╨Р╨Э╨Ю╨Т╨Р ╨┐╤А╨╛╤В╨╕╨▓ ╨Р╨Э╨Ъ╨Ю╨Т╨Р

╨а╨░╨╖╨╜╨╕╤Ж╨░ ╨╝╨╡╨╢╨┤╤Г ANOVA ╨╕ ANCOVA

╨Т ANOVA vs ANCOVA ANOVA ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╨░╨╜╨░╨╗╨╕╨╖ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕, ╨░ ANCOVA ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╨░╨╜╨░╨╗╨╕╨╖ ╨║╨╛╨▓╨░╤А╨╕╨░╤Ж╨╕╨╕. ╨Ю╤Б╨╜╨╛╨▓╨╜╨╛╨╡ ╤А╨░╨╖╨╗╨╕╤З╨╕╨╡ ╨╝╨╡╨╢╨┤╤Г ╨╛╨▒╨╛╨╕╨╝╨╕ ╨╝╨╡╤В╨╛╨┤╨░╨╝╨╕, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╤Л╨╝╨╕ ╨┤╨╗╤П ╨░╨╜╨░╨╗╨╕╨╖╨░ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕ ╤Б╤А╨╡╨┤╨╜╨╕╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣, ╨╖╨░╨║╨╗╤О╤З╨░╨╡╤В╤Б╤П ╨▓ ╤В╨╛╨╝, ╤З╤В╨╛ ╨╝╨╡╤В╨╛╨┤ ANCOVA ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П, ╨║╨╛╨│╨┤╨░ ╨╡╤Б╤В╤М ╨║╨╛╨▓╨░╤А╨╕╨░╤В╤Л (╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╤О╤Й╨╕╨╡ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╤Г╤О ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Г╤О ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Г╤О), ╨░ ANOVA ╨┐╨╛╨┤╤Е╨╛╨┤╨╕╤В, ╨║╨╛╨│╨┤╨░ ╨╜╨╡╤В ╨║╨╛╨▓╨░╤А╨╕╨░╤В. ╨Я╨╛ ╤Б╤Г╤В╨╕, ╨▓ ANOVA ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╨╝╨╕ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╝╨╕ ╤П╨▓╨╗╤П╤О╤В╤Б╤П ╨▓╤Б╨╡ ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╤Л╨╡ ╤В╨╕╨┐╤Л, ╨░ ╨▓ ANCOVA ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡ ╨╝╨╛╨│╤Г╤В ╨▒╤Л╤В╤М ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╤Л╨╝╨╕ ╨╕ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╤Л╨╝╨╕ ╤В╨╕╨┐╨░╨╝╨╕.

╨Ю╨│╨╗╨░╨▓╨╗╨╡╨╜╨╕╨╡

• ╨а╨░╨╖╨╜╨╕╤Ж╨░ ╨╝╨╡╨╢╨┤╤Г ANOVA ╨╕ ANCOVA
  • ANOVA ╨┐╤А╨╛╤В╨╕╨▓ ANCOVA ╨Ш╨╜╤Д╨╛╨│╤А╨░╤Д╨╕╨║╨░
  • ╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╨Р╨╜╨╛╨▓╨░?
  • ╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╨Р╨Э╨Ъ╨Ю╨Т╨Р?
  • ╨б╤А╨░╨▓╨╜╨╕╤В╨╡╨╗╤М╨╜╨░╤П ╤В╨░╨▒╨╗╨╕╤Ж╨░
  • ╨б╤Е╨╛╨┤╤Б╤В╨▓╨░
  • ╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

