????? ? ?????? ???? (? ???????? Shapiro-Wilk test ) ? ???? ?? ???? ?????? ?????? ???? ????? ?? : ?????? ???????? ?????? ??? ??? ????? ????? (?????).

????? ? ?????? ???? ??????? ? ?????? ??? ?????? ???? ?????? ??????? ????? (??? ?? 50). ??? ????? ????? ??? ??? ^[1] ?? ??? ????????? ?????? ?????? ( ???????? ) ? ????? ???? ( ?????? ) ? 1965. ^[2]

?????????? ? ????? [ ??? | ??? ???? ]

??? ??????? ???? ???? ${\displaystyle n}$ ???? ? ??????? ??????? ? ???? ???????? ????? ${\displaystyle X}$ ??????????? ? ????? ${\displaystyle W}$ ??:

${\displaystyle W={\frac {[\textstyle \sum _{i=1}^{\left\lceil {\frac {n}{2}}\right\rceil }\displaystyle a_{i}(x_{n-i+1}-x_{i})]^{2}}{\textstyle \sum _{i=1}^{n}\displaystyle (x_{i}-{\overline {x}})^{2}}}}$ ???

• ${\displaystyle (x_{i})}$ ???? ?????? ???? ???????? ${\displaystyle X}$ ????? ?? ?????? ? ??????.
• ${\displaystyle [{\frac {n}{2}}]}$ ?? ???? ????? ${\displaystyle {\frac {n}{2}}}$.
• ${\displaystyle {\overline {x}}}$ ?? ?????? ?????? ???? ????? ???? ${\displaystyle X}$.
• ${\displaystyle a_{i}}$ ???? ????? ??????? ???????? ?? ????? ???? ?????? ????????? ??? ???? ???? ????? ????? (???? ?????? ${\displaystyle n}$) ? ?????? ?????? ?????.

?????????? ${\displaystyle W}$ ???? ???? ???? ????? ????? ???? ?????? ? ???????? ?? ??? 2 ???? ???????: ???? ?????????? ?????? ? ????????? ????? ???????. ????? ???? ${\displaystyle W}$ ?????? ?????? ?????? ???? ?????? ?????? ????? ??? ???? ?????. ^[3]

????? ??????? ????? [ ??? | ??? ???? ]

????? ??? ??????? ?????? ?????? ??? ???? ????? ????????? ${\displaystyle \alpha }$ ? ???????? ? ????? ${\displaystyle n}$. ??? ???? ${\displaystyle W<W(\alpha ,n)}$ ????????? ?????? ? ?????? ?????? ?????????.

??? ????? ? ? (p-value) ? ?? ???? ${\displaystyle \alpha }$ (?????? ? ?????? ??????? 0.05):

• ??? ???? ? p-value ??? ?? ????? ${\displaystyle \alpha }$ ?? ???????? ?????? ????.
• ??? ???? ? p-value ??? ?? ????? ${\displaystyle \alpha }$? ?? ???????? ?????? ????.

???? ????? [ ??? | ??? ???? ]