Graphics Programs Reference
In-Depth Information
quantity
2
is defi ned as the sum of the these squared differences devided by
the expected frequencies.
χ
chi2 = sum((n_exp - n_syn).^2 ./n_syn)
ans =
2.1685
The critical
χ
2
can be calculated using
chi2inv
. The
χ
2
-test requires the
degrees of freedom
. In our example, we test the hypothesis that the data are
gaussian distributed, i.e., we estimate two parameters
Φ
µ
and
σ
. The number
of degrees of freedom is
=8-(2+1)=5. We test our hypothesis on a
p
=95%
signifi cance level. The function
chi2inv
computes the inverse of the
Φ
χ
2
CDF with parameters specifi ed by
Φ
for the corresponding probabilities in
p
.
chi2inv(0.95,5)
ans =
11.0705
The critical
2
of 2.1685. We
therefore cannot reject the null hypothesis. Hence, we conclude that our data
follow a gaussian distribution.
χ
2
of 11.0705 is well above the measured
χ
Recommended Reading
Bernoulli J (1713) Ars Conjectandi. Reprinted by Ostwalds Klassiker Nr. 107-108.
Leipzig 1899
Fisher RA (1935) Design of Experiments. Oliver and Boyd, Edinburgh
Helmert FR (1876) Über die Wahrscheinlichkeit der Potenzsummen der Beobachtungsfehler
und über einige damit im Zusammenhang stehende Fragen. Zeitschrift für Mathematik
und Physik 21:192-218
Pearson ES (1990) Student·, A Statistical Biography of William Sealy Gosset. In: Plackett
RL, with the Assistance of Barnard G.A., Oxford, University Press
Pearson K (1900) On the criterion that a given system of deviations from the probable in the
case of a correlated system of variables is such that it can be reasonably supposed to have
arisen from random sampling. Philos. Mag. 5, 50:157-175
Poisson SD (1837) Recherches sur la Probabilité des Jugements en Matière Criminelle et
en Matière Civile, Précédées des Regles Générales du Calcul des Probabilités, Bachelier,
Imprimeur-Libraire pour les Mathematiques. Paris, 1837
Sachs L (2000) Angewandte Statistik - Anwendung statistischer Methoden, Zehnte,
überarbeitete und aktualisierte Aufl age. Springer Berlin Heidelberg New York
Snedecor GW, Cochran WG (1989) Statistical Methods, Eighth Edition. Iowa State University
Press
Spiegel MR (1994) Theory and Problems of Statistics, 2nd Edition. Schaum·s Outline Series,
McGraw-Hill
