Samenvatting Voortgezette Statistiek en ‘R’
Proportions
Binomial test: test whether a proportion found in a sample differs significantly from an assumed
(null-hypothesized) proportion
- Hypotheses:
o H0: p= 0.5 (geen verschil, kan elke waarde zijn)
o HA: p≠ 0.5
- In R:
- Confidence interval
Z-test: comparing two proportions -> difference between proportions p1 and p2?
- Hypotheses:
o H0: p₁= p₂, or p₁ – p₂= 0
o HA: p₁≠ p₂, or p₁ – p₂≠ 0
- In R: wordt eigenlijk chi^2 test uitgevoerd (chi^2 = Z^2)
1
, Samenvatting Voortgezette Statistiek en ‘R’
Probability models
χ2-goodness-of-fit test: comparing proportions of categorical or discrete variables to the probabilities
of a null model
- Hypotheses:
o H0: for each item/individual in the sample, the probabilities that it falls into each
class/level are p₁= p=, ...= pk (allemaal gelijk)
o HA: probabilities zijn niet allemaal gelijk
- χ2 distribution (W&S Statistical Table A)
- Practical rule of thumb: at least 80% of the expected frequencies Ei must be at least 5 (Ei ≥ 5),
and none of the expected frequencies can be smaller than 1 (Ei < 1)
- In R:
- If your null model has a parameter that you estimate using your data, you need to calculate
the P-value yourself
Contingency analysis
Odds for an event (O): the probability that it occurs, divided by the probability that it does not occur
- Format
2
Proportions
Binomial test: test whether a proportion found in a sample differs significantly from an assumed
(null-hypothesized) proportion
- Hypotheses:
o H0: p= 0.5 (geen verschil, kan elke waarde zijn)
o HA: p≠ 0.5
- In R:
- Confidence interval
Z-test: comparing two proportions -> difference between proportions p1 and p2?
- Hypotheses:
o H0: p₁= p₂, or p₁ – p₂= 0
o HA: p₁≠ p₂, or p₁ – p₂≠ 0
- In R: wordt eigenlijk chi^2 test uitgevoerd (chi^2 = Z^2)
1
, Samenvatting Voortgezette Statistiek en ‘R’
Probability models
χ2-goodness-of-fit test: comparing proportions of categorical or discrete variables to the probabilities
of a null model
- Hypotheses:
o H0: for each item/individual in the sample, the probabilities that it falls into each
class/level are p₁= p=, ...= pk (allemaal gelijk)
o HA: probabilities zijn niet allemaal gelijk
- χ2 distribution (W&S Statistical Table A)
- Practical rule of thumb: at least 80% of the expected frequencies Ei must be at least 5 (Ei ≥ 5),
and none of the expected frequencies can be smaller than 1 (Ei < 1)
- In R:
- If your null model has a parameter that you estimate using your data, you need to calculate
the P-value yourself
Contingency analysis
Odds for an event (O): the probability that it occurs, divided by the probability that it does not occur
- Format
2
