1. SPSS for Beginners: Lesson 6SPSS for Beginners: Lesson 6
‫وﻋﻴﻨﺘﻴﻦ‬ ‫ﻟﻌﻴﻨﺔ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻻﺧﺘﺒﺎرات‬‫وﻋﻴﻨﺘﻴﻦ‬ ‫ﻟﻌﻴﻨﺔ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻻﺧﺘﺒﺎرات‬
‫اﻋﺪاد‬‫اﻋﺪاد‬
‫د‬‫د‬..‫ﻣﺤﻤﺪ‬ ‫ﻣﺼﻄﻔﻰ‬ ‫ﻋﺒﺪاﻟﻔﺘﺎح‬‫ﻣﺤﻤﺪ‬ ‫ﻣﺼﻄﻔﻰ‬ ‫ﻋﺒﺪاﻟﻔﺘﺎح‬
‫اﻟﺮﻳﺎﺿﻴﺎت‬ ‫ﻗﺴﻢ‬‫اﻟﺮﻳﺎﺿﻴﺎت‬ ‫ﻗﺴﻢ‬––‫اﻟﻌﻠﻮم‬ ‫آﻠﻴﻪ‬‫اﻟﻌﻠﻮم‬ ‫آﻠﻴﻪ‬
‫اﻟﻤﻨﺼﻮرة‬ ‫ﺟﺎﻣﻌﺔ‬‫اﻟﻤﻨﺼﻮرة‬ ‫ﺟﺎﻣﻌﺔ‬--‫ﻣﺼﺮ‬‫ﻣﺼﺮ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 1 of 38

2. 66--11‫ﻣﻘﺪﻣﺔ‬‫ﻣﻘﺪﻣﺔ‬IntroductionIntroduction
‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬ ‫اﺧﺘﺒﺎرات‬ ‫ﺗﻌﺘﺒﺮ‬Testing Statistical
Hypotheses‫آﺤﻞ‬ ‫اﻻﺣﺼﺎء‬ ‫ﻋﻠﻢ‬ ‫ﻗﺪﻣﻬﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺘﻄﺒﻴﻘﺎت‬ ‫أهﻢ‬ ‫ﻣﻦ‬ ‫واﺣﺪة‬
‫اﻟﻌﻠﻢ‬ ‫ﻓﺮوع‬ ‫ﺑﺸﺘﻰ‬ ‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﻌﻠﻤﻴﺔ‬ ‫ﻟﻠﻤﺸﺎآﻞ‬.‫اﻻﺣﺘﻤﺎﻻت‬ ‫ﻧﻈﺮﻳﺔ‬ ‫ﻓﺒﺎﺳﺘﺨﺪام‬
‫اﻟﻔﺮو‬ ‫ﺑﺎﺧﺘﺒﺎرات‬ ‫ﻳﺴﻤﻰ‬ ‫ﻣﺎ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﻌﺮف‬ ‫اﻣﻜﻦ‬ ‫اﻟﻌﻴﻨﻴﺔ‬ ‫اﻟﺘﻮزﻳﻌﺎت‬ ‫وﺧﺼﺎﺋﺺ‬‫ض‬
‫ﻓﺮض‬ ‫ﻗﺒﻮل‬ ‫أو‬ ‫ﺑﺮﻓﺾ‬ ‫ﻗﺮار‬ ‫ﻳﺘﺨﺬ‬ ‫ان‬ ‫ﺷﺨﺺ‬ ‫ﻷى‬ ‫ﻳﻤﻜﻦ‬ ‫ﺧﻼﻟﻬﺎ‬ ‫وﻣﻦ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬
‫اﻟﺤﻴﺎﻩ‬ ‫ﻓﻰ‬ ‫ﻣﻮﺟﻮدﻩ‬ ‫ﻣﻌﻴﻨﺔ‬ ‫ﺑﻤﺸﻜﻠﺔ‬ ‫اﻟﻤﺘﻌﻠﻘﺔ‬ ‫اﻟﻔﺮوض‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أو‬ ‫ﻣﻌﻴﻦ‬
‫اﻟﻌﺎﻣﻪ‬.
