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Samenvatting statistiek
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Statistiek 2De student kan een experimenteel bepaald gemiddelde vergelijken
met de werkelijke waarde en toetsen op significantie (t-toets).
The term null is used to imply that there is no difference between the observed and
known values apart from that due to random variation. Assuming that the null
hypothesis is true, statistical theory can be used to calculate the probability that the
observe difference (or a greater one) between the sample mean, χ , and the true
value, μ, arises solely as a result of random errors. Usually the null hypothesis is
rejected if the probability of such a difference occurring by chance is less then 1 in
20. In such a case the difference between χ ∧μ is said to be significant at the P=0.05
(or 5% level) (there is a 1:20 chance for a false rejection of a true null hypothesis).
In order to decide whether the difference between χ ∧μ is significant, i.e. to test Η 0 :
mean of the population from which the sample is drawn= μ, the statistic t is calculated
from :
t=( χ −μ ) √ n /s (eq ARA)
Where χ = sample mean, s= sample standard deviation and n=sample size.
μ=known value of themean
As the equation implies, when the difference between μ∧ χ increases, t also
increases, if t exceeds a certain critical value then the null hypothesis H 0 is rejected.
The critical value of t for a give significance level can be found from Table A.2. for
example, for a sample of size 10 (9 degrees of freedom) and a significance level of
0.01 (99%), the critical value of t9 is 3.25 (as in chapter 2, the subscript is used here
to denote the number of degrees of freedom).
If the observed value of t is less than the critical value the null hypothesis is retained:
there is no evidence of systematic error.
T-toets
, vergelijken van een experimenteel bepaald gemiddelde x met een werkelijke
waarde μ
Ho = er is geen verschil tussen het gemiddelde en de werkelijke waarde (naast
toevallige fouten). En er is geen systematische fout aanwezig :
x=μ
H1 = Er is wel verschil tussen het gemiddelde en de werkelijke waarde (naast
toevallige fouten). En er is wel een systematische fout aanwezig
x≠ μ
Bij de t-toets wordt de t waarde berekend worden volgens :
t=( χ −μ ) √
n
s
Als berekende t-waarde groter is dan t critical word Ho verworpen en H1
aangenomen.
Als t kleiner dan t critical wordt H1 verworpen en Ho aangenomen
Ho aannemen betekent dat μ binnen het B.I. ligt.
H1 aannemen betekent dat μ buiten het B.I. ligt.
De student een significantie toets uitvoeren op verschillende gemiddelden
(mogelijk verkregen met 2 methodieken (gepaarde t-toets)). / welch t-test
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