╨Ъ╨╗╤О╤З╨╡╨▓╤Л╨╡ ╨▓╤Л╨▓╨╛╨┤╤Л

• ╨Т ANOVA vs ANCOVA ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖ ╨╜╨╡ ╤Г╤З╨╕╤В╤Л╨▓╨░╨╡╤В ╨▓╨╗╨╕╤П╨╜╨╕╨╡ ╨║╨╛╨▓╨░╤А╨╕╨░╤В, ╤В╨╛╨│╨┤╨░ ╨║╨░╨║ ANCOVA ╤Г╤З╨╕╤В╤Л╨▓╨░╨╡╤В ╨╕ ╨║╨╛╨╜╤В╤А╨╛╨╗╨╕╤А╤Г╨╡╤В ╨▓╨╗╨╕╤П╨╜╨╕╨╡ ╨║╨╛╨▓╨░╤А╨╕╨░╤В. ╨Ю╨╜ ╤Г╨║╨░╨╖╤Л╨▓╨░╨╡╤В ╨╜╨░ ╨╛╨┤╨╕╨╜ ╨╕╨╖ ╨╛╤В╨▓╨╡╤В╨╛╨▓ ╨╜╨░ ╨▓╨╛╨┐╤А╨╛╤Б ┬л╨▓ ╤З╨╡╨╝ ╤А╨░╨╖╨╜╨╕╤Ж╨░ ╨╝╨╡╨╢╨┤╤Г ╨░╨╜╨╛╨▓╨░ ╨╕ ╨░╨╜╨║╨╛╨▓╨░┬╗.
• ╨Ф╤А╤Г╨│╨╕╨╡ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨╝╨╡╤В╨╛╨┤╤Л, ╤В╨░╨║╨╕╨╡ ╨║╨░╨║ MANOVA, ╤З╨░╤Б╤В╨╛ ╤Б╤А╨░╨▓╨╜╨╕╨▓╨░╤О╤В ╤Б ANOVA ╨╕ ANCOVA.
• ╨Т ╨╛╨┤╨╜╨╛╤Д╨░╨║╤В╨╛╤А╨╜╨╛╨╝ ╨╕╨╗╨╕ ╨┤╨▓╤Г╤Б╤В╨╛╤А╨╛╨╜╨╜╨╡╨╝ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╨╛╨╝ ╨░╨╜╨░╨╗╨╕╨╖╨╡ ╨┐╨╛ ╤Б╤А╨░╨▓╨╜╨╡╨╜╨╕╤О ╤Б ANCOVA ╨╕ MANOVA ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖ ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖, ANCOVA ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╨║╨╛╨▓╨░╤А╨╕╨░╤Ж╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖, ╨░ MANOVA ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╨╝╨╜╨╛╨│╨╛╨╝╨╡╤А╨╜╤Л╨╣ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖.

ANOVA ╨┐╤А╨╛╤В╨╕╨▓ ANCOVA ╨Ш╨╜╤Д╨╛╨│╤А╨░╤Д╨╕╨║╨░

╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╨Р╨╜╨╛╨▓╨░?

Anova ╤А╨░╤Б╤И╨╕╤Д╤А╨╛╨▓╤Л╨▓╨░╨╡╤В╤Б╤П ╨║╨░╨║ ┬л╨Р╨╜╨░╨╗╨╕╨╖ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕┬╗ ╨╕ ╨▓╨║╨╗╤О╤З╨░╨╡╤В ╨▓ ╤Б╨╡╨▒╤П ╨░╨╜╨░╨╗╨╕╨╖ ╤А╨░╨╖╨╗╨╕╤З╨╕╨╣ ╨▓ ╤Б╤А╨╡╨┤╨╜╨╕╤Е ╨│╤А╤Г╨┐╨┐╨╛╨▓╤Л╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П╤Е ╨╕ ╤А╨░╨╖╨╜╨╛╤Б╤В╨╕ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╣. ╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П, ╨║╨╛╨│╨┤╨░ ╨▓ ╨╕╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╨╜╨╕╨╕ ╤Г╤З╨░╤Б╤В╨▓╤Г╤О╤В ╤В╤А╨╕ ╨╕ ╨▒╨╛╨╗╨╡╨╡ ╨│╤А╤Г╨┐╨┐. ╨Ю╨╜ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В ╨╝╨╡╨╢╨│╤А╤Г╨┐╨┐╨╛╨▓╤Л╨╡ ╨╕ ╨▓╨╜╤Г╤В╤А╨╕╨│╤А╤Г╨┐╨┐╨╛╨▓╤Л╨╡ ╤А╨░╨╖╨╗╨╕╤З╨╕╤П ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕. ╨Ш╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М ╨░╨╜╨░╨╗╨╕╨╖╨╕╤А╤Г╨╡╤В ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╤О ╤Б╤А╨╡╨┤╨╜╨╕╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣ ╨│╤А╤Г╨┐╨┐, ╨▓╨╖╤П╤В╤Л╤Е ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╛╨╝ ╤В╨╡╤Б╤В╨╡. ╨а╨╡╨╖╤Г╨╗╤М╤В╨░╤В╤Л ╨╕╤Б╨┐╤Л╤В╨░╨╜╨╕╨╣ ╨┐╨╛╨┤╤В╨▓╨╡╤А╨╢╨┤╨░╤О╤В ╨╕╨╗╨╕ ╨╛╨┐╤А╨╛╨▓╨╡╤А╨│╨░╤О╤В ╨╜╨░╨╗╨╕╤З╨╕╨╡ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕ ╨╖╨╜╨░╤З╨╕╨╝╤Л╤Е ╤А╨░╨╖╨╗╨╕╤З╨╕╨╣ ╨╝╨╡╨╢╨┤╤Г ╤Б╤А╨░╨▓╨╜╨╕╨▓╨░╨╡╨╝╤Л╨╝╨╕ ╤Б╤А╨╡╨┤╤Б╤В╨▓╨░╨╝╨╕.