‫وهﻰ‬ ‫ﻣﺮاﺣﻞ‬ ‫ﺑﻌﺪة‬ ‫ﻳﻤﺮ‬ ‫ان‬ ‫ﻳﺠﺐ‬ ‫ﻗﺮار‬ ‫اى‬ ‫رﻓﺾ‬ ‫او‬ ‫ﻗﺒﻮل‬ ‫ﻓﺎن‬ ‫ﻋﺎﻣﻪ‬ ‫وﺑﺼﻔﻪ‬:
.1‫ﻟﻠﻤﺠﺘﻤﻊ‬ ‫ﺗﻤﺜﻴﻞ‬ ‫اﺣﺴﻦ‬ ‫ﻣﻤﺜﻠﻪ‬ ‫ﺗﻜﻮن‬ ‫ﺑﺤﻴﺚ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻦ‬ ‫ﻋﻴﻨﺔ‬ ‫ﺳﺤﺐ‬
.2‫اﻟﻌﻴﻨﺔ‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﻤﺸﻜﻠﺔ‬ ‫اﻟﻤﺘﻌﻠﻘﺔ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺗﺠﻤﻴﻊ‬
.3‫وهﻰ‬ ‫اﻟﺒﺎﺣﺚ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫اﻟﻤﻮﺿﻮﻋﻪ‬ ‫اﻟﻔﺮوض‬ ‫ﻻﺧﺘﺒﺎر‬ ‫ﻣﻌﻴﻨﻪ‬ ‫ﻗﻮاﻋﺪ‬ ‫ﺗﻄﺒﻴﻖ‬
‫اﺣﺼﺎﺋﻴﺔ‬ ‫ﻟﺨﺒﺮﻩ‬ ‫ﺗﺤﺘﺎج‬ ‫ﻣﺸﻜﻠﻪ‬
.4‫ﻧﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺒﺎﺣﺚ‬ ‫اﻟﻴﻪ‬ ‫ﺗﻮﺻﻞ‬ ‫ﻣﺎ‬ ‫ﻋﻠﻰ‬ ‫ﺑﻨﺎء‬ ‫اﻟﻘﺮار‬ ‫اﺗﺨﺎذ‬.
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 2 of 38

3. ‫ا‬ ‫اﻟﻔﺮوض‬ ‫اﺧﺘﺒﺎرات‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻻ‬ ‫ﻳﺘﻢ‬ ‫ﻻ‬ ‫ﻗﺮار‬ ‫اى‬ ‫اﺗﺨﺎذ‬ ‫ان‬ ‫اﻟﻤﻌﺮوف‬ ‫ﻣﻦ‬‫ﺑﺪورهﺎ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﺘﻰ‬ ‫ﻻﺣﺼﺎﺋﻴﺔ‬
‫ا‬ ‫اﻟﺪور‬ ‫اهﻤﻴﺔ‬ ‫ﻳﺆآﺪ‬ ‫وهﺬا‬ ‫اﻟﻤﻌﺎﻳﻨﻪ‬ ‫وﺗﻮزﻳﻌﺎت‬ ‫اﻻﺣﺘﻤﺎﻻت‬ ‫ﻋﻠﻰ‬ ‫ﺳﺒﻖ‬ ‫آﻤﺎ‬‫ﻧﻈﺮﻳﻪ‬ ‫ﺗﻠﻌﺒﻪ‬ ‫ﻟﺬى‬
‫اهﻤﻴﺘ‬ ‫اﻟﻰ‬ ‫ﺑﺎﻻﺿﺎﻓﻪ‬ ‫اﻟﻘﺮارات‬ ‫واﺗﺨﺎذ‬ ‫واﻟﺘﺨﻄﻴﻂ‬ ‫اﻟﺘﻨﺒﺆ‬ ‫ﻓﻰ‬ ‫اﻻﺣﺘﻤﺎﻻت‬‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻌﺎﻟﻢ‬ ‫ﺗﻘﺪﻳﺮ‬ ‫ﻓﻰ‬ ‫ﻬﺎ‬
‫اﻟﺒﺎﺣﺜﻴﻦ‬ ‫اهﺘﻤﺎﻣﺎت‬ ‫اﺣﺪ‬ ‫ﺗﻌﺘﺒﺮ‬ ‫واﻟﺘﻰ‬ ‫اﻟﻤﺠﻬﻮﻟﻪ‬.
‫ﺑﺎﻻﺳﺘﺪﻻل‬ ‫ﻳﺴﻤﻰ‬ ‫ﺑﻤﺎ‬ ‫اﻟﻤﺠﻬﻮﻟﻪ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻌﺎﻟﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﻌﺮف‬ ‫ﻣﺸﻜﻠﻪ‬ ‫ﺗﺒﺪأ‬‫اﻻﺣﺼﺎﺋﻰ‬Statistical
Inferences‫ﻓﺮﻋﻴﻦ‬ ‫اﻟﻰ‬ ‫ﻳﻨﻘﺴﻢ‬ ‫ﺣﻴﺚ‬.‫ﺑﺘﻘﺪﻳﺮ‬ ‫ﻳﻬﺘﻢ‬ ‫اﻷول‬ ‫اﻟﻔﺮع‬Estimation‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻌﺎﻟﻢ‬
‫اﻟ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻌﺎﻟﻢ‬ ‫ﺣﻮل‬ ‫ﺗﺪور‬ ‫ﻓﺮوض‬ ‫اﺧﺘﺒﺎرات‬ ‫ﺑﺎﺟﺮاء‬ ‫ﻳﺨﺘﺺ‬ ‫اﻷﺧﺮ‬ ‫واﻟﻔﺮع‬‫ﻤﺠﻬﻮﻟﻪ‬.
