From 45266aacc3ab2a3ed86fbc73dbebd2fd7e663667 Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Sat, 19 Jun 2021 13:15:24 +0200 Subject: [PATCH] lab7 --- podsumowanie/README.md | 138 ++++++++++++++++++++++++++++++++- podsumowanie/lab7/bartlett.png | Bin 0 -> 55603 bytes podsumowanie/lab7/jeden.png | Bin 0 -> 89287 bytes podsumowanie/lab7/nir.png | Bin 0 -> 48382 bytes podsumowanie/lab7/tabela.png | Bin 0 -> 91003 bytes podsumowanie/lab7/tukey.png | Bin 0 -> 56900 bytes zajecia7/README.md | 2 +- 7 files changed, 138 insertions(+), 2 deletions(-) create mode 100644 podsumowanie/lab7/bartlett.png create mode 100644 podsumowanie/lab7/jeden.png create mode 100644 podsumowanie/lab7/nir.png create mode 100644 podsumowanie/lab7/tabela.png create mode 100644 podsumowanie/lab7/tukey.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index ecf5413..10e52f4 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -335,7 +335,7 @@ Jeżeli konstruujemy jakiś przedział z poziomem ufności 0,95 to na 100 prób Podstawiamy funkcję centralną do prawdopodobieństwa oraz 1-a, wsadzamy parametr pomiędzy funkcję i wyliczamy a i b. a i b to przedział ufności. Jest przykład w pdfie w labach 5.
![ufnosc](lab5/ufnosc.png) -- Rozkład t-Studenta - kolejny typ rozkładu. Podobny to rozkładu normalnego.
+- Rozkład t-Studenta - kolejny typ rozkładu. Podobny to rozkładu normalnego. Rozkład t studenta stosujemy tylko w sytuacji, gdy odchylenie standardowe populacji jest nieznane, a rozmiar próby(ilość obserwacji) jest mniejsza niż 30. W przypadku gdy rozmiar próby jest większy lub równy 30 wtedy zamiast brać rozkład t bierzemy rozkład normalny. Wynika to z faktu, że rozkład t studenta dla 𝑛≥30 jest bardzo podobny do rozkładu normalnego. Dla n < 30 rozkład studenta jest „szerszy”, tzn. bardziej prawdopodobne są wartości mocno odbiegające od średniej niż w przypadku rozkładu normalnego.
![student](lab5/student.png) - Dodatkowe
@@ -433,3 +433,139 @@ Są gotowe wzory do których podstawiamy wartości w zalezności od rodzaju pró - Var.test (test F dla dwóch wariancji) - wariancja - Intuicyjnie utożsamiana ze zróżnicowaniem zbiorowości. Wg dokumentacji jest to test pozwalający porównać wariancje z dwóch rozkładów normalnych. + + + +--- +## LAB 7 +Zagadnienia: + - analiza wariancji ANOVA - w skróce badanie zależności między obserwacjami + + - wykład 8 na stronie + + +### R +```r +# założenia +rests <- lm(number ~ context, data = dane)$residuals +shapiro.test(rests)$p.value +qqnorm(rests) +qqline(rests) +bartlett.test(number ~ context, data = dane)$p.value +fligner.test(number ~ context, data = dane)$p.value +library(car) +leveneTest(number ~ context, data = dane)[[3]][1] +leveneTest(number ~ context, data = dane, center = "mean")[[3]][1] + +# jednoczynnikowa ANOVA +summary(aov(number ~ context, data = dane)) + +# testy post-hoc +pairwise.t.test(number, context, data = dane) +TukeyHSD(model_aov)$context +plot(TukeyHSD(model_aov)) +install.packages("agricolae") +library(agricolae) +HSD.test(model_aov, "context", console = TRUE) +SNK.test(model_aov, "context", console = TRUE) +LSD.test(model_aov, "context", p.adj = "holm", console = TRUE) +scheffe.test(model_aov, "context", console = TRUE) + +# kontrasty +C1 <- c(-3, 2, 2, -3, 2) +C2 <- c(0, -1, -1, 0, 2) +C3 <- c(0, 1, -1, 0, 0) +C4 <- c(1, 0, 0, -1, 0) +con <- cbind(C1, C2, C3, C4) +contrasts(dane$context) <- con +model_aov_2 <- aov(number ~ context, data = dane) +summary(model_aov_2, split = list(context = list('C1' = 1, 'C2' = 2, 'C3' = 3, 'C4' = 4))) +``` + + + +### Wstęp +- Analiza wariancji ANOVA - metoda statystyczna służąca do badania obserwacji, które zależą od jednego lub wielu działających równocześnie czynników. Metoda ta wyjaśnia, z jakim prawdopodobieństwem wyodrębnione czynniki mogą być powodem różnic między obserwowanymi średnimi grupowymi. + - Modele jednoczynnikowe – wpływ każdego czynnika jest rozpatrywany oddzielnie, tą klasą zagadnień zajmuje się jednoczynnikowa analiza wariancji. Chcemy sprawdzić, czy jakiś pojedynczy czynnik ma wpływ na mierzoną zmienną zależną. + + - Modele wieloczynnikowe – wpływ różnych czynników jest rozpatrywany łącznie, tą klasą zagadnień zajmuje się wieloczynnikowa analiza wariancji. + + +### Jednoczynnikowa analiza wariancji +Na test jednoczynnikowej analizy wariancji możemy patrzeć jak na uogólnienie testu t-Studenta dla dwóch prób niezależnych.