╨в╨╡╤Б╤В Anova ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╗╨╕╨▒╨╛ ╨╛╨┤╨╜╨╛╤Б╤В╨╛╤А╨╛╨╜╨╜╨╕╨╝, ╨╗╨╕╨▒╨╛ ╨┤╨▓╤Г╤Б╤В╨╛╤А╨╛╨╜╨╜╨╕╨╝ ╨▓ ╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛╤Б╤В╨╕ ╨╛╤В ╨▓╤Е╨╛╨┤╨╜╤Л╤Е ╨┤╨░╨╜╨╜╤Л╤Е. ╨Ю╨┤╨╜╨╛╤Д╨░╨║╤В╨╛╤А╨╜╤Л╨╣ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖ ╨╕╨╝╨╡╨╡╤В ╨╛╨┤╨╜╤Г ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Г╤О ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Г╤О, ╤В╨╛╨│╨┤╨░ ╨║╨░╨║ ╨┤╨▓╤Г╤Б╤В╨╛╤А╨╛╨╜╨╜╨╕╨╣ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖ ╨╕╨╝╨╡╨╡╤В ╨┤╨▓╨╡ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡. ╨б ╨┐╨╛╨╝╨╛╤Й╤М╤О ╤В╨╡╤Б╤В╨░ Anova ╨╗╤О╨▒╨╛╨╡ ╤Г╤В╨▓╨╡╤А╨╢╨┤╨╡╨╜╨╕╨╡, ╤Б╨╕╤В╤Г╨░╤Ж╨╕╤П ╨╕╨╗╨╕ ╤Г╤В╨▓╨╡╤А╨╢╨┤╨╡╨╜╨╕╨╡ ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╨╗╨╕╨▒╨╛ ╨┐╤А╨╕╨╜╤П╤В╨╛, ╨╗╨╕╨▒╨╛ ╨╛╤В╨▓╨╡╤А╨│╨╜╤Г╤В╨╛ ╨╕╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╨╡╨╝.

╨б╤А╨░╨▓╨╜╨╡╨╜╨╕╨╡ ANOVA ╨╕ ANCOVA ╤Г╨║╨░╨╖╤Л╨▓╨░╨╡╤В ╨╜╨░ ╨▓╨░╨╢╨╜╨╛╤Б╤В╤М ╤В╤Й╨░╤В╨╡╨╗╤М╨╜╨╛╨│╨╛ ╨▓╤Л╨▒╨╛╤А╨░ ╨╜╤Г╨╗╨╡╨▓╨╛╨╣ ╨╕ ╨░╨╗╤М╤В╨╡╤А╨╜╨░╤В╨╕╨▓╨╜╨╛╨╣ ╨│╨╕╨┐╨╛╤В╨╡╨╖. ╨Т ╤В╨╡╤Б╤В╨╡ Anova ╨╜╤Г╨╗╨╡╨▓╨░╤П ╨│╨╕╨┐╨╛╤В╨╡╨╖╨░ ╨▒╤Г╨┤╨╡╤В ╨▓╤Л╨│╨╗╤П╨┤╨╡╤В╤М ╤В╨░╨║: ┬л╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╤В╤А╨╡╤Е ╨│╤А╤Г╨┐╨┐ ╨╛╨┤╨╕╨╜╨░╨║╨╛╨▓╤Л┬╗, ╨░ ╨░╨╗╤М╤В╨╡╤А╨╜╨░╤В╨╕╨▓╨╜╨░╤П ╨│╨╕╨┐╨╛╤В╨╡╨╖╨░ ╤Г╤В╨▓╨╡╤А╨╢╨┤╨░╨╡╤В, ╤З╤В╨╛ ┬л╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╤В╤А╨╡╤Е ╨│╤А╤Г╨┐╨┐ ╤А╨░╨╖╨╗╨╕╤З╨╜╤Л┬╗ ╨╕╨╗╨╕ ┬л╨╝╨╕╨╜╨╕╨╝╤Г╨╝ ╨╛╨┤╨╜╨╛ ╨╕╨╖ ╤Б╤А╨╡╨┤╨╜╨╕╤Е ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╣ ╤В╤А╨╡╤Е ╨│╤А╤Г╨┐╨┐ ╤А╨░╨╖╨╜╤Л╨╡.» ╨Х╤Б╨╗╨╕ ╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨║╨░╨║╨╛╨╣-╨╗╨╕╨▒╨╛ ╨╛╨┤╨╜╨╛╨╣ ╨╕╨╗╨╕ ╨┤╨▓╤Г╤Е ╨│╤А╤Г╨┐╨┐ ╤А╨░╨╖╨╗╨╕╤З╨░╤О╤В╤Б╤П, ╨╜╤Г╨╗╨╡╨▓╨░╤П ╨│╨╕╨┐╨╛╤В╨╡╨╖╨░ ╨╛╤В╨║╨╗╨╛╨╜╤П╨╡╤В╤Б╤П ╨╕ ╨┐╤А╨╕╨╜╨╕╨╝╨░╨╡╤В╤Б╤П ╨░╨╗╤М╤В╨╡╤А╨╜╨░╤В╨╕╨▓╨╜╨░╤П ╨│╨╕╨┐╨╛╤В╨╡╨╖╨░.