‫و‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺤﻮﺑﻪ‬ ‫ﻋﺸﻮاﺋﻴﺔ‬ ‫ﻋﻴﻨﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ﻳﺘﻢ‬ ‫اﻻﺣﺼﺎﺋﻰ‬ ‫اﻻﺳﺘﺪﻻل‬‫ﻣﻊ‬ ‫اﻟﺘﻌﺎﻣﻞ‬ ‫ﻻﺳﺘﺤﺎﻟﺔ‬ ‫ذﻟﻚ‬
‫اﻟ‬ ‫هﺬﻩ‬ ‫ﺳﻬﻠﺖ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻘﻮاﻧﻴﻦ‬ ‫ﻗﺪﻣﺖ‬ ‫اﻟﺘﺤﻠﻴﻠﻴﺔ‬ ‫ﻓﺎﻻﺣﺼﺎءات‬ ،‫آﻜﻞ‬ ‫اﻟﻤﺠﺘﻤﻊ‬‫ﺑﺎﻗﻞ‬ ‫ﺗﺘﻢ‬ ‫وﺟﻌﻠﺘﻬﺎ‬ ‫ﻌﻤﻠﻴﺔ‬
‫اﻟﻤﻤﻜﻨﻪ‬ ‫اﻟﺨﻄﺎء‬.
66--22‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬ ‫اﺧﺘﺒﺎرات‬‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬ ‫اﺧﺘﺒﺎرات‬
Testing Statistical HypothesesTesting Statistical Hypotheses
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 3 of 38

4. ‫ﻓﺎن‬ ‫ﻣﺠﻬﻮل‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫وﺳﻂ‬ ‫آﺎن‬ ‫اذا‬ ‫اﻧﻪ‬ ‫اﺛﺒﺎت‬ ‫ﺗﻢ‬ ‫ﻗﺪ‬ ‫اﻟﺘﻘﺪﻳﺮات‬ ‫ﻧﻈﺮﻳﺔ‬ ‫ﻓﻰ‬‫ﻷى‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬
‫ﻋﺸﻮا‬ ‫اﻟﻤﺴﺤﻮﺑﻪ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﺑﺸﺮط‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻟﻮﺳﻂ‬ ‫ﺟﻴﺪ‬ ‫ﺗﻘﺪﻳﺮ‬ ‫هﻮ‬ ‫ﻋﻴﻨﺔ‬‫ﺋﻴﺔ‬.
‫اﻧﻨﺎ‬ ‫اﻳﻀﺎ‬ ‫وﻧﻔﺮض‬ ‫ﻣﺎ‬ ‫ﻟﻤﺠﺘﻤﻊ‬ ‫اﻟﺤﺴﻠﺒﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﺑﺘﻘﺪﻳﺮ‬ ‫ﻣﻬﺘﻤﻴﻦ‬ ‫اﻧﻨﺎ‬ ‫ﺑﻔﺮض‬‫اﻟﻌﻴﻨﺎت‬ ‫ﺟﻤﻴﻊ‬ ‫ﺳﺤﺒﻨﺎ‬
‫ﻣ‬ ‫ﻧﻌﻠﻢ‬ ‫وآﻨﺎ‬ ‫ﻋﻴﻨﻪ‬ ‫ﻟﻜﻞ‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫وﺣﺴﺒﻨﺎ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ذﻟﻚ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻤﻜﻨﻪ‬‫اﻟﻮﺳﻂ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻘﺪﻣﺎ‬
‫ﻟﻠﻤﺠﺘﻤﻊ‬ ‫اﻟﺤﺴﺎﺑﻰ‬)‫ﻓﺮﺿﺎ‬(‫ﺗﻘﻞ‬ ‫او‬ ‫ﺗﺘﺴﺎوى‬ ‫ﻗﺪ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻟﺒﻌﺾ‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ان‬ ‫ﻧﻼﺣﻆ‬ ‫ﻓﺎﻧﻨﺎ‬
‫اﻟﻌﻴﻨﺎت‬ ‫ﻣﻨﻪ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫ﻟﻠﻤﺠﺘﻤﻊ‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﻋﻦ‬ ‫ﺗﺰﻳﺪ‬ ‫او‬.
