From 3578d063280b6fbfa48e72542913088fbc2b1d71 Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Sat, 19 Jun 2021 10:58:29 +0200 Subject: [PATCH] lab6 --- podsumowanie/README.md | 74 ++++++++++++++++++++++++++++- podsumowanie/lab6/bledy.png | Bin 0 -> 88196 bytes podsumowanie/lab6/krytyczny.png | Bin 0 -> 70476 bytes podsumowanie/lab6/wiarygodnosc.png | Bin 0 -> 69384 bytes zajecia6/README.md | 3 +- 5 files changed, 74 insertions(+), 3 deletions(-) create mode 100644 podsumowanie/lab6/bledy.png create mode 100644 podsumowanie/lab6/krytyczny.png create mode 100644 podsumowanie/lab6/wiarygodnosc.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index ea0ebdf..a1d85c5 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -310,7 +310,9 @@ attach(Awarie) m <- mean(Czas) n <- length(Czas) a <- 0.05 -L <- qchisq(a/2,2*n)/(2*n*m) + +# chi-kwadrat +L <- qchisq(a/2,2*n)/(2*n*m) R <- qchisq(1-(a/2),2*n)/(2*n*m) # bootstrapowe przedziały ufności @@ -356,8 +358,78 @@ Zagadnienia: ### R +```r +x <- c(78.2, 78.5, 75.6, 78.5, 78.5, 77.4, 76.6) +y <- c(76.1, 75.2, 75.8, 77.3, 77.3, 77.0, 74.4, 76.2, 73.5, 77.4) +boxplot(x, y) + +shapiro.test(x)$p.value +qqnorm(x) +qqline(x) + +shapiro.test(y)$p.value +qqnorm(y) +qqline(y) + +var(x) +var(y) +var.test(x, y, alternative = "less")$p.value +``` + + +## Testy statystyczne +- Testujemy czy wartość parametru jest istotnie różna od zadanej wartości. Musimy podać hipotezę alternatywną - działanie które podejmujemy jeśli hipoteza zerowa jest fałszywa. + +- Obszary krytyczne
+![krytyczne](lab6/krytyczne.png) + +- Błędy pierwszego i drugiego rodzaju. Przez to możemy podjąć dwie decyzje - "odrzucamy hipotezę zerową" lub "nie ma podstaw do odrzucenia hipotezy zerowej". + - Odrzucamy hipotezę zerową gdy jest ona prawdziwa - błąd I rodzaju. + + - Przyjmujemy hipotezę zerową gdy jest ona fałszywa - błąd II rodzaju.
+ ![bledy](lab6/bledy.png)

+ + +- Wybór wartości krytycznej - Ustalamy poziom istotności testu α i dobieramy wartość krytyczną tak, aby + - prawdopodobieństwo popełnienia błędu I rodzaju było mniejsze lub równe α, + + - prawdopodobieństwo popełnienia błędu II rodzaju było minimalne.

+ + +- Testy ilorazu wiarogodności
+![wiarygodnosc](lab6/wiarygodnosc.png) + + ### Zagadnienia +- P-wartość (p-value) to graniczny poziom istotności - najmniejszy, przy którym zaobserwowana wartość statystyki testowej prowadzi do odrzucenia hipotezy zerowej. Im p-wartość jest większa, tym bardziej hipoteza H0 jest prawdziwa. Im mniejsza tym niej prawdopodobna jest hipoteza H0. Wartość p, p-wartość, prawdopodobieństwo testowe. Sposoby obliczania z obszaru: + - Prawostronny obszar krytyczny + + - Lewostronny obszar krytyczny + + - Dwustronny obszar krytyczny

+- Test t Studenta jest metodą statystyczną służącą do porównania dwóch średnich między sobą jeśli znamy liczbę badanych osób, średnią arytmetyczną oraz wartość odchylenia standardowego lub wariancji. +

+Jest to jeden z mniej skomplikowanych i bardzo często wykorzystywanych testów statystycznych używanych do weryfikacji hipotez. Dzięki niemu możemy dowiedzieć się czy dwie różne średnie są różne niechcący (w wyniku przypadku) czy są różne istotnie statystycznie (np. z uwagi na naszą manipulację eksperymentalna). +

+Są gotowe wzory do których podstawiamy wartości w zalezności od rodzaju próby. **Przykład w pdf w labach 6 - dla jednej próby lub dla dwóch wzory są na stronie**. + - Założenie normalności rozkładów błędów możemy (ewentualnie) zastąpić założeniem mówiącym o dysponowaniu dużą próbą, tzn. + + - Próby niezależne - obserwacje w poszczególnych populacjach (grupach) dokonywane są na różnych jednostkach eksperymentalnych. + + - Próby zależne - obserwacje dokonywane są dwukrotnie na tych samych jednostkach eksperymentalnych.

+ + +- Test Shapiro-Wilka- hipotezy: + - H0 : Próba pochodzi z populacji o rozkładzie normalnym + + - H1 : Próba nie pochodzi z populacji o rozkładzie normalnym. + + + Hipoteza zerowa tego testu mówi nam o tym, że nasza próba badawcza pochodzi z populacji o normalnym rozkładzie. Jeśli test Shapiro-Wilka osiąga istotność statystyczną (p < 0,05), świadczy to o rozkładzie oddalonym od krzywej Gaussa. W przypadku tego testu najczęściej chcemy otrzymać wartości nieistotne statystyczne (p > 0,05), ponieważ świadczą one o zgodności rozkładu zmiennej z rozkładem normalnym. + +- Var.test (test F dla dwóch wariancji) - wariancja - Intuicyjnie utożsamiana ze zróżnicowaniem zbiorowości. 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