╨а╨░╤Б╤Б╨╝╨╛╤В╤А╨╕╨╝ ╨┐╤А╨╕╨╝╨╡╤А, ╨▓ ╨║╨╛╤В╨╛╤А╨╛╨╝ ╨╕╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М ╨░╨╜╨░╨╗╨╕╨╖╨╕╤А╤Г╨╡╤В ╨▓╨╗╨╕╤П╨╜╨╕╨╡ ╨┤╨╕╨╡╤В╤Л ╨╜╨░ ╨┐╨╛╤В╨╡╤А╤О ╨▓╨╡╤Б╨░. ╨б╨╜╨░╤З╨░╨╗╨░ ╨╕╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М ╨┤╨╡╨╗╨╕╤В ╨╛╨▒╤Й╨╡╨╡ ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╤Г╤З╨░╤Б╤В╨╜╨╕╨║╨╛╨▓ ╨╜╨░ ╤В╤А╨╕ ╨│╤А╤Г╨┐╨┐╤Л. ╨Ч╨░╤В╨╡╨╝ ╨║╨░╨╢╨┤╨░╤П ╨│╤А╤Г╨┐╨┐╨░ ╨▓ ╤В╨╡╤З╨╡╨╜╨╕╨╡ ╤В╤А╨╡╤Е ╨╝╨╡╤Б╤П╤Ж╨╡╨▓ ╨┐╤А╨╕╨┤╨╡╤А╨╢╨╕╨▓╨░╨╡╤В╤Б╤П ╤А╨░╨╖╨╜╤Л╤Е ╨┤╨╕╨╡╤В ╨┐╨╛╨┤ ╤А╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛╨╝ ╨┐╤А╨╛╤Д╨╡╤Б╤Б╨╕╨╛╨╜╨░╨╗╤М╨╜╨╛╨│╨╛ ╤В╤А╨╡╨╜╨╡╤А╨░. ╨Т ╨║╨╛╨╜╤Ж╨╡ ╤В╤А╨╡╤В╤М╨╡╨│╨╛ ╨╝╨╡╤Б╤П╤Ж╨░ ╨▓╤Б╨╡ ╤Г╤З╨░╤Б╤В╨╜╨╕╨║╨╕ ╨┐╤А╨╛╤Е╨╛╨┤╤П╤В ╤В╨╡╤Б╤В ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨┐╨╛╤В╨╡╤А╨╕ ╨▓╨╡╤Б╨░, ╨╕ ╨▓╤Л╨┐╨╛╨╗╨╜╨╡╨╜╨╕╨╡ ╤В╨╡╤Б╤В╨░ ANOVA ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨░ ╨┐╨╛╨╝╨╛╨│╨░╨╡╤В ╤Г╨╖╨╜╨░╤В╤М, ╨▓╨╗╨╕╤П╨╡╤В ╨╗╨╕ ╤В╨╕╨┐ ╨┤╨╕╨╡╤В╤Л ╨╜╨░ ╨┐╨╛╤В╨╡╤А╤О ╨▓╨╡╤Б╨░, ╨┐╤Г╤В╨╡╨╝ ╨┐╤А╨╛╨▓╨╡╤А╨║╨╕ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕ ╨╖╨╜╨░╤З╨╕╨╝╨╛╨╣ ╤А╨░╨╖╨╜╨╕╤Ж╤Л. ╨╝╨╡╨╢╨┤╤Г ╤Б╤А╨╡╨┤╨╜╨╕╨╝╨╕ ╨▒╨░╨╗╨╗╨░╨╝╨╕ ╤В╤А╨╡╤Е ╨│╤А╤Г╨┐╨┐.

╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╨Р╨Э╨Ъ╨Ю╨Т╨Р?

ANCOVA ╨╛╨╖╨╜╨░╤З╨░╨╡╤В ╨░╨╜╨░╨╗╨╕╨╖ ╨║╨╛╨▓╨░╤А╨╕╨░╤Ж╨╕╨╕, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨╝╨╛╨╢╨╜╨╛ ╨┐╨╛╨╜╨╕╨╝╨░╤В╤М ╨║╨░╨║ ╤А╨░╤Б╤И╨╕╤А╨╡╨╜╨╜╤Л╨╣ ╨┐╤А╨╛╤Ж╨╡╤Б╤Б ╤В╨╡╤Б╤В╨░ Anova. Ancova ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В ╨║╨╛╨╝╨▒╨╕╨╜╨░╤Ж╨╕╤О ANOVA ╨╕ ╤А╨╡╨│╤А╨╡╤Б╤Б╨╕╨╕. ╨Э╨░╨┐╤А╨╕╨╝╨╡╤А, ╨╡╤Б╨╗╨╕ ╨▓╤Б╨╡ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡ ╨┤╨╡╨╣╤Б╤В╨▓╤Г╤О╤В ╨║╨░╨║ ╨║╨╛╨▓╨░╤А╨╕╨░╤В╤Л, ANCOVA ╨┐╤А╨╡╨▓╤А╨░╤Й╨░╨╡╤В╤Б╤П ╨▓ ╤А╨╡╨│╤А╨╡╤Б╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖; ╤Б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╨╛╨╜ ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╨│╨╕╨▒╤А╨╕╨┤ Anova ╨╕ ╤А╨╡╨│╤А╨╡╤Б╤Б╨╕╨╛╨╜╨╜╨╛╨│╨╛ ╨░╨╜╨░╨╗╨╕╨╖╨░. ╨в╨╡╤Б╤В ╤Г╤З╨╕╤В╤Л╨▓╨░╨╡╤В ╨╕ ╨║╨╛╨╜╤В╤А╨╛╨╗╨╕╤А╤Г╨╡╤В ╨▓╨╗╨╕╤П╨╜╨╕╨╡ ╨║╨╛╨▓╨░╤А╨╕╨░╤В, ╨┐╨╛╨▓╤Л╤И╨░╤П ╨┐╤А╨░╨▓╨╕╨╗╤М╨╜╨╛╤Б╤В╤М ╤Н╨║╤Б╨┐╨╡╤А╨╕╨╝╨╡╨╜╤В╨░. ╨Ъ╨╛╨▓╨░╤А╨╕╨░╤В╤Л тАФ ╤Н╤В╨╛ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╜╤Л╨╡ ╤Е╨░╤А╨░╨║╤В╨╡╤А╨╕╤Б╤В╨╕╨║╨╕ ╤Г╤З╨░╤Б╤В╨╜╨╕╨║╨╛╨▓ ╤В╨╡╤Б╤В╨░, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╜╨╡ ╨╕╨╝╨╡╤О╤В ╨╛╤В╨╜╨╛╤И╨╡╨╜╨╕╤П ╨║ ╨╕╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╨╜╨╕╤О. ╨Э╨╛ ╨╛╨╜ ╨╝╨╛╨╢╨╡╤В ╨┐╨╛╨▓╨╗╨╕╤П╤В╤М ╨╜╨░ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Г╤О ╨╛╤В╨║╨╗╨╕╨║╨░ (╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В).

