From 10b32babc13fd5b4c58b7709a2347c91c558169c Mon Sep 17 00:00:00 2001 From: nikola-grubor Date: Wed, 30 Oct 2024 00:26:38 +0100 Subject: [PATCH] week 05 --- changelog.md | 3 +- docs/index.html | 48 ++-- docs/search.json | 59 ++++- docs/slides/05_uzorak/prezentacija.html | 237 ++++++++++-------- .../figure-revealjs/unnamed-chunk-10-1.png | Bin 0 -> 134098 bytes .../figure-revealjs/unnamed-chunk-8-1.png | Bin 127613 -> 0 bytes .../figure-revealjs/unnamed-chunk-9-1.png | Bin 0 -> 135707 bytes docs/slides/05_uzorak/video/clt.mov | Bin 0 -> 6989580 bytes index.qmd | 6 +- slides/05_uzorak/prezentacija.qmd | 121 ++++++--- 10 files changed, 294 insertions(+), 180 deletions(-) create mode 100644 docs/slides/05_uzorak/prezentacija_files/figure-revealjs/unnamed-chunk-10-1.png delete mode 100644 docs/slides/05_uzorak/prezentacija_files/figure-revealjs/unnamed-chunk-8-1.png create mode 100644 docs/slides/05_uzorak/prezentacija_files/figure-revealjs/unnamed-chunk-9-1.png create mode 100644 docs/slides/05_uzorak/video/clt.mov diff --git a/changelog.md b/changelog.md index 0f09461..2a1e763 100644 --- a/changelog.md +++ b/changelog.md @@ -13,7 +13,8 @@ Pogledati sve prezentacije na kraju da li raspored ima smisla. - dodati zadatak ## 04_verovatnoća -- preraspodeliti slajdove tako da imaju smisla +- sve: srediti zarez na elementarnim ishodima +- eng: fix typo on slide for axioms ## 05_uzorak diff --git a/docs/index.html b/docs/index.html index 6dbb17b..d4baaa3 100644 --- a/docs/index.html +++ b/docs/index.html @@ -131,10 +131,10 @@

Lista prezentacija

- tinytable_e8h3jr83dqwnxrkigtr6 + tinytable_k6jj631i35064hy32ffd @@ -152,7 +152,7 @@

