11.8: Sura ya Mfumo wa Mapitio

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Ukweli Kuhusu Usambazaji wa Chi-Square

\(x^{2}=\left(Z_{1}\right)^{2}+\left(Z_{2}\right)^{2}+\ldots\left(Z_{d f}\right)^{2}\)chi-mraba usambazaji random variable

\(\mu_{\chi}^{2}=d f\)chi-mraba usambazaji idadi ya watu maana

\(\sigma_{\chi^{2}}=\sqrt{2(d f)}\)Chi-Square usambazaji idadi ya watu kiwango kupotoka

Mtihani wa Tofauti moja

\(\chi^{2}=\frac{(n-1) s^{2}}{\sigma_{0}^{2}}\)Mtihani wa moja ugomvi takwimu ambapo:: sampuli ukubwa
\(n\)
\(s\): sampuli kiwango kupotoka
\(\sigma_{0}\): nadharia thamani ya idadi ya watu kiwango kupotoka

\(df = n – 1\)Degrees ya uhuru

Mtihani wa Tofauti moja

Tumia mtihani ili kuamua tofauti.
Daraja la uhuru ni idadi ya sampuli — 1.
Takwimu za mtihani ni\(\frac{(n-1) s^{2}}{\sigma_{0}^{2}}\), ambapo\(n\) = ukubwa wa sampuli,\(s^2\) = sampuli ugomvi, na\(\sigma^2\) = ugomvi wa idadi ya watu.
Jaribio linaweza kushoto-, haki-, au mbili-tailed.

Nzuri-ya-fit mtihani

\(\sum_{k} \frac{(O-E)^{2}}{E}\)nzuri-ya-fit mtihani takwimu ambapo:

\(O\): maadili aliona
\(E\): inatarajiwa maadili

\(k\): idadi ya seli tofauti data au makundi

\(df = k − 1\)digrii za uhuru

Mtihani wa Uhuru

Idadi ya digrii za uhuru ni sawa na (idadi ya nguzo - 1) (idadi ya safu - 1).
Takwimu za mtihani ni\(\sum_{i \cdot j} \frac{(O-E)^{2}}{E}\) wapi\(O\) = maadili\(E\) yaliyozingatiwa,\(i\) = maadili yaliyotarajiwa, = idadi ya safu katika meza, na\(j\) = idadi ya nguzo katika meza.
Kama hypothesis null ni kweli, idadi inatarajiwa\(E=\frac{(\text { row total })(\text { column total })}{\text { total surveyed }}\).

Mtihani wa Homogeneity

\(\sum_{i . j} \frac{(O-E)^{2}}{E}\)Takwimu za mtihani wa homogeneity ambapo:\(O\) = maadili yaliyozingatiwa
\(E\) = maadili yaliyotarajiwa
\(i\) = idadi ya safu katika meza ya dharura ya data
\(j\) = idadi ya nguzo katika meza ya dharura ya data

\(df = (i −1)(j −1)\)Degrees ya uhuru