╨а╨░╤Б╤Б╨╝╨╛╤В╤А╨╕╨╝ ╨┐╤А╨╕╨╝╨╡╤А ╨░╨╜╨╛╨▓╨░ ╨╕ ╨░╨╜╨║╨╛╨▓╨░. ANCOVA ╨╝╨╛╨╢╨╜╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М, ╨╜╨░╨┐╤А╨╕╨╝╨╡╤А, ╨▓ ╨╕╤Б╤Б╨╗╨╡╨┤╨╛╨▓╨░╨╜╨╕╨╕, ╤З╤В╨╛╨▒╤Л ╨┐╤А╨╛╨▓╨╡╤А╨╕╤В╤М ╨▓╨╗╨╕╤П╨╜╨╕╨╡ ╨╗╨╡╤З╨╡╨╜╨╕╤П ╤Б ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨╝ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╜╨╛╨│╨╛ ╨┐╤А╨╡╨┐╨░╤А╨░╤В╨░ ╨╜╨░ ╨║╨╛╨╜╨║╤А╨╡╤В╨╜╨╛╨╡ ╨╖╨░╨▒╨╛╨╗╨╡╨▓╨░╨╜╨╕╨╡ ╤Г ╤Г╤З╨░╤Б╤В╨╜╨╕╨║╨╛╨▓ ╤А╨░╨╖╨╜╨╛╨│╨╛ ╨▓╨╛╨╖╤А╨░╤Б╤В╨░. ╨Ч╨┤╨╡╤Б╤М ╤Д╨░╨║╤В╨╛╤А╨╛╨╝ ╨╕╨╗╨╕ ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╨╛╨╣ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛╨╣ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╗╨╡╤З╨╡╨╜╨╕╨╡, ╨▓╨╛╨╖╤А╨░╤Б╤В ╨┤╨╡╨╣╤Б╤В╨▓╤Г╨╡╤В ╨║╨░╨║ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨░╤П ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╨░╤П ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨░╤П, ╨░ ╨╕╨╖╨╝╨╡╨╜╨╡╨╜╨╕╨╡ ╤Б╨╛╤Б╤В╨╛╤П╨╜╨╕╤П ╨▒╨╛╨╗╨╡╨╖╨╜╨╕ ╨┐╨╛╤Б╨╗╨╡ ╨╗╨╡╤З╨╡╨╜╨╕╤П ╤П╨▓╨╗╤П╨╡╤В╤Б╤П ╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛╨╣ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╨╕╨╗╨╕ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╤А╨╡╨░╨║╤Ж╨╕╨╕. ╨Т ╤В╨╛ ╨╢╨╡ ╨▓╤А╨╡╨╝╤П ANOVA ╨╝╨╛╨╢╨╜╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М, ╨╡╤Б╨╗╨╕ ╨▓╨╛╨╖╤А╨░╤Б╤В ╨╜╨╡ ╤Г╨║╨░╨╖╨░╨╜ ╨║╨░╨║ ╨╝╨╡╤В╤А╨╕╨║╨░ ╨╕╨╗╨╕ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨░╤П ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╨░╤П ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨░╤П. ╨Т ╤Н╤В╨╛╨╝ ╤Б╨╗╤Г╤З╨░╨╡ ╨╛╤Б╨╜╨╛╨▓╨╜╨╛╨╡ ╨▓╨╜╨╕╨╝╨░╨╜╨╕╨╡ ╤Г╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨╗╨╡╤З╨╡╨╜╨╕╤О (╤Д╨░╨║╤В╨╛╤А╨╜╨░╤П ╨╕╨╗╨╕ ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╨░╤П ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╨░╤П ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨░╤П) ╨╕ ╨╕╨╖╨╝╨╡╨╜╨╡╨╜╨╕╤О ╤Б╨╛╤Б╤В╨╛╤П╨╜╨╕╤П ╨▒╨╛╨╗╨╡╨╖╨╜╨╕ ╨┐╨╛╤Б╨╗╨╡ ╨╗╨╡╤З╨╡╨╜╨╕╤П (╨╖╨░╨▓╨╕╤Б╨╕╨╝╨░╤П ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨░╤П ╨╕╨╗╨╕ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨░╤П ╨╛╤В╨▓╨╡╤В╨░).