Lista prezentacija

- +
@@ -178,17 +178,21 @@

Lista prezentacija

+ + + +
4 Verovatnoća i raspodele verovatnoća (eng)
5Populacija i uzorak
diff --git a/docs/search.json b/docs/search.json index 47f75da..de92062 100644 --- a/docs/search.json +++ b/docs/search.json @@ -431,7 +431,7 @@ "href": "index.html", "title": "Osnovni kurs medicinske statistike i informatike", "section": "", - "text": "Osnovni kurs medicinske statistike i informatike\n\n\n\n\n\n\n\n\n\nDobrodošli na kurs medicinske statistike i informatike! Sve informacije vezane za kurs i termine polaganja možete pronaći na sajtu instituta. Ova web stranica služi kao lični repozitorijum kako bi prezentacije sa vežbi bile uvek dostupne onima koji to žele.\nLista prezentacija\n\n\n \n\n \n \n \n tinytable_e8h3jr83dqwnxrkigtr6\n \n \n \n \n \n\n \n \n \n \n \n \n Nedelja\n Tema\n \n \n \n \n \n 1\n Uvod u medicinsku statistiku (eng)\n \n \n 2\n Sređivanje podataka\n \n \n 3\n Statističko opisivanje podataka\n \n \n 4\n Verovatnoća i raspodele verovatnoća (eng)" + "text": "Osnovni kurs medicinske statistike i informatike\n\n\n\n\n\n\n\n\n\nDobrodošli na kurs medicinske statistike i informatike! Sve informacije vezane za kurs i termine polaganja možete pronaći na sajtu instituta. Ova web stranica služi kao lični repozitorijum kako bi prezentacije sa vežbi bile uvek dostupne onima koji to žele.\nLista prezentacija\n\n\n \n\n \n \n \n tinytable_k6jj631i35064hy32ffd\n \n \n \n \n \n\n \n \n \n \n \n \n Nedelja\n Tema\n \n \n \n \n \n 1\n Uvod u medicinsku statistiku (eng)\n \n \n 2\n Sređivanje podataka\n \n \n 3\n Statističko opisivanje podataka\n \n \n 4\n Verovatnoća i raspodele verovatnoća (eng)\n \n \n 5\n Populacija i uzorak" }, { "objectID": "slides/04_verovatnoca/prezentacija.html#de-méréov-problem", @@ -683,7 +683,7 @@ "href": "slides/05_uzorak/prezentacija.html#zašto-uzorkujemo", "title": "Populacija i uzorak", "section": "Zašto uzorkujemo", - "text": "Zašto uzorkujemo\n\n\n\nOgraničenja: vreme i novac.\nKako da zaključimo ispravno, a da nismo videli svaki primer onoga što nas interesuje?\n\n\n\n\n\n\n\n%%{ init: { 'flowchart': { 'curve': 'monotoneX' } } }%%\n%%| fig-width: 10\n\nflowchart TD\n A[Ciljna populacija] --> B[\"Uzoračka populacija\"]\n B --> C[Uzorak]\n C --\"Zaključak\"--> A" + "text": "Zašto uzorkujemo\n\n\n\nOgraničenja: vreme i novac.\nKako da zaključimo ispravno, a da nismo videli svaki primer onoga što nas interesuje?\n\n\n\n\n\n\n\n%%{ init: { 'flowchart': { 'curve': 'monotoneX' } } }%%\n\nflowchart TD\n A[Ciljna populacija] --> B[\"Uzoračka populacija\"]\n B --> C[Uzorak]\n C --\"Zaključak\"--> A" }, { "objectID": "slides/05_uzorak/prezentacija.html#urgentno-lečenje-septičnog-šoka", @@ -746,7 +746,7 @@ "href": "slides/05_uzorak/prezentacija.html#uzorkovanje", "title": "Populacija i uzorak", "section": "Uzorkovanje", - "text": "Uzorkovanje\n\nUzorački okvir\n\ntest.\n\nSlučajni uzorak\n\nTačno znamo verovatnoću da neko bude izabran\n\nNeslučajni\n\nMože biti pristrasan" + "text": "Uzorkovanje\n\nUzorački okvir\n\nSpisak ili lista svih elemenata populacije koju želimo da uzorkujemo.\n\n\n\nSlučajni uzorak\n\nTačno znamo verovatnoću da neko bude izabran\n\nNeslučajni\n\nMože biti pristrasan" }, { "objectID": "slides/05_uzorak/prezentacija.html#slučajni-uzorci", @@ -774,7 +774,7 @@ "href": "slides/05_uzorak/prezentacija.html#klaster-slučajan-uzorak", "title": "Populacija i uzorak", "section": "Klaster slučajan uzorak", - "text": "Klaster slučajan uzorak" + "text": "Klaster slučajan uzorak\nKoristan kada nemamo definisan uzorački okvir ili nas zanima opsežna populacija koju nije lako uzorkovati." }, { "objectID": "slides/05_uzorak/prezentacija.html#stratifikovan-slučajan-uzorak", @@ -802,21 +802,21 @@ "href": "slides/05_uzorak/prezentacija.html#terminologija-i-notacija", "title": "Populacija i uzorak", "section": "Terminologija (i notacija)", - "text": "Terminologija (i notacija)\n\n\n \n\n \n \n \n tinytable_1gr6r5qavtsj8tfmzwme\n \n \n \n \n \n\n \n \n \n \n \n \n \n Populacija (parametar)\n Uzorak (statistika)\n \n \n \n \n \n Aritmetička sredina \n $\\mu$ \n $\\bar x$\n \n \n Varijansa \n $\\sigma^2$\n $sd^2$ \n \n \n Standardna devijacija\n $\\sigma$ \n $sd$ \n \n \n Proporcija \n $\\pi$ \n $p$" + "text": "Terminologija (i notacija)\n\n\n \n\n \n \n \n tinytable_gzg1yp9o6i30bso2t83o\n \n \n \n \n \n\n \n \n \n \n \n \n \n Populacija (parametar)\n Uzorak (statistika)\n \n \n \n \n \n Aritmetička sredina \n $\\mu$ \n $\\bar x$\n \n \n Varijansa \n $\\sigma^2$\n $sd^2$ \n \n \n Standardna devijacija\n $\\sigma$ \n $sd$ \n \n \n Proporcija \n $\\pi$ \n $p$" }, { "objectID": "slides/05_uzorak/prezentacija.html#vežba", "href": "slides/05_uzorak/prezentacija.html#vežba", "title": "Populacija i uzorak", "section": "Vežba", - "text": "Vežba\nIz baze “Sistolni pritisak.xlsx” odrediti prost i sistematski uzorak veličine 10.