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Formule en tabelblad Premaster Beschrijvende en inferentiële statistiek (S_PMBIS)
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Formule en tabelblad Premaster Beschrijvende en inferentiële statistiek (S_PMBIS)
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FormulebladBeschrijvende statistiek
∑𝑥 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑤𝑤𝑤𝑤𝑤𝑤 − 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔
Gemiddelde 𝑥̅ = Z-score 𝑧 − 𝑠𝑠𝑠𝑠𝑠 =
𝑛 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
Gewogen 𝑛1 𝑥1 + 𝑛2 𝑥2 1 1 𝑥 − 𝑥̅ 𝑦 − 𝑦�
𝑥̅ = Correlatiecoëfficiënt 𝑟= � 𝑧𝑥 𝑧𝑦 = �� �� �
gemiddelde 𝑛1 + 𝑛2 𝑛−1 𝑛−1 𝑠𝑥 𝑠𝑦
𝑦� = 𝑎 + 𝑏𝑏
Standaard ∑(𝑥 − 𝑥̅ )2
deviatie 𝑠=� Regressielijn 𝑠
𝑛−1 𝑏 = 𝑟 � 𝑦� en 𝑎 = 𝑦� − 𝑏(𝑥̅ )
𝑠
𝑥
∑(𝑥 − 𝑥̅ ) 2
Variantie 𝑠2 =
𝑛−1
Kansberekening en kansverdelingen
Kans op niet A 𝑃(𝐴𝑐 ) = 1 – 𝑃(𝐴)
𝑃(𝐴 𝑒𝑒 𝐵)
Conditionele kans op A gegeven B 𝑃(𝐴|𝐵) =
𝑃(𝐵)
Kans op A óf B 𝑃(𝐴 𝑜𝑜 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) – 𝑃(𝐴 𝑒𝑒 𝐵)
Kans op A èn B
𝑃(𝐴 𝑒𝑒 𝐵) = 𝑃(𝐴) × 𝑃(𝐵)
(bij onafhankelijkheid)
Verwachte celwaarde (“expected cell (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟) × (𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑎𝑎𝑎)
count”) 𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
Gemiddelde van kansverdeling/
𝜇 = 𝐸(𝑦) = � 𝑥𝑥(𝑥)
verwachte waarde
Eén proportie of gemiddelde
Proportie (𝑝) Gemiddelde (𝜇)
Betrouwbaarheidsinterval
𝑝̂ ± 𝑧(𝑠𝑠) 𝑥̅ ± 𝑡(𝑠𝑠)
(“confidence interval”)
Vrijheidsgraden (df) - 𝑑𝑑 = 𝑛 − 1
𝑝̂ (1 − 𝑝̂ ) 𝑠
Standaardfout (“standard error”) 𝑠𝑠 = � 𝑠𝑠 =
𝑛 √𝑛
𝑝̂ − 𝑝0 𝑥̅ − 𝜇0
Testwaarde (“test statistic”) 𝑧= 𝑡=
𝑠𝑠0 𝑠𝑠
𝑝0 (1 − 𝑝0 )
Exacte standaardfout 𝑠𝑠0 = � -
𝑛
Twee gemiddelden
onafhankelijke steekproeven afhankelijke steekproeven
Betrouwbaarheidsinterval (𝑥̅1 − 𝑥̅2 ) ± 𝑡(𝑠𝑠) (𝑥̅𝑑 ) ± 𝑡(𝑠𝑠)
𝑠12 𝑠 2 𝑠𝑑
Standaardfout 𝑠𝑠 = � + 2 𝑠𝑠 =