╨б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨╝╨╡╤В╨╛╨┤╤Л, ╤В╨░╨║╨╕╨╡ ╨║╨░╨║ ╤А╨╡╨│╤А╨╡╤Б╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖ ╨╕ MANOVA, ╤З╨░╤Б╤В╨╛ ╤Б╤А╨░╨▓╨╜╨╕╨▓╨░╤О╤В ╤Б ANOVA ╨╕ ANCOVA. MANOVA ╨┐╨╛╤Е╨╛╨╢ ╨╜╨░ ANOVA, ╨╜╨╛ ╤Б╨╛╨┤╨╡╤А╨╢╨╕╤В ╨▒╨╛╨╗╨╡╨╡ ╨╛╨┤╨╜╨╛╨╣ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛╨╣ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╨╛╤В╨║╨╗╨╕╨║╨░, ╨▓ ╨╛╤В╨╗╨╕╤З╨╕╨╡ ╨╛╤В ANOVA ╤Б ╨╛╨┤╨╜╨╛╨╣ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╨╛╤В╨║╨╗╨╕╨║╨░. ╨Т ╤А╨╡╨│╤А╨╡╤Б╤Б╨╕╨╕ ╨╕ ANOVA ╤Д╨░╨║╤В╨╛╤А╨╛╨╝ ╤А╨╡╨│╤А╨╡╤Б╤Б╨╕╨╕ ╨╝╨╛╨│╤Г╤В ╨▒╤Л╤В╤М ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡-╨┐╤А╨╡╨┤╨╕╨║╤В╨╛╤А╤Л, ╤В╨╛╨│╨┤╨░ ╨║╨░╨║ ANOVA ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡-╨┐╤А╨╡╨┤╨╕╨║╤В╨╛╤А╤Л ╨┤╨╗╤П ╨░╨╜╨░╨╗╨╕╨╖╨░ ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В╨░.

╨б╤А╨░╨▓╨╜╨╕╤В╨╡╨╗╤М╨╜╨░╤П ╤В╨░╨▒╨╗╨╕╤Ж╨░

╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╛╤Б╤В╨╕╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╛╨╜╨╜╤Л╨╣ ╨░╨╜╨░╨╗╨╕╨╖╨Р╨Э╨Ъ╨Ю╨Т╨Р╨Ю╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В╨Р╨╜╨░╨╗╨╕╨╖ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕╨Р╨╜╨░╨╗╨╕╨╖ ╨║╨╛╨▓╨░╤А╨╕╨░╤Ж╨╕╨╕╨Ч╨╜╨░╤З╨╡╨╜╨╕╨╡╨н╤В╨╛ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕╨╣ ╨╝╨╡╤В╨╛╨┤ ╨┤╨╗╤П ╨┐╤А╨╛╨▓╨╡╤А╨║╨╕ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╨╕ ╨╕╨╗╨╕ ╤А╨░╨╖╨╗╨╕╤З╨╕╨╣ ╨╝╨╡╨╢╨┤╤Г ╤Б╤А╨╡╨┤╨╜╨╕╨╝╨╕ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П╨╝╨╕ ╤В╤А╨╡╤Е ╨╕╨╗╨╕ ╨▒╨╛╨╗╨╡╨╡ ╨│╤А╤Г╨┐╨┐. ╨Ю╨╜ ╨╛╤Ж╨╡╨╜╨╕╨▓╨░╨╡╤В ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛╨╣ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╨╛╨╣ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛╨╣ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣ ╨┐╤А╨╕ ╤А╨░╤Б╤Б╨╝╨╛╤В╤А╨╡╨╜╨╕╨╕ ╨╕ ╨║╨╛╨╜╤В╤А╨╛╨╗╨╡ ╨▓╨╗╨╕╤П╨╜╨╕╤П ╨║╨╛╨▓╨░╤А╨╕╨░╤В.╨Ш╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨Ь╨╛╨╢╨╡╤В ╤Б╨╛╤З╨╡╤В╨░╤В╤М ╨╗╨╕╨╜╨╡╨╣╨╜╤Л╨╡ ╨╕ ╨╜╨╡╨╗╨╕╨╜╨╡╨╣╨╜╤Л╨╡ ╨╝╨╛╨┤╨╡╨╗╨╕. ╨Ы╨╕╨╜╨╡╨╣╨╜╨░╤П ╨╝╨╛╨┤╨╡╨╗╤М ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨╛╤В╨┤╨╡╨╗╤М╨╜╨╛.╨Т╨║╨╗╤О╤З╨░╨╡╤В╨Ъ╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╤Л╨╡ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡╨Ъ╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╤Л╨╡ ╨╕ ╨╝╨╡╤В╤А╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡╨Ъ╨╛╨▓╨░╤А╨╕╨░╤Ж╨╕╤П╨Я╤А╨╡╨╜╨╡╨▒╤А╨╡╨│╨░╨╡╤В ╨▓╨╗╨╕╤П╨╜╨╕╨╡╨╝ ╨║╨╛╨▓╨░╤А╨╕╨░╤В╨╛╨▓ ╨г╤З╨╕╤В╤Л╨▓╨░╨╡╤В ╨╕ ╨║╨╛╨╜╤В╤А╨╛╨╗╨╕╤А╤Г╨╡╤В ╨▓╨╗╨╕╤П╨╜╨╕╨╡ ╨║╨╛╨▓╨░╤А╨╕╨░╤В