+![jeden](lab7/jeden.png) + +- Wyniki przedstawiamy w postaci tabeli
+![tabela](lab7/tabela.png) + +- Założenia: + - Niezależność obserwacji dla poszczególnych jednostek eksperymentalnych. + + - Błędy mają rozkłady normalne z zerową wartością oczekiwaną (brak błędu systematycznego) i jednorodną wariancją. - to możemy sprawdzić **testem Bartletta** + + + +## Testy post hoc +Testy post-hoc (po fakcie) wykonuje się jako kolejny krok analizy wariancji. Znane są również pod nazwą porównań wielokrotnych lub porównań parami. Sama analiza wariancji mówi nam o tym czy różnice w porównywanych średnich występują czy nie. Nie wiemy jednak między którymi grupami zachodzą te różnice. Istotny współczynnik F wskazuje jedynie na słuszność (lub brak słuszności) odrzucenia hipotezy zerowej. Jeśli ją odrzucimy musimy dowiedzieć się czy wszystkie średnie różnią się między sobą czy tylko niektóre. Stąd też nazwa “po fakcie” – wykonujemy je dopiero po sprawdzeniu czy wynik F jest istotny statystycznie. Jeśli nie jest, nie musimy wykonywać testów post-hoc. +- Procedura NIR – Fishera.
+![nir](lab7/nir.png) + +- Tukey, test HSD i SNK są pochodnymi Tukeya
+![tukey](lab7/tukey.png) + +- LSD - Multiple comparisons, "Least significant difference" and Adjust P-values. Wynik też grupy. + +- Scheffe - method is very general in that all possible contrasts can be tested for significance and confidence intervals can be constructed for the corresponding linear. The test is conservative. Wynik też grupy. + +- pairwise.t.test - daje wynik w postaci tabeli jak różnią się od siebie wyniki poszczególnych grup + + + +### Zagadnienia +- bartlett.test, fligner.test oraz leveneTest użyte do sprawdzenia czy wariancje dwóch grup są takie same. +![bartlett](lab7/bartlett.png)
+ +- Układ losowych bloków kompletnych. W celu wyeliminowania niejednorodności jednostek eksperymentalnych możemy pogrupować je w bloki. Po prostu przed testami grupujemy. + +- Jednoczynnikowa ANOVA - układ doświadczalny. Na stronie analiza wariancji była wytłumaczona bardziej opisowo - na podstawie analogii do układu doświadczalengo. + +- Kontrasty - by można było zdefiniować wybrane hipotezy należy dla każdej średniej przypisać wartość kontrastu. +Wartości kontrastu są tak wybierane by ich sumy dla porównywanych stron były liczbami przeciwnymi, a ich wartość dla średnich nie biorących udziału w analizie wynosi 0!! +

+Wykonując później test ANOVA - analiza wariancji możemy zobaczyć czy porównywane grupy (wyszczególnione za pomocą kontrastów) różnią się od siebie. + +- Ortogonalny - prostopadły + + + + +--- +## LAB 8 +Zagadnienia: + - + + +### R + + + +### Zagadnienia + + + + + +--- +## LAB 9 +Zagadnienia: + - + + +### R + + + +### Zagadnienia + + + diff --git a/podsumowanie/lab7/bartlett.png b/podsumowanie/lab7/bartlett.png new file mode 100644 index 0000000000000000000000000000000000000000..382adce8aa7e869ef78f4feebdeed87bd85f367a GIT binary patch literal 55603 zcmeFYWmH^S*ENU*3+^F7gFA!}+@)}L5AFmn+zAleg1ZHGhXBFd3GNyw+@(*Rd*Am- zzW&>Px<}U-HR`a>IosCWYtJ?3B2+<60u`AM843ytRT3ns1O)}l0R;uafd~(j_;V6n zLO~IDS%`=zNQ#J%Dmd7gT3DMvL1_dffL~~+j!ivhq%I9@PcHxdq{Ac~+oDKOs0a&U zDhRz0dJ&GHh$$qBDf9wGR5)GGZSVF>FTQeED@xk`Fh5;Sgyu^#Co$|2b z{<$Nlx9`KkYp8zIUOoPam24JU1Sr*GB1~LZDAVxK*Cg0gLCOX)_%Gx!dd0NoeGv5L zyYzS(ZBqM2#qoO|p`tNCc{DyypWm{i(~mBaB#P*S+?#iK!gNDrg{VhPoS>23LVdS< 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