𝑛1 𝑛2 √𝑛
(𝑥̅1 − 𝑥̅2 ) − 0 (𝑥̅𝑑 ) − 0
Testwaarde 𝑡= 𝑡=
𝑠𝑠 𝑠𝑠
Vrijheidsgraden df = n1 + n2 - 2 df = n - 1
1
, Categorische variabelen
(𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑎𝑎𝑎𝑎𝑎𝑎 − 𝑣𝑣𝑣𝑣𝑣𝑣ℎ𝑡 𝑎𝑎𝑎𝑎𝑎𝑎)2
Testwaarde 𝒳2 = �
𝑣𝑣𝑣𝑣𝑣𝑣ℎ𝑡 𝑎𝑎𝑎𝑎𝑎𝑎
Vrijheidsgraden 𝑑𝑑 = (𝑟 − 1) × (𝑘 − 1)
𝑝1
Relatief risico (“relative risk”)
𝑝2
𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑎𝑎𝑎𝑎𝑎𝑎 − 𝑣𝑣𝑣𝑣𝑣𝑣ℎ𝑡 𝑎𝑎𝑎𝑎𝑎𝑎
Gestandaardiseerd residu
𝑠𝑠
Regressie
Residual sum of squares 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆 = �(𝑦 − 𝑦�)2
Total sum of squares 𝑡𝑡𝑡𝑡𝑡 𝑆𝑆 = �(𝑦 − 𝑦�)2
Regression sum of squares 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆 = 𝑡𝑡𝑡𝑡𝑡 𝑆𝑆 − 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆 = �(𝑦� − 𝑦�)2
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆
Proportionele error reductie (= 𝑟 2 ) 𝑃𝑃𝑃 = = 𝑟 2 𝑜𝑜 𝑅 2
𝑡𝑡𝑡𝑡𝑡 𝑆𝑆
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆
Residu standaard deviatie 𝑦 𝑠𝑟𝑟𝑟 = �
𝑑𝑑
𝑑𝑑 = 𝑛 − (𝑘 + 1)
𝑦 − 𝑦�
Gestandaardiseerd residu
𝑠𝑠(𝑦 − 𝑦�)
Bivariate regressie Multipele regressie
Regressiemodel 𝜇𝑦 = 𝛼 + 𝛽𝛽 𝜇𝑦 = 𝛼 + 𝛽1 𝑥1 + 𝛽2 𝑥2 + ⋯ + 𝛽𝑘 𝑥𝑘
Steekproef schattingsformule 𝑦� = 𝑎 + 𝑏𝑏 𝑦� = 𝑎 + 𝑏1 𝑥1 + 𝑏2 𝑥2 + ⋯ + +𝑏𝑘 𝑥𝑘
Gelijktijdige
Afzonderlijke effecten
effecten
𝑏−0 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆 / 𝑑𝑑1 𝑏1 − 0
Testwaarde voor H0: 𝛽 = 0 𝑡= 𝐹= 𝑡=
𝑠𝑠 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑆𝑆/ 𝑑𝑑2 𝑠𝑠
𝑑𝑑1 = 𝑘
Vrijheidsgraden 𝑑𝑑 = 𝑛 − 2 𝑑𝑑 = 𝑛 − (𝑘 + 1)
𝑑𝑑2 = 𝑛 − (𝑘 + 1)
Betrouwbaarheidsinterval 𝛽 𝑏 ± 𝑡(𝑠𝑠) - 𝑏1 ± 𝑡(𝑠𝑠)
Betrouwbaarheidsinterval voor 𝑠𝑟𝑟𝑟 𝑠𝑟𝑟𝑟
𝑦� ± 𝑡 � � - 𝑦� ± 𝑡 � �
𝜇𝑦 voor gegeven waarde van 𝑥 √𝑛 √𝑛
Schattingsinterval (“prediction
𝑦� ± 𝑡(𝑠𝑟𝑟𝑟 ) - 𝑦� ± 𝑡(𝑠𝑟𝑟𝑟 )
interval”) voor 𝑦
Betrouwbaarheidsanalyse
Cronbach’s alfa (bij gelijke standaard 𝑘𝑟̅
𝛼=
deviaties) 1 + (𝑘 − 1)𝑟̅
2
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