\nProst:\n\nsample(1:99, 10, replace = F)\n\n [1] 80 95 98 91 53 8 48 41 26 75\n\n\nSistematski:\n\nsample(1:99, 1, replace = F)\n\n[1] 13\n\n\n\nOdrediti početnu jedinicu\n\nKorak \\(k = \\frac{99}{10} \\approx 10\\)\nIzabrati svaku 10-tu jedinicu" + "text": "Vežba\nIz baze “Sistolni pritisak.xlsx” odrediti prost i sistematski uzorak veličine 10.\nProst:\n\nsample(1:99, 10, replace = F)\n\n [1] 60 17 73 25 49 39 91 58 92 43\n\n\nSistematski:\n\nsample(1:99, 1, replace = F)\n\n[1] 40\n\n\n\nOdrediti početnu jedinicu\n\nKorak \\(k = \\frac{99}{10} \\approx 10\\)\nIzabrati svaku 10-tu jedinicu" }, { "objectID": "slides/05_uzorak/prezentacija.html#greška-uzorkovanja", "href": "slides/05_uzorak/prezentacija.html#greška-uzorkovanja", "title": "Populacija i uzorak", "section": "Greška uzorkovanja", - "text": "Greška uzorkovanja\nRegardless of how representative our sample is, it’s likely that the statistic that we compute from the sample is going to differ at least slightly from the population parameter. We refer to this as sampling error. If we take multiple samples, the value of our statistical estimate will also vary from sample to sample; we refer to this distribution of our statistic across samples as the sampling distribution." + "text": "Greška uzorkovanja\n\nRazlika između statistike izračunate na uzorku i parametra populacije.\nPonavljanjim uzorkovanjem možemo da saznamo raspodelu greške (uzoračka raspodela) statistike.\n\n\nStandardna greška\n\nStandardna greška je standardna devijacija uzoračke raspodele.\n\n\n\\[ SE_{\\bar x} = \\frac{sd}{\\sqrt{n}} \\]" }, { "objectID": "slides/05_uzorak/prezentacija.html#standardna-greška-aritmetičke-sredine", @@ -837,7 +837,7 @@ "href": "slides/05_uzorak/prezentacija.html#centralna-granična-teorema", "title": "Populacija i uzorak", "section": "Centralna granična teorema", - "text": "Centralna granična teorema\nThe Central Limit Theorem tells us that as sample sizes get larger, the sampling distribution of the mean will become normally distributed, even if the data within each sample are not normally distributed.\n\nThe Central Limit Theorem is important for statistics because it allows us to safely assume that the sampling distribution of the mean will be normal in most cases. This means that we can take advantage of statistical techniques that assume a normal distribution" + "text": "Centralna granična teorema" }, { "objectID": "slides/05_uzorak/prezentacija.html#primer-clt", @@ -858,7 +858,7 @@ "href": "slides/05_uzorak/prezentacija.html#ocenjivanje-populacionih-parametara-na-osnovu-uzorka", "title": "Populacija i uzorak", "section": "Ocenjivanje populacionih parametara na osnovu uzorka", - "text": "Ocenjivanje populacionih parametara na osnovu uzorka\n\\[ CI = \\bar x \\pm t \\times SE \\]\n\\[ SE = \\frac{sd}{\\sqrt{n}} \\]" + "text": "Ocenjivanje populacionih parametara na osnovu uzorka\nJedan od najvažnijih istraživačkih zadataka jeste ocena populacionih parametara, najčešće aritmetičke sredine ili proporcije." }, { "objectID": "slides/05_uzorak/prezentacija.html#interval-poverenja-i-ponovljena-istraživanja", @@ -885,8 +885,8 @@ "objectID": "slides/05_uzorak/prezentacija.html#inverval-poverenja", "href": "slides/05_uzorak/prezentacija.html#inverval-poverenja", "title": "Populacija i uzorak", - "section": "Inverval poverenja", - "text": "Inverval poverenja\nci.png" + "section": "99% Inverval poverenja", + "text": "99% Inverval poverenja" }, { "objectID": "slides/05_uzorak/prezentacija.html#zadatak-1", @@ -907,7 +907,7 @@ "href": "slides/05_uzorak/prezentacija.html#struktura-kursa", "title": "Populacija i uzorak", "section": "Struktura kursa", - "text": "Struktura kursa\n\n\n \n\n \n \n \n tinytable_c6zpm4m5as9bpmtjtboc\n \n \n \n \n \n\n \n \n \n \n \n \n Nedelja\n Tema\n \n \n \n \n \n 1\n Uvod u medicinsku statistiku \n \n \n 2\n Sređivanje podataka \n \n \n 3\n Statističko opisivanje podataka \n \n \n 4\n Verovatnoća i raspodele verovatnoća \n \n \n 5\n Populacija i uzorak \n \n \n 6\n Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama\n \n \n 7\n Testiranje hipoteza o učestalostima \n \n \n 8\n Testiranje hipoteza o rangovima \n \n \n 9\n Korelacija \n \n \n 10\n Regresija / Kolokvijum \n \n \n 11\n Podaci, informacije i znanje \n \n \n 12\n Zdravstveni informacioni sistem \n \n \n 13\n Mere dijagnostičke tačnosti \n \n \n 14\n Medicinsko odlučivanje \n \n \n 15\n Bioinformatika" + "text": "Struktura kursa\n\n\n \n\n \n \n \n tinytable_ojo5xo0fzjyothms3d9m\n \n \n \n \n \n\n \n \n \n \n \n \n Nedelja\n Tema\n \n \n \n \n \n 1\n Uvod u medicinsku statistiku \n \n \n 2\n Sređivanje podataka \n \n \n 3\n Statističko opisivanje podataka \n \n \n 4\n Verovatnoća i raspodele verovatnoća \n \n \n 5\n Populacija i uzorak \n \n \n 6\n Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama\n \n \n 7\n Testiranje hipoteza o učestalostima \n \n \n 8\n Testiranje hipoteza o rangovima \n \n \n 9\n Korelacija \n \n \n 10\n Regresija / Kolokvijum \n \n \n 11\n Podaci, informacije i znanje \n \n \n 12\n Zdravstveni informacioni sistem \n \n \n 13\n Mere dijagnostičke tačnosti \n \n \n 14\n Medicinsko odlučivanje \n \n \n 15\n Bioinformatika" }, { "objectID": "slides/04_verovatnoca/pres.html#de-mérés-problem", @@ -1181,5 +1181,40 @@ "title": "A short introduction to probability", "section": "Chi-square distribution", "text": "Chi-square distribution\n\n\nUzorci iz Z-dist2 (postaju pozitivni) i to postane hi-kvadrat. (sum of square deviations) / (pop. variance) -> kako idu df inf hi postaje z. F dist. (dist of ratio of two variances)" + }, + { + "objectID": "slides/05_uzorak/prezentacija.html#section", + "href": "slides/05_uzorak/prezentacija.html#section", + "title": "Populacija i uzorak", + "section": "", + "text": "The Central Limit Theorem is important for statistics because it allows us to safely assume that the sampling distribution of the mean will be normal in most cases. This means that we can take advantage of statistical techniques that assume a normal distribution" + }, + { + "objectID": "slides/05_uzorak/prezentacija.html#title", + "href": "slides/05_uzorak/prezentacija.html#title", + "title": "Populacija i uzorak", + "section": "Title", + "text": "Title\n\nThe Central Limit Theorem is important for statistics because it allows us to safely assume that the sampling distribution of the mean will be normal in most cases. This means that we can take advantage of statistical techniques that assume a normal distribution" + }, + { + "objectID": "slides/05_uzorak/prezentacija.html#generalizacija", + "href": "slides/05_uzorak/prezentacija.html#generalizacija", + "title": "Populacija i uzorak", + "section": "Generalizacija", + "text": "Generalizacija\nSaznanje o celoj populaciji bez da smo ih videli.\n\n\n\n\n\n%%{ init: { 'flowchart': { 'curve': 'monotoneX' } } }%%\n\nflowchart TD\n A[Ciljna populacija] --> B[\"Uzoračka populacija\"]\n B --> C[Uzorak]\n C --\"Zaključak\"--> A" + }, + { + "objectID": "slides/05_uzorak/prezentacija.html#interval-poverenja-i-tačkasta-procena", + "href": "slides/05_uzorak/prezentacija.html#interval-poverenja-i-tačkasta-procena", + "title": "Populacija i uzorak", + "section": "Interval poverenja i tačkasta procena", + "text": "Interval poverenja i tačkasta procena\n\\[ CI = \\bar x \\pm t \\times SE \\]\ngde je: \\(\\bar x\\), aritmetička sredina; \\(t\\), kritična vrednost; \\(SE\\), standardna greška.\n\\[ SE = \\frac{sd}{\\sqrt{n}} \\]" + }, + { + "objectID": "slides/05_uzorak/prezentacija.html#interval-poverenja", + "href": "slides/05_uzorak/prezentacija.html#interval-poverenja", + "title": "Populacija i uzorak", + "section": "95% interval poverenja", + "text": "95% interval poverenja" } ] \ No newline at end of file diff --git a/docs/slides/05_uzorak/prezentacija.html b/docs/slides/05_uzorak/prezentacija.html index 0dcbede..4bc26d7 100644 --- a/docs/slides/05_uzorak/prezentacija.html +++ b/docs/slides/05_uzorak/prezentacija.html @@ -11,7 +11,7 @@ - + Medicinska statistika i informatika – Populacija i uzorak @@ -405,7 +405,7 @@

