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Statistics II Formula Overview $4.85   Add to cart
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Statistics II Formula Overview
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  • Course
  • Statistics 2 (PSBE207)
  • Institution
  • Rijksuniversiteit Groningen (RuG)

This documents contains the formulas learned in Statistics II. It mentions when and where to use them. There is also an overview of ANOVA tables, as well as the assumption checklist for regressions.

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Document information

  • July 26, 2024
  • 3
  • 2022/2023
  • Other
  • Unknown

Subjects

  • formulas
  • assumptions
  • when and where to use formulas

Written for

  • Rijksuniversiteit Groningen (RuG)
  • Psychologie
  • Statistics 2 (PSBE207)
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Correlation:
T-tests Hypothesis Df Where to use
t=
.√&'( H0: r=0 Df= n – 2 To test if there is a correlation
0'. ! between x and y. 1 predictor
!
variable.
t = 12 H0: b=0

03. H0: r=0
rz= 0.5 × ln(0'.)

Linear regression:
T-tests and CI Hypothesis Df Where to use
!" H0: bi=0 Df= n – p – 1 To test if one of the predictors
t = #$!"
has an effect on y.
Df= n – p – 1
CI: 𝑏" ± 𝑡 ∗ × 𝑆𝐸!"
The confidence for the model
∗
𝑏 ± 𝑡&'( × 𝑆𝐸! Df= n – 2 parameter 𝛽.

The confidence interval for the
∗
𝐸(𝑦) ± 𝑡&'( × 𝑆𝐸)*+, Df= n – 2 mean response.

The prediction interval for a
∗
𝑦ℎ𝑎𝑡 ± 𝑡&'( × 𝑆𝐸-*+, Df= n – 2 value of y, for one individual.

2-ANOVA CI:
CI Df Where to use
𝑠𝑝 Df= n – g (one-way) The confidence interval of the population
𝑦𝑏𝑎𝑟𝑖 ± 𝑡 ∗
√𝑛𝑖 Df= n – (I x J) (two- mean.
way)
𝑠𝑖 Df= ni- 1 The confidence interval for an individual in
𝑦𝑏𝑎𝑟𝑖 ± 𝑡 ∗ group i.
√𝑛𝑖

1-ANOVA table regression:
SS Df MS F
Model Sum(yhati – ybar)2 p (= g – 1) SSM/Dfm MSM/MSE
Error Sum(yi – yhati)2 n–p–1 SSE/Dfe = s2
Total Sum(yi – ybar)2 n–1 TSS/Dft= sy2

1-ANOVA table groups:
SS Df MS F
Group Sum(ybari – ybar)2 g–1 SSGr/DfGr MSGr/MSE
Error Sum(yij – ybari)2 n–g SSE/DfE
Total Sum(yij – ybar)2 n-1 TSS/DfT

2-ANOVA table:
SS Df MS F
Factor A SSA i–1 SSA/DfA MSA/MSE
Factor B SSB j–1 SSB/DfB MSB/MSE
Interaction SSAB (i – 1 )(j – 1) SSAB/DfAB MSAB/MSE

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