حسابداری کارشناسی ارشد حسابداری - تحلیل واریانس آنوا


تحلیل واریانس آنوا

» نوع مطلب : نحلیل آماری ،

حلیل واریانس Analysis of Variance ANOVA

مقدمه: وقتی بخواهیم فرض برابری میانگین‌ها را برای بیش از دو جامعه آزمون کنیم و یا به عبارتی دیگر آیا تفاوتی بین میانگین‌های چند جامعه وجود دارد یا خیر، از تست تحلیل واریانس استفاده می شود.

تحلیل واریانس

کابرد: برای آزمون کردن میزان تاثیرگذاری سطوح مختلف یک (یا چند) عامل روی یک سیستم، استفاده می شود.

به طور مثال: ۱- اگر بخواهیم بر اساس نمونه‌گیری تصمیم بگیریم که آیا واقعا تفاوتی بین میزان موثر بودن سه روش تدریس یک زبان خارجی وجود دارد یا خیر. ۲- در میزان برداشت محصول در یک زمین کشاورزی، آیا آبیاری به روش‌های مختلف تاثیرگذار است یا خیر.
تحلیل واریانس یک طرفه

فرض کنید k سطح مختلف از یک عامل را قرار است بررسی کنیم. در نتیجه ما k جامعه داریم. فرض می‌شود این جوامع دارای توزیع نرمال  و واریانس مشترک و مجهول هستند. می‌خواهیم فرض برابری میانگین‌های این جوامع را آزمون کنیم. از هر جامعه یک نمونه  n تائی می‌گیریم.

فرض کنید میخواهیم k سطح مختلف از یک عامل را قرار است بررسی کنیم. در نتیجه ما k جامعه داریم. می‌خواهیم فرض برابری میانگین‌های این جوامع را آزمون کنیم. از هر جامعه یک نمونه n می‌گیریم.

واریانس 1


فرض می‌شود این جوامع دارای توزیع نرمال با میانگین‌های

واریانس 2و واریانس مشترک و مجهول هستند.

واریانس 3

xij مشاهده jام از تیمارi  است که دارای توزیع نرمال با میانگین μi و واریانس σ۲ است.

برای هر xij ، می توان مدل ریاضی زیر را نوشت

واریانس 4

واریانس 5

دوباره می توان آن را به شکل زیر باز نویسی کرد:

واریانس 6

در نتیجه آزمون از

واریانس 7

به شکل زیر تغییر می‌کند:

واریانس 8

نکته: تحلیل از طریق بررسی تغییرپذیری کل داده‌ها انجام می‌شود.

واریانس 9

softazir@gmail.com تحلیل آماری پایان نامه های کارشناسی ارشد

نوشته شده در : یکشنبه 10 خرداد 1394  توسط : صادقی صلذقی.    نظرات() .

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