Populacija i uzorak

-

2024-10-02

+

2024-10-30

Zašto uzorkujemo

@@ -422,7 +422,6 @@

Zašto uzorkujemo

%%{ init: { 'flowchart': { 'curve': 'monotoneX' } } }%%
-%%| fig-width: 10
 
 flowchart TD
   A[Ciljna populacija] --> B["Uzoračka populacija"]
@@ -579,17 +578,19 @@ 

Uzorkovanje

Uzorački okvir
-test. -
-
Slučajni uzorak
-
-Tačno znamo verovatnoću da neko bude izabran -
-
Neslučajni
-
-Može biti pristrasan +Spisak ili lista svih elemenata populacije koju želimo da uzorkujemo.
+
    +
  1. Slučajni uzorak +
      +
    • Tačno znamo verovatnoću da neko bude izabran
    • +
  2. +
  3. Neslučajni +
      +
    • Može biti pristrasan
    • +
  4. +

Slučajni uzorci

@@ -600,9 +601,9 @@

Slučajni uzorci

  • Klaster
  • -
    +

    Prost slučajan uzorak

    -

    Najjednostavniji oblik uzorkovanja. Bira se \(n\) jedinica iz izmešane populacije (npr. uzorak krvi).

    +

    Najjednostavniji oblik uzorkovanja. Bira se \(n\) jedinica iz izmešane populacije (npr. uzorak krvi).

    -
    +

    Sistematski slučajan uzorak

    -

    Koristi se kao zamena za prost slučajan uzorak kada nemamo spisak jedinica ili je spisak nasumičnog redosleda.

    +

    Koristi se kao zamena za prost slučajan uzorak kada nemamo spisak jedinica ili je spisak nasumičnog redosleda.

    -
    +

    Klaster slučajan uzorak

    +

    Koristan kada nemamo definisan uzorački okvir ili nas zanima opsežna populacija koju nije lako uzorkovati.

    @@ -678,10 +680,10 @@

    Terminologija (i notacija)

    - tinytable_1gr6r5qavtsj8tfmzwme + tinytable_gzg1yp9o6i30bso2t83o @@ -699,7 +701,7 @@

    Terminologija (i notacija)

    - +
    @@ -735,12 +737,12 @@

    Terminologija (i notacija)

    @@ -806,14 +808,14 @@

    Vežba

    sample(1:99, 10, replace = F)
    -
     [1] 80 95 98 91 53  8 48 41 26 75
    +
     [1] 60 17 73 25 49 39 91 58 92 43

    Sistematski:

    sample(1:99, 1, replace = F)
    -
    [1] 13
    +
    [1] 40
      @@ -826,20 +828,25 @@

      Vežba

      Greška uzorkovanja

      -

      Regardless of how representative our sample is, it’s likely that the statistic that we compute from the sample is going to differ at least slightly from the population parameter. We refer to this as sampling error. If we take multiple samples, the value of our statistical estimate will also vary from sample to sample; we refer to this distribution of our statistic across samples as the sampling distribution.

      +
        +
      1. Razlika između statistike izračunate na uzorku i parametra populacije.

      2. +
      3. Ponavljanjim uzorkovanjem možemo da saznamo raspodelu greške (uzoračka raspodela) statistike.