╨б╤Е╨╛╨┤╤Б╤В╨▓╨░

• ╨Ю╨▒╨░ ╨┐╤А╨╡╨┤╨┐╨╛╨╗╨░╨│╨░╤О╤В ╨░╨╜╨░╨╗╨╕╨╖ ╤Б╤А╨╡╨┤╤Б╤В╨▓ ╨╜╨╡╤Б╨║╨╛╨╗╤М╨║╨╕╤Е ╨│╤А╤Г╨┐╨┐.
• ╨Ю╨▒╨░ ╨╝╨╡╤В╨╛╨┤╨░ ╨┐╤А╨╕╨╜╨╕╨╝╨░╤О╤В ╨║╨░╤В╨╡╨│╨╛╤А╨╕╨░╨╗╤М╨╜╤Л╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╨╡.
• ANCOVA ╤Б╨╛╨┤╨╡╤А╨╢╨╕╤В ╨┐╤А╨╕╨╗╨╛╨╢╨╡╨╜╨╕╨╡ ANOVA.
• ╨Ю╨▒╨░ ╤В╨╡╤Б╤В╨░ ╨▒╤Л╨╗╨╕ ╨▓╨▓╨╡╨┤╨╡╨╜╤Л ╨▒╤А╨╕╤В╨░╨╜╤Б╨║╨╕╨╝ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╛╨╝ ╨а╨╛╨╜╨░╨╗╤М╨┤╨╛╨╝ ╨н╨╣╨╗╨╝╨╡╤А╨╛╨╝ ╨д╨╕╤И╨╡╤А╨╛╨╝ ╨╕ ╨┐╨╛╨┤╤А╨╛╨▒╨╜╨╛ ╤Г╨┐╨╛╨╝╤П╨╜╤Г╤В╤Л ╨▓ ╨╡╨│╨╛ ╨║╨╗╨░╤Б╤Б╨╕╤З╨╡╤Б╨║╨╛╨╣ ╨║╨╜╨╕╨│╨╡. ╨б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╨╝╨╡╤В╨╛╨┤╤Л ╨┤╨╗╤П ╨╜╨░╤Г╤З╨╜╤Л╤Е ╤А╨░╨▒╨╛╤В╨╜╨╕╨║╨╛╨▓

╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

╨н╤В╨╛ ╨▒╤Л╨╗╨╛ ╨а╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛ ╨┐╨╛ ╤В╨╛╨╝╤Г, ╤З╤В╨╛ ╤В╨░╨║╨╛╨╡ ANOVA ╨╕ ANCOVA. ╨Ь╤Л ╨╛╨▒╤К╤П╤Б╨╜╤П╨╡╨╝ ╤А╨░╨╖╨╗╨╕╤З╨╕╤П ╨╝╨╡╨╢╨┤╤Г ANOVA ╨╕ ANCOVA, ╨╕╨╜╤Д╨╛╨│╤А╨░╤Д╨╕╨║╨╛╨╣, ╨┐╤А╨╕╨╝╨╡╤А╨░╨╝╨╕, ╤Б╤Е╨╛╨┤╤Б╤В╨▓╨░╨╝╨╕ ╨╕ ╤Б╤А╨░╨▓╨╜╨╡╨╜╨╕╨╡╨╝ ╤Б Manova. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╨╛ ╨╜╨╕╤Е ╨▓╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Г╨╖╨╜╨░╤В╤М ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤Б╤В╨░╤В╨╡╨╣ тАФ

• ╨а╨╡╨│╤А╨╡╤Б╤Б╨╕╤П ╨┐╤А╨╛╤В╨╕╨▓ ANOVA
• ╨Э╤Г╨╗╤М ╨┐╤А╨╛╤В╨╕╨▓ ╨░╨╗╤М╤В╨╡╤А╨╜╨░╤В╨╕╨▓╨╜╨╛╨╣ ╨│╨╕╨┐╨╛╤В╨╡╨╖╤Л
• ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨┐╤А╨╛╤В╨╕╨▓ ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П