تبلیغات تحلیل واریانس آنوا
» نوع مطلب : نحلیل آماری ،
حلیل واریانس Analysis of Variance ANOVAمقدمه: 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.
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http://azaccount.ir
0938-433-0138
softazir@gmail.com
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
http://azaccount.ir
0938-433-0138
softazir@gmail.com
http://azaccount.ir
0938-433-0138
softazir@gmail.com
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
http://azaccount.ir
0938-433-0138
softazir@gmail.com
http://azaccount.ir
0938-433-0138
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