      4. +
      +
      +
      Standardna greška
      +
      +Standardna greška je standardna devijacija uzoračke raspodele. +
      +
      +

      \[ SE_{\bar x} = \frac{sd}{\sqrt{n}} \]

      Standardna greška aritmetičke sredine

      -
      -

      Standardna greška definicija

      -

      Standardna greška je …

      -

      \[ SE_{\bar x} = \frac{sd}{\sqrt{n}} \]

      -
      -
      -

      Centralna granična teorema

      -

      The Central Limit Theorem tells us that as sample sizes get larger, the sampling distribution of the mean will become normally distributed, even if the data within each sample are not normally distributed.

      +
      + +
    +
    @@ -1024,12 +1053,12 @@

    Struktura kursa

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Tačno znamo verovatnoću da neko bude izabran +1. Slučajni uzorak + - Tačno znamo verovatnoću da neko bude izabran -Neslučajni - : Može biti pristrasan +2. Neslučajni + - Može biti pristrasan ## Slučajni uzorci @@ -159,9 +158,9 @@ Neslučajni - Stratifikovani - Klaster -## Prost slučajan uzorak +## Prost slučajan uzorak {.smaller} -Najjednostavniji oblik uzorkovanja. Bira se $n$ jedinica iz *izmešane* populacije (npr. uzorak krvi). +[Najjednostavniji]{.yellow} oblik uzorkovanja. Bira se $n$ jedinica iz *izmešane* populacije (npr. uzorak krvi). ![](slike/simple_random.png){fig-align="center"} @@ -169,9 +168,9 @@ Najjednostavniji oblik uzorkovanja. Bira se $n$ jedinica iz *izmešane* populaci ::: -## Sistematski slučajan uzorak +## Sistematski slučajan uzorak {.smaller} -Koristi se kao zamena za prost slučajan uzorak kada nemamo spisak jedinica ili je spisak nasumičnog redosleda. +Koristi se kao [zamena]{.yellow} za prost slučajan uzorak kada nemamo spisak jedinica ili je spisak nasumičnog redosleda. ![](slike/systematic_sample.png){fig-align="center"} @@ -179,7 +178,9 @@ Koristi se kao zamena za prost slučajan uzorak kada nemamo spisak jedinica ili Ako su jedinice nekako poređane, uzorak će se ponašati kao prost slučajan ukoliko način na koji su poređani (pozicija) nema veze sa ispitivanom karakteristikom ali ne ako je lista ciklicna ili prati neku formu. Sistematski uzorak je forma klaster uzorka. I dalje ima okvir: svaki 10ti čovek koji izađe iz aviona je reprezentativan za ljude u avionu, dok svaki 10ti student koji udje u biblioteku nije. ::: -## Klaster slučajan uzorak +## Klaster slučajan uzorak {.smaller} + +Koristan kada nemamo definisan uzorački okvir ili nas zanima opsežna populacija koju nije lako uzorkovati. ![](slike/cluster.png) @@ -243,7 +244,14 @@ sample(1:99, 1, replace = F) ## Greška uzorkovanja -Regardless of how representative our sample is, it’s likely that the statistic that we compute from the sample is going to differ at least slightly from the population parameter. We refer to this as sampling error. If we take multiple samples, the value of our statistical estimate will also vary from sample to sample; we refer to this distribution of our statistic across samples as the sampling distribution. +1. Razlika između [statistike]{.yellow} izračunate na uzorku i [parametra]{.blue} populacije. + +2. Ponavljanjim uzorkovanjem možemo da saznamo [raspodelu greške]{.yellow} (uzoračka raspodela) statistike. + +Standardna greška + : Standardna greška je standardna devijacija uzoračke raspodele. + +$$ SE_{\bar x} = \frac{sd}{\sqrt{n}} $$ ## Standardna greška aritmetičke sredine @@ -273,17 +281,9 @@ pop %>% y = "standardizovana gustina") ``` -## Standardna greška definicija - -Standardna greška je ... - -$$ SE_{\bar x} = \frac{sd}{\sqrt{n}} $$ - -## Centralna granična teorema +___ -The Central Limit Theorem tells