‫ﻳﺴﻤﻰ‬ ‫واﻟﻤﺠﺘﻤﻊ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻣﻦ‬ ‫اﻟﻤﺤﺴﻮب‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺑﻴﻦ‬ ‫واﻟﻔﺮوق‬‫ﺑﺨﻄﺄ‬
‫اﻟﻤﻌﺎﻳﻨﻪ‬Sampling Error‫اﻟﻌﻴﻨﻪ‬ ‫ان‬ ‫وﺣﻴﺚ‬ ‫ﻓﻴﻪ‬ ‫اﻟﺘﺤﻜﻢ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻋﺸﻮاﺋﻰ‬ ‫ﻣﺘﻐﻴﺮ‬ ‫وهﻮ‬
‫ﺣﻘﻴﻘﻰ‬ ‫ﻏﻴﺮ‬ ‫ﺧﻄﺄ‬ ‫اﻟﻤﻌﺎﻳﻨﻪ‬ ‫ﺧﻄﺄ‬ ‫ان‬ ‫اﺛﺒﺎت‬ ‫ﻓﺎﻣﻜﻦ‬ ‫ﻋﺸﻮاﺋﻴﻪ‬.
‫ﻟﻠ‬ ‫ﺟﻴﺪا‬ ‫ﺗﻘﺪﻳﺮا‬ ‫ﻳﻜﻮن‬ ‫ﻻن‬ ‫ﻳﺼﻠﺢ‬ ‫واﺣﺪﻩ‬ ‫ﻟﻌﻴﻨﻪ‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﻓﺎن‬ ‫وﺑﺬﻟﻚ‬‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻓﻰ‬ ‫ﻮﺳﻂ‬
‫اﻟﺘﺤ‬ ‫ﻓﺎﻻﺣﺼﺎءات‬ ،‫واﻟﺘﻘﺪﻳﺮ‬ ‫اﻟﻤﻌﻠﻤﻪ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮوق‬ ‫ﺑﻌﺾ‬ ‫وﺟﻮد‬ ‫ﻣﻦ‬ ‫وﺑﺎﻟﺮﻏﻢ‬‫ان‬ ‫اﻋﺘﺒﺮت‬ ‫ﻠﻴﻠﻴﺔ‬
‫اﻟﻐﻴﺮ‬ ‫ﺑﺎﻟﻔﺮوق‬ ‫وﺳﻤﻴﺖ‬ ‫اﻟﺼﺪﻓﻪ‬ ‫اﻟﻰ‬ ‫وﺗﺮﺟﻊ‬ ‫ﺣﻘﻴﻘﻴﺔ‬ ‫ﻏﻴﺮ‬ ‫ﻓﺮوﻗﺎ‬ ‫اﻟﻔﺮوق‬ ‫هﺬﻩ‬‫ﻣﻌﻨﻮﻳﻪ‬Not
Significant
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 4 of 38

5. ‫ﻣ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺤﻮﺑﻪ‬ ‫ﻏﻴﺮ‬ ‫اﺧﺮى‬ ‫ﻋﻴﻨﻪ‬ ‫هﻨﺎك‬ ‫ان‬ ‫ﺟﺪﻻ‬ ‫ﻓﺮﺿﻨﺎ‬ ‫ﻓﻠﻮ‬‫ﻓﺎن‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻨﻪ‬
‫اﻟﻤﺠﻬ‬ ‫اﻟﻤﻌﻠﻤﻪ‬ ‫وﺑﻴﻦ‬ ‫اﻟﻌﻴﻨﻪ‬ ‫هﺬﻩ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺤﺴﻮب‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮق‬‫ﻓﺮﻗﺎ‬ ‫ﻳﻜﻮن‬ ‫ﻗﺪ‬ ‫ﻮﻟﻪ‬
‫ﻣﻌﻨﻮﻳﺎ‬Significant‫ﻟﻠﺼﺪﻓﻪ‬ ‫راﺟﻊ‬ ‫ﻏﻴﺮ‬.
‫ﺣﻴ‬ ‫ﻣﻨﻬﺎ‬ ‫اﺳﻤﻬﺎ‬ ‫واﺷﺘﻘﺖ‬ ‫اﻟﻔﻜﺮﻩ‬ ‫هﺬﻩ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺎﺳﺎ‬ ‫ﺗﺮﺗﻜﺰ‬ ‫اﻟﻔﺮوض‬ ‫اﺧﺘﺒﺎرات‬‫ﻃﺮﻳﻘﻬﺎ‬ ‫ﻋﻦ‬ ‫ﺚ‬
‫اﻟﻌﻴﻨ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺤﺴﻮﺑﺔ‬ ‫اﻟﻤﻌﻠﻮﻣﺎت‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮوق‬ ‫هﻞ‬ ‫وﺑﺴﻬﻮﻟﻪ‬ ‫ﻧﺤﺪد‬ ‫ان‬ ‫ﻧﺴﺘﻄﻴﻊ‬‫اﻟﻤﻌﻠﻮﻣﺎت‬ ‫وﺑﻴﻦ‬ ‫ﺔ‬
‫أ‬ ‫وﺑﺄﺳﻠﻮب‬ ،