞❛ ✈❛r✐â♥❝✐❛ ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ ❛♥❛❧✐s❛r ❞❛❞♦s ♦❜t✐❞♦s t❛♥t♦ ❞❡ ✉♠ ❡st✉❞♦ ♦❜s❡r✈❛❝✐♦♥❛❧ ❝♦♠♦ ❞❡ ✉♠ ❡st✉❞♦ ❡①♣❡r✐♠❡♥t❛❧✳ ❱❛♠♦s ❡♥t❡♥❞❡r ♦s ❝♦♥❝❡✐t♦s ❞❡ ✈❛r✐á✈❡❧ r❡s♣♦st❛✱ ❢❛t♦r ❡ tr❛t❛♠❡♥t♦ q✉❡ sã♦ ❝♦♠✉♥s ❛♦s ❞♦✐s t✐♣♦s ❞❡ ❡st✉❞♦✳ ❆s ❞✉❛s ✈❛r✐á✈❡✐s ❞♦ ❡①❡♠♣❧♦ ❛♥t❡r✐♦r sã♦✿ ❛ ❧♦❝❛❧✐③❛çã♦ ❞❛s ❢á❜r✐❝❛s ❡ ❛s ♥♦t❛s ♦❜t✐❞❛s ♥♦ ❡①❛♠❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ s♦❜r❡ q✉❛❧✐❞❛❞❡✳ ❯♠❛ ✈❡③ q✉❡ ♦ ♦❜❥❡t✐✈♦ é ❞❡t❡r♠✐♥❛r s❡ ❛ ♠é❞✐❛ ❞❛s ♥♦t❛s ❞♦ ❡①❛♠❡ é ❛ ♠❡s♠❛ ♣❛r❛ ❛s ❢á❜r✐❝❛s ❧♦❝❛❧✐③❛❞❛s ❡♠ ❆✱ ❇ ❡ ❈✱ ❛s ♥♦t❛s ❞❡ ❡①❛♠❡ sã♦ ❝❤❛♠❛❞❛s ✈❛r✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡ ♦✉ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❡ ♦ ❧♦❝❛❧ ❞❛ ❢á❜r✐❝❛ ❝♦♠♦ ❛ ✈❛r✐á✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❡ ♦✉ ❢❛t♦r✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✼ ✴ ✸✶ ❆◆❖❱❆ ❈♦♥❝❡✐t♦s ❆❧❣✉♥s ❝♦♥❝❡✐t♦s ✲ ❡①❡♠♣❧♦ ❊♠ ❣❡r❛❧✱ ♦s ✈❛❧♦r❡s ❞❡ ✉♠ ❢❛t♦r s❡❧❡❝✐♦♥❛❞♦ ♣❛r❛ s❡r❡♠ s✉❜♠❡t✐❞♦s ❛ ✉♠❛ ✐♥✈❡st✐❣❛çã♦ ❞❡♥♦♠✐♥❛✲s❡ ♥í✈❡✐s ❞♦ ❢❛t♦r ♦✉ tr❛t❛♠❡♥t♦s✳ ❘❡s✉♠✐♥❞♦✱ ♥♦ ❡①❡♠♣❧♦ ❛♥t❡r✐♦r t❡♠♦s✿ ❚r❛t❛♠❡♥t♦s → ❊st❛❞♦s ❆✱ ❇ ❡ ❈ ❱❛r✐á✈❡❧ r❡s♣♦st❛ → ◆♦t❛ ♦❜t✐❞❛ ♥♦ ❡①❛♠❡ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✽ ✴ ✸✶ A estrutura dos dados tem a seguinte forma: Obewagies | —st~~SC*dStiaSSid 1 Y11 Y21 Ye1 2 Y12 Y22 Yo ny Ying Yano Ykng Total [| Medes |v, *(| |---| Soma de drados dos — 2 = 2 — 2 quai __7 7 _7 desvios em X (yj Y1) X (Yj Yo) d (Ynj Yn) relagdéo a média a a = = = ac Unidade III MAT023 - 2021.2 9/31 ❆◆❖❱❆ ▼♦❞❡❧♦ ▼♦❞❡❧♦ ❙✉♣♦♥❤❛ ❦ tr❛t❛♠❡♥t♦s ✭♦✉ ♣♦♣✉❧❛çõ❡s✮ ❝❛❞❛ ✉♠ ❝♦♠ ♥ r❡♣❡t✐çõ❡s✳ ❯♠ ♠♦❞❡❧♦ ♣❛r❛ ❞❡s❝r❡✈❡r ♦s ❞❛❞♦s é ②✐❥ = µ✐ + ǫ✐❥ , ✐ = ✶, . . . , ❦ ❡ ❥ = ✶, . . . , ♥, ✭✶✮ ②✐❥ é ❛ ♦❜s❡r✈❛çã♦ ❞♦ ✐✲és✐♠♦ tr❛t❛♠❡♥t♦ ♥❛ ❥ ✲és✐♠❛ ✉♥✐❞❛❞❡ ❡①♣❡r✐✲ ♠❡♥t❛❧❀ µ✐ é ❛ ♠é❞✐❛ ❞♦ ✐✲és✐♠♦ ♥í✈❡❧ ❞♦ ❢❛t♦r ♦✉ tr❛t❛♠❡♥t♦✱ s❡♥❞♦ ✉♠ ✈❛❧♦r ✜①♦ ❡ ❞❡s❝♦♥❤❡❝✐❞♦✱ ǫ✐❥ é ♦ ❡rr♦ ❛❧❡❛tór✐♦ ❛ss♦❝✐❛❞♦ ❛♦ ✐✲és✐♠♦ tr❛t❛♠❡♥t♦ ♥❛ ❥ ✲és✐♠❛ ✉♥✐❞❛❞❡ ❡①♣❡r✐♠❡♥t❛❧✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✵ ✴ ✸✶ ❆◆❖❱❆ ▼♦❞❡❧♦ ▼♦❞❡❧♦ ❯♠❛ ❢♦r♠❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ❡s❝r❡✈❡r ♦ ♠♦❞❡❧♦ ✭✶✮ ♣❛r❛ ♦s ❞❛❞♦s é µ✐ = µ + τ✐, ✐ = ✶, . . . , ❦. ❊ ♦ ♠♦❞❡❧♦ ✭✶✮ t♦r♥❛✲s❡ ②✐❥ = µ + τ✐ + ǫ✐❥ , ✐ = ✶, . . . , ❦ ❡ ❥ = ✶, . . . , ♥ ✭✷✮ µ é ♦ ♣❛râ♠❡tr♦ ♠é❞✐❛ ❝♦♠✉♠ ❛ t♦❞♦s ♦s tr❛t❛♠❡♥t♦s✱ ❝❤❛♠❛❞♦ ❞❡ ♠é❞✐❛ ❣❧♦❜❛❧❀ τ✐ é ♦ ♣❛râ♠❡tr♦ ❞♦ ✐✲és✐♠♦ tr❛t❛♠❡♥t♦✱ ❞❡♥♦♠✐♥❛❞♦ ❡❢❡✐t♦ ❞♦ tr❛✲ t❛♠❡♥t♦✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✶ ✴ ✸✶ ❆◆❖❱❆ ▼♦❞❡❧♦ ▼♦❞❡❧♦ ❖s ♠♦❞❡❧♦s ✭✶✮ ❡ ✭✷✮ sã♦ t❛♠❜é♠ ❞❡♥♦♠✐♥❛❞♦s ❞❡ ❆♥á❧✐s❡ ❞❡ ❱❛✲ r✐â♥❝✐❛ ❞❡ ❢❛t♦r ú♥✐❝♦ ✭❆◆❖❱❆✮ ♣♦rq✉❡ ❛♣❡♥❛s ✉♠ ú♥✐❝♦ ❢❛t♦r é ✐♥✈❡st✐❣❛❞♦✳ ❆ ✉♥✐❞❛❞❡ ❡①♣❡r✐♠❡♥t❛❧ s❡rá ❛❧♦❝❛❞❛ ❞❡ ♠❛♥❡✐r❛ ❛❧❡❛tór✐❛ ❡ q✉❡ s❡❥❛♠ ❝♦♥tr♦❧❛❞♦s ♦s ♦✉tr♦s ♣♦ssí✈❡✐s ❢❛t♦r❡s✳ ❖ ♣❧❛♥❡❥❛♠❡♥t♦ ❡①♣❡r✐♠❡♥t❛❧ é ❞❡♥♦♠✐♥❛❞♦ ❞❡ ❝♦♠♣❧❡t❛♠❡♥t❡ ❛❧❡❛✲ t♦r✐③❛❞♦✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✷ ✴ ✸✶ ❆◆❖❱❆ ▼♦❞❡❧♦ ▼♦❞❡❧♦ ❆ ❛♥á❧✐s❡ ❞♦s ❡❢❡✐t♦s ❞♦s tr❛t❛♠❡♥t♦s ♣♦❞❡ s❡r ❢❡✐t❛ ❞❡ ❞✉❛s ♠❛♥❡✐r❛s✿ ♠♦❞❡❧♦ ❞❡ ❡❢❡✐t♦s ✜①♦s ❡ ♠♦❞❡❧♦ ❞❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✸ ✴ ✸✶ ❆◆❖❱❆ ●❡♥❡r❛❧✐③❛çã♦ ●❡♥❡r❛❧✐③❛çã♦ ❆ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛s ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ t❡st❛r ❛ ✐❣✉❛❧❞❛❞❡ ❞❡ ❦ ♠é❞✐❛s ♣♦♣✉❧❛❝✐♦♥❛✐s✳ ❆ ❢♦r♠❛ ❣❡r❛❧ ❞❛s ❤✐♣ót❡s❡s t❡st❛❞❛s é✿ ❍✵ : µ✶ = µ✷ = . . . = µ❦ ❍✶ : P❡❧♦ ♠❡♥♦s ✉♠❛ ❞❛s ♠é❞✐❛s é ❞✐❢❡r❡♥t❡, ❡♠ q✉❡ µ✐ é ❛ ♠é❞✐❛ ❞❛ ✐✲és✐♠❛ ♣♦♣✉❧❛çã♦✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✹ ✴ ✸✶ ❆◆❖❱❆ ❙✉♣♦s✐çõ❡s ❚rês s✉♣♦s✐çõ❡s ❜ás✐❝❛s ♥❡❝❡ssár✐❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛ ✶ P❛r❛ ❝❛❞❛ ♣♦♣✉❧❛çã♦✱ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❡stá ♥♦r♠❛❧♠❡♥t❡ ❞✐str✐✲ ❜✉í❞❛✳ ◆♦ ❡①❡♠♣❧♦✱ ❛s ♥♦t❛s ♦❜t✐❞❛s ♥♦ ❡①❛♠❡ ✭✈❛r✐á✈❡❧ r❡s♣♦st❛✮ ❞❡✈❡♠ s❡r ♥♦r♠❛❧♠❡♥t❡ ❞✐str✐❜✉í❞❛s ❡♠ ❝❛❞❛ ❢á❜r✐❝❛✳ ✷ ❆ ✈❛r✐â♥❝✐❛ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛✱ ❞❡♥♦t❛❞❛ ♣♦r σ✷✱ é ✐❞ê♥t✐❝❛ ♣❛r❛ t♦❞❛s ❛s ♣♦♣✉❧❛çõ❡s✳ ◆♦ ❡①❡♠♣❧♦✱ ❛ ✈❛r✐â♥❝✐❛ ❞❛s ♥♦t❛s ♦❜t✐❞❛s ♥♦ ❡①❛♠❡ ❞❡✈❡ s❡r ✐❞ê♥t✐❝❛ ♣❛r❛ t♦❞❛s ❛s três ❢á❜r✐❝❛s✳ ✸ ❆s ♦❜s❡r✈❛çõ❡s ❞❡✈❡♠ s❡r ✐♥❞❡♣❡♥❞❡♥t❡s✳ ◆♦ ❡①❡♠♣❧♦✱ ❛ ♥♦t❛ q✉❡ ❝❛❞❛ ❡♠♣r❡❣❛❞♦ ♦❜t❡✈❡ ♥♦ ❡①❛♠❡ ❞❡✈❡ s❡r ✐♥✲ ❞❡♣❡♥❞❡♥t❡ ❞❛q✉❡❧❛ ♦❜t✐❞❛ ♣♦r q✉❛❧q✉❡r ♦✉tr♦ ❡♠♣r❡❣❛❞♦✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✺ ✴ ✸✶ ❆◆❖❱❆ ❉❛❞♦s ❉❛❞♦s ❞♦ ❡①❡♠♣❧♦ ❖❜s❡r✈❛çã♦ ❋á❜r✐❝❛ ✶ ❋á❜r✐❝❛ ✷ ❋á❜r✐❝❛ ✸ ❆ ❇ ❈ ✶ ✽✺ ✼✶ ✺✾ ✷ ✼✺ ✼✺ ✻✹ ✸ ✽✷ ✼✸ ✻✷ ✹ ✼✻ ✼✹ ✻✾ ✺ ✼✶ ✻✾ ✼✺ ✻ ✽✺ ✽✷ ✻✼ ❚♦t❛❧ ✹✼✹ ✹✹✹ ✸✾✻ ▼é❞✐❛ ❛♠♦str❛❧ ✼✾ ✼✹ ✻✻ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✻ ✴ ✸✶ ❆◆❖❱❆ ❋♦♥t❡s ❋♦♥t❡s ❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡ ◆♦t❛s ❞♦ ❡①❛♠❡ ♣❛r❛ ❛s três ❢á❜r✐❝❛s ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✶✼ ✴ ✸✶ Tabela de andalise de variancia A tabela de andlise de variancia fica: Fonte de variagio F Tratamentos SQrat | &—-1 | QMarat | Featc Residuo SQre, | 7—k | QMpR,, Total SQroa[m—1) | em que SQ significa soma de quadrados, GL denota graus de liber- k dade, QM é 0 quadrado médio, n = > n; e k 60 numero de trata- i=1 mentos. Unidade III : 7 TOTS Z var 7 s/ aL Poulan Formulas da tabela de andlise de variancia k k 2 (x! ye us) _ =2 ye i=1 Lj=1 Vy SQrrat = 1 (GiB) | ou] SQrrae = YS — i=1 i=1 ” kn; kon k 2 — \2 “ SQres =) Dd (wi - 9) ou | SQres -)dw-Le w=1 j=1 i=1j=1 i-1 kon 5 kon ; (xh, rn, us) SQrwa = 3 (vB)? |0u]SQnar = FJ vg — i=1j=1 i=1 j=1 “ oe ~ = = Mace ae eceT en MAT023 - 2021.2 19/31 Algumas equivaléncias SQt, QMrrat = — L SQr M = es Fo c= QMryat alc —_ QMpes 1 k t - ye Dey Di wy em que y;. = > vii, ¥,=—, y= —— e 0 experimento jal Ny n for desbalanceado, ou seja, o nttmero de observagées diferente em cada ko tratamento e y= Rath caso contrario. Além disso, tem-se que SQres = SQrotal ~~ SQtrat o> «&# = = = ac Unidade III MAT023 - 2021.2 20/31 ❆◆❖❱❆ ❚❡st❡ ❋ ❚❡st❡ ❋ ❙♦❜ ❍✵ ❛ r❛③ã♦ ❋❈❛❧❝ = ◗▼❚r❛t ◗▼❘❡s = (❙◗❚r❛t/❦ − ✶) (❙◗❘❡s/♥ − ❦) , t❡♠ ❞✐str✐❜✉✐çã♦ ❋ ❝♦♠ (❦ − ✶; ♥ − ❦) ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡✳ ❘❡❣✐ã♦ ❞❡ r❡❥❡✐çã♦✿ ❘❡❥❡✐t❛✲s❡ ❍✵ s❡ ❋❈❛❧❝ > ❋α(❦ − ✶; ♥ − ❦) , ❡♠ q✉❡ ❋α(❦ − ✶; ♥ − ❦) é ♦ ♣♦♥t♦ α s✉♣❡r✐♦r ❞❛ ❞✐str✐❜✉✐çã♦ ❋ ❝♦♠ (❦ − ✶; ♥ − ❦) ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✶ ✴ ✸✶ ❆◆❖❱❆ ❉✐str✐❜✉✐çã♦ ❋ ❉✐str✐❜✉✐çã♦ ❋ ❆ ❞✐str✐❜✉✐çã♦ ❋ t❡♠ ❣r❛♥❞❡ ❛♣❧✐❝❛çã♦ ♥❛ ❝♦♠♣❛r❛çã♦ ❞❡ ❞✉❛s ✈❛r✐✲ â♥❝✐❛s ♦✉ ❡♠ ♣r♦❜❧❡♠❛s q✉❡ ❡♥✈♦❧✈❡♠ ❞✉❛s ♦✉ ♠❛✐s ❛♠♦str❛s✳ ❙❡ ❍✵ ❢♦r r❡❥❡✐t❛❞❛✱ ♣❡❧♦ ♠❡♥♦s ✉♠❛ ❞❛s ♠é❞✐❛s é ❞✐❢❡r❡♥t❡ ❞❛s ❞❡♠❛✐s✱ ♠❛s q✉❛✐s ♠é❞✐❛s ❞❡✈❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ❞✐❢❡r❡♥t❡s❄ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✷ ✴ ✸✶ ❚✉❦❡② ■♥tr♦❞✉çã♦ ■♥tr♦❞✉çã♦ ❆♣ós ❝♦♥❝❧✉✐r q✉❡ ❡①✐st❡ ❞✐❢❡r❡♥ç❛ s✐❣♥✐✜❝❛t✐✈❛ ❡♥tr❡ tr❛t❛♠❡♥t♦s✱ ♣♦r ♠❡✐♦ ❞♦ t❡st❡ ❋✱ ♣♦❞❡✲s❡ ❡st❛r ✐♥t❡r❡ss❛❞♦ ❡♠ ❛✈❛❧✐❛r ❛ ♠❛❣♥✐t✉❞❡ ❞❡st❛s ❞✐❢❡r❡♥ç❛s ✉t✐❧✐③❛♥❞♦ ✉♠ t❡st❡ ❞❡ ❝♦♠♣❛r❛çõ❡s ♠ú❧t✐♣❧❛s✳ ■r❡♠♦s ✉t✐❧✐③❛r ♦ t❡st❡ ❞❡ ❚✉❦❡②✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✸ ✴ ✸✶ ❚✉❦❡② ❚✉❦❡② ❚❡st❡ ❞❡ ❚✉❦❡② ❖ t❡st❡ ❞❡ ❚✉❦❡② é r❡❝♦♠❡♥❞❛❞♦ q✉❛♥❞♦ ❞❡s❡❥❛♠♦s ❝♦♠♣❛r❛r ♠é❞✐❛s ❞✉❛s ❛ ❞✉❛s✱ ♦✉ s❡❥❛✱ q✉❛♥❞♦ ❞❡s❡❥❛♠♦s t❡st❛r ❛s ❤✐♣ót❡s❡s✿ ❍✵ : µ✐ − µ❤ = ✵ ❍✶ : µ✐ − µ❤ ̸= ✵, ❝♦♠ ✐ ̸= ❤ ❡ ✐, ❤ = ✶, . . . , ❦✳ ❊st❡ t❡st❡ é ❡s♣❡❝✐❛❧♠❡♥t❡ r❡❝♦♠❡♥❞❛❞♦ ♣♦rq✉❡ ❡❧❡ é ❡①❛t♦ ♥♦s ❝❛s♦s ❡♠ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ ♦❜s❡r✈❛çõ❡s é ✐❣✉❛❧ ❡♠ t♦❞♦s ♦s tr❛t❛♠❡♥t♦s ✭❡①♣❡r✐♠❡♥t♦ ❜❛❧❛♥❝❡❛❞♦✮✳ ◆♦ ❝❛s♦ ❞❡ s❡r❡♠ ❞✐❢❡r❡♥t❡s ♦s ♥ú♠❡r♦s ❞❡ r❡♣❡t✐çõ❡s ♦ t❡st❡ ❞❡ ❚✉❦❡② ♣♦❞❡ ❛✐♥❞❛ s❡r ✉s❛❞♦✱ ♠❛s ❡♥tã♦ é ❛♣❡♥❛s ❛♣r♦①✐♠❛❞♦✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✹ ✴ ✸✶ Teste de Tukey - Férmulas O teste baseia-se na Diferenga Minima Significativa (DMS) A. A estatistica do teste é dada por: M . A=q|/ QMres para experimentos balanceados Ny ou M 1 1 . A=q/ QMaes (.. + a) para experimentos desbalanceados, 2 nn TH em que os valores da distribuigdo da estatistica ¢ = Q(k:n—k,.) Sao tabu- lados, n; € o ntiimero de observagoes em cada tratamento, k é o nimero de tratamentos, n — k os graus de liberdade do residuo e « é€ o nivel de significancia do teste. Unidade III MAT023 - 2021.2 25/31 ❚✉❦❡② ❚❛❜❡❧❛ ❞❛ q ❚❛❜❡❧❛ ❞❛ q ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✻ ✴ ✸✶ ❚✉❦❡② ❘❡❥❡✐çã♦ ❘❡❣r❛ ❞❡ r❡❥❡✐çã♦ ❍✵ : µ✐ − µ❤ = ✵ ❍✶ : µ✐ − µ❤ ̸= ✵, ❝♦♠ ✐ ̸= ❤ ❡ ✐, ❤ = ✶, . . . , ❦✳ ❘❡❣✐ã♦ ❞❡ r❡❥❡✐çã♦✿ ❘❡❥❡✐t❛✲s❡ ❍✵ s❡ |②✐ − ②❤| > ∆ . ❈♦♠♦ ♦ t❡st❡ ❞❡ ❚✉❦❡② é✱ ❞❡ ❝❡rt❛ ❢♦r♠❛✱ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ t❡st❡ ❋✱ é ♣♦ssí✈❡❧ q✉❡✱ ♠❡s♠♦ s❡♥❞♦ s✐❣♥✐✜❝❛t✐✈♦ ♦ ✈❛❧♦r ❞❡ ❋ ❝❛❧❝✉❧❛❞♦✱ ♥ã♦ s❡ ❡♥❝♦♥tr❡♠ ❞✐❢❡r❡♥ç❛s s✐❣♥✐✜❝❛t✐✈❛s ❡♥tr❡ ❛s ♠é❞✐❛s ❞♦s tr❛t❛♠❡♥t♦s✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✼ ✴ ✸✶ ❚✉❦❡② ❊①❡♠♣❧♦ ❊①❡♠♣❧♦ ❯t✐❧✐③❛♥❞♦ ♦s ❞❛❞♦s ❞♦ ❡①❡♠♣❧♦ ❛♥t❡r✐♦r✱ ✐❞❡♥t✐✜q✉❡ s❡ ❡①✐st❡ ❞✐❢❡r❡♥ç❛s s✐❣♥✐✜❝❛t✐✈❛s ❡♥tr❡ ❛s ♠é❞✐❛s ❞♦s tr❛t❛♠❡♥t♦s✳ ❖❜s❡r✈❛çã♦ ❋á❜r✐❝❛ ✶ ❋á❜r✐❝❛ ✷ ❋á❜r✐❝❛ ✸ ❆ ❇ ❈ ✶ ✽✺ ✼✶ ✺✾ ✷ ✼✺ ✼✺ ✻✹ ✸ ✽✷ ✼✸ ✻✷ ✹ ✼✻ ✼✹ ✻✾ ✺ ✼✶ ✻✾ ✼✺ ✻ ✽✺ ✽✷ ✻✼ ❚♦t❛❧ ✹✼✹ ✹✹✹ ✸✾✻ ▼é❞✐❛ ❛♠♦str❛❧ ✼✾ ✼✹ ✻✻ ❋❱ ❙◗ ●▲ ◗▼ ❋ ❚r❛t❛♠❡♥t♦ ✺✶✻ ✷ ✷✺✽✱✵✵ ✾✱✵✵ ❘❡sí❞✉♦ ✹✸✵ ✶✺ ✷✽✱✻✼ ❚♦t❛❧ ✾✹✻ ✶✼ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✽ ✴ ✸✶ ❚✉❦❡② ❊①❡r❝í❝✐♦ ❊①❡r❝í❝✐♦ ❞❡ ❋✐①❛çã♦ ✶✳ ❊♠ ✉♠ ❡①♣❡r✐♠❡♥t♦ ♣❛r❛ ❛✈❛❧✐❛r ♦ ❝♦♥s✉♠♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❡♠ ❑❲❤✭×✶✵✵✵✮ ❞❡ três ♠♦t♦r❡s ❞✉r❛♥t❡ ✉♠ ❤♦r❛ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦✱ ♦❜t❡✈❡✲ s❡ ♦s s❡❣✉✐♥t❡s r❡s✉❧t❛❞♦s✿ ✐ ▼♦t♦r ✶ ▼♦t♦r ✷ ▼♦t♦r ✸ ✶ ✷✱✷✶ ✷✱✷✵ ✶✱✼✼ ✷ ✷✱✵✸ ✷✱✵✸ ✶✱✽✵ ✸ ✶✱✾✾ ✶✱✽✽ ✶✱✽✺ ✹ ✷✱✷✸ ✶✱✼✺ ✶✱✼✼ ✺ ✷✱✵✸ ✶✱✵✻ ❚♦t❛❧ ✶✵✱✹✾ ✽✱✾✶ ✼✱✶✾ ▼é❞✐❛ ✷✱✶✵ ✶✱✼✽ ✶✱✽✵ ❈♦♠♣❧❡t❡ ❛ t❛❜❡❧❛ ❞❡ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛ ❡ ✐♥t❡r♣r❡t❡ ♦ r❡s✉❧t❛❞♦✳ ❈❛s♦ ❛ ❤✐♣ót❡s❡ ♥✉❧❛ s❡❥❛ r❡❥❡✐t❛❞❛ r❡❛❧✐③❡ ♦ t❡st❡ ❞❡ ❚✉❦❡②✳ ❋❱ ❙◗ ●▲ ◗▼ ❋ ❚r❛t❛♠❡♥t♦ ✵✱✸✶ ❘❡sí❞✉♦ ❚♦t❛❧ ✶✱✶✸ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✷✾ ✴ ✸✶ ❚✉❦❡② ❊①❡r❝í❝✐♦ ❊①❡r❝í❝✐♦ ❞❡ ❋✐①❛çã♦ ✷✳ ❆ ✜♠ ❞❡ ✈❡r✐✜❝❛r ♦ ❡❢❡✐t♦ ❞❡ q✉❛tr♦ t✐♣♦s ❞❡ ♣r♦♣❛❣❛♥❞❛ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♠❛r❝❛ ❞❡ ❣♦♠❛ ❞❡ ♠❛s❝❛r✱ ❝r✐❛♥ç❛s ❢♦r❛♠ ❛tr✐❜✉í❞❛s ❛❧❡❛t♦r✐❛♠❡♥t❡ ❛ ❝❛❞❛ ✉♠❛ ❞❡ ✹ s❛❧❛s q✉❡ ♠♦str❛✈❛♠ ❞❡s❡♥❤♦s ❛♥✐♠❛✲ ❞♦s✱ ❝♦♠ ✐♥t❡r✈❛❧♦s r❡❣✉❧❛r❡s ❡♠ q✉❡ ❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ♣r♦♣❛❣❛♥❞❛s ❡r❛♠ ✐♥s❡r✐❞❛s✳ ❆♣ós ❛ s❡ssã♦✱ ❛s ❝r✐❛♥ç❛s ❢♦r❛♠ ❡♥tr❡✈✐st❛❞❛s ♣♦r ♣s✐❝ó❧♦❣♦s✱ q✉❡ ❛tr✐❜✉ír❛♠ ✉♠ í♥❞✐❝❡ ❞❡ ❛ss✐♠✐❧❛çã♦ ❛ ❝❛❞❛ ❝r✐❛♥ç❛ ✭❞❛❞♦s ❛ s❡❣✉✐r✮✳ ◗✉❛♥t♦ ♠❛✐♦r ❡ss❡ í♥❞✐❝❡✱ ♠❛✐♦r s❡r✐❛ ❛ ❧❡♠❜r❛♥ç❛ ❞♦ ♣r♦❞✉t♦✳ ❙❡ ♦ ❡❢❡✐t♦ ❡①✐st✐r✱ ✐♥❞✐q✉❡ q✉❛✐s t✐♣♦s ❞❡ ♣r♦♣❛❣❛♥❞❛ ❞✐❢❡r❡♠ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ✉t✐❧✐③❛♥❞♦ ♦ t❡st❡ ❚✉❦❡②✳ ❯s❡ α = ✺✪✳ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✸✵ ✴ ✸✶ ❚✉❦❡② ❊①❡r❝í❝✐♦ ❚✐♣♦ ❞❡ Pr♦♣❛❣❛♥❞❛ ■ ■■ ■■■ ■❱ ✶✺ ✼ ✷✷ ✷✷ ✽ ✶✺ ✶✼ ✶✵ ✼ ✻ ✷✶ ✶✻ ✽ ✶✶ ✶✻ ✶✶ ✻ ✼ ✷✸ ✶✺ ✼ ✶✻ ✶✾ ✶✽ ✶✵ ✻ ✷✵ ✷✷ ✶✵ ✽ ✶✶ ✶✶ ✺ ✻ ✶✽ ✶✽ ✶✸ ✶✺ ✶✶ ✶✵ ✺ ✽ ✷✶ ✷✷ ✽ ✽ ✶✸ ✶✾ ✭❯❋❇❆ ✲ ❉❊❙❚✮ ❯♥✐❞❛❞❡ ■■■ ▼❆❚✵✷✸ ✲ ✷✵✷✶✳✷ ✸✶ ✴ ✸✶