us that as sample sizes get larger, the sampling -distribution of the mean will become normally distributed, even if the data -within each sample are not normally distributed. +{{< video https://youtu.be/zeJD6dqJ5lo?t=381 width="100%" height="100%" >}} ::: {.notes} The Central Limit Theorem is important for statistics because it allows us to @@ -329,21 +329,40 @@ sample_mean %>% y = "standardizovana gustina") ``` -## Ciljna grupa throwback +## Generalizacija + +Saznanje o celoj populaciji bez da smo ih videli. + +```{mermaid} +%%| fig-align: "center" +%%{ init: { 'flowchart': { 'curve': 'monotoneX' } } }%% + +flowchart TD + A[Ciljna populacija] --> B["Uzoračka populacija"] + B --> C[Uzorak] + C --"Zaključak"--> A +``` -Kako da saznam nesto o grupi pacijenata ## Ocenjivanje populacionih parametara na osnovu uzorka +Jedan od najvažnijih istraživačkih zadataka jeste [ocena]{.yellow} populacionih parametara, najčešće aritmetičke sredine ili proporcije. + +## Interval poverenja i tačkasta procena + $$ CI = \bar x \pm t \times SE $$ +gde je: $\bar x$, aritmetička sredina; $t$, kritična vrednost; $SE$, standardna greška. + $$ SE = \frac{sd}{\sqrt{n}} $$ -## Interval poverenja i ponovljena istraživanja +## 95% interval poverenja ```{r} #| fig-align: "center" +set.seed(55224) + n_rep <- 100 mu <- 6 sigma <- 4 @@ -351,25 +370,26 @@ sigma <- 4 tibble( sim_id = 1:n_rep, est = rnorm(n_rep, mu, sigma), - conf_67_low = est - 0.674*sigma, - conf_67_high = est + 0.674*sigma, - conf_low = est - 1.960*sigma, - conf_high = est + 1.960*sigma -) %>% + conf_67_low = est - 0.674 * sigma, + conf_67_high = est + 0.674 * sigma, + conf_low = est - 1.960 * sigma, + conf_high = est + 1.960 * sigma +) %>% + mutate(outside_ci = if_else(mu < conf_low | mu > conf_high, "Nije obuhvaćen", "Obuhvaćen")) %>% ggplot(aes(y = est, x = sim_id)) + geom_hline(yintercept = mu, color = "#F7F8F9") + - geom_point(color = "#F4BA02") + - geom_pointrange(aes(ymin = conf_low, ymax = conf_high), color = "#F4BA02") + - geom_pointrange(aes(ymin = conf_67_low, ymax = conf_67_high), - linewidth = 1.1, color = "#F4BA02") + + geom_point(aes(color = outside_ci)) + + geom_pointrange(aes(ymin = conf_low, ymax = conf_high, color = outside_ci)) + + geom_pointrange(aes(ymin = conf_67_low, ymax = conf_67_high, color = outside_ci), linewidth = 1.1) + + scale_color_manual(values = c("Obuhvaćen" = "#F4BA02", "Nije obuhvaćen" = "red")) + theme_blue() + labs( y = "Ocena, 50%, i 95% interval poverenja", - x = "Simulacija" - ) + x = "Simulacija", + color = "") + + theme(legend.position = "bottom") ``` - ## Definicija {.center} ::: {.r-fit-text} @@ -390,9 +410,32 @@ rizik greške) ali je širi od 95%. ::: -## Inverval poverenja +## 99% Inverval poverenja + +```{r} +tibble( + sim_id = 1:n_rep, + est = rnorm(n_rep, mu, sigma), + conf_67_low = est - 0.674 * sigma, + conf_67_high = est + 0.674 * sigma, + conf_low = est - 2.576 * sigma, + conf_high = est + 2.576 * sigma +) %>% + mutate(outside_ci = if_else(mu < conf_low | mu > conf_high, "Nije obuhvaćen", "Obuhvaćen")) %>% + ggplot(aes(y = est, x = sim_id)) + + geom_hline(yintercept = mu, color = "#F7F8F9") + + geom_point(aes(color = outside_ci)) + + geom_pointrange(aes(ymin = conf_low, ymax = conf_high, color = outside_ci)) + + geom_pointrange(aes(ymin = conf_67_low, ymax = conf_67_high, color = outside_ci), linewidth = 1.1) + + scale_color_manual(values = c("Obuhvaćen" = "#F4BA02", "Nije obuhvaćen" = "red")) + + theme_blue() + + labs( + y = "Ocena, 50%, i 99% interval poverenja", + x = "Simulacija", + color = "") + + theme(legend.position = "bottom") +``` -ci.png ## Zadatak 1

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