Statistics Agresti Flashcards
hypothesis
statement claiming that a population parameter takes a certain value or lies within a particular range of values
significance test
summarize the data that is evidence for or against a hypothesis
null hypothesis
statements that a population parameter takes a certain value (no effect)
alternative hypothesis
statement that a population parameter takes an alternative value
test statistic describesβ¦
how far the point estimate falls from the population parameter, given the null hypothesis.
p-value
probability that the test statistic equals the observed value or a more extreme value.
the p value is calculated presuming that H⦠is true
H0
smaller p values provide stronger evidenceβ¦
against the H0
H0 is never about β¦
sample statistics (such as p dakje of x met streepje boven!!!)
relatie H0 en Ha alsin hoe je het schrijft
H0 altijd met = teken, Ha is altijd in relatie tot H0.
explanatory variable
independent
response variable
dependent
proportions 2 groups alsβ¦
explanatory (indep) = binary, response (dep) = categorical
standard error of the difference between sample proportions describesβ¦
the difference in population proportions
large enough sample bij proportions
10 successes and 10 failures
CI interval for two population proportions
(πΜ1β πΜ2) Β± π§(π β )
CI interpreteren
- als er een 0 in zit: plausibel dat er geen effect is (verschil tussen de twee groepen = 0)
- als het positief is: p1 > p2
- als het negatief is: p1 < p2
Dus het gaat echt om het verschil tussen de twee groepen! Dus als deze value dicht bij de 1 zit, is er waarschijnlijk een klein verschil.
πΜ naam
pooled estimate
hoe bereken je de πΜ voor de se formule van z score
The number of successes in both groups and then dividing this number by the total number of participants used in both groups (π1 + π2).
total successes/total n
wat is de 0 in de formule
de value van de H0!! (H0: p = β¦)
quantitative dependent variable (sigaretten -> bloeddruk)
Based on the difference in sample means, π₯1 β π₯2, we want to draw conclusions about the difference
in population means, π1β π2
verschil o, s en se
- o is standard deviation of population,
- s is standard deviation of sample,
- se is the standard deviation of its sampling distribution or an estimate of that standard deviation.
wat gebruik je bij quantitative dependent variable
de mean!
z score is R/L tail, t score is R/L tail
z = left, t = right
CI for mean difference between two groups
(π₯1 βπ₯2) Β± π‘.975(π β )
how to calculate the df for means two groups
if π 1= π 2 and π1= π2, then ππ = (π1+ π2β 2).
the degrees of freedom will usually fall betweenβ¦
(π1+ π2 β 2), with a minimum of (π1β 1)and (π2β 1)
t test is ook robust bij samples kleiner dan 30
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mean assumptions
qualitative, random, large sample
if a two-sided test rejects the null hypothesis of the population being equal, then the confidence
interval for the same error probability (e.g. Ξ±=0.05 and confidence level is 95%) will not contain 0.
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dependent samples
within-group design, repeated measures, matched pairs β> when they use the same subjects (even if it is a pair)
independent samples
when the observations in one sample are independent from the observations in another sample
paired differences
use with matched pairs: calculate xd (score 1 - score2)
xd is ook gelijk aanβ¦.
the difference between the means of two samples:
xd = (xΜ1 β xΜ2)
wat is makkelijk aan dependent samples
het wordt een one sample analysis, want je kan gewoon de scores van elkaar aftrekken.
CI voor dependent samples
(xd.) Β± π‘.975(π β )
z score is β¦ tail
left
hoe bereken je de p value voor =/=
- eerst z score (formule met wortel)
- norm.s.dist
- 1-norm.s.dist
- 2 * vorige antwoord
hoe bereken je de p waarde voor Ha: p < p0
- z score berekenen: formule met wortel
- norm.s.dist
hoe bereken je de p waarde voor p > p0
- z score (formule met wortel)
- norm.s.dist
- 1-β¦
als je % ziet dan is hetβ¦.
proportion -> z score!
P(type 1 error) =
significance level
we do not know if a decision is correct, altijd een kans dat het niet zo is.
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type 1 error
reject H0 when it is true false positive
type 2 error
accept H0 when it is not true, false negative
CI is more useful than p value
want bevat alle plausibele waardes; p value laat alleen zien of de H0 plausibel is
p-value definitie nog een keer
A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true.
CI definition
For a 95 % confidence interval, if many samples are collected and the confidence interval computed, in the long run about 95 % of these intervals would contain the true mean.
P(type 1 error) decreases ifβ¦
- bigger sample size
- parameter moves further away from H0, towards Ha.
Power =
1-P(type 2 error)
3 assumptions t test
Data are quantitative and have been produced randomly and have an approximate normal population distribution.
when a p value lies underneith 0,05, does the CI contain the H0?
No, the interval does not contain H0 in 95% CI if it is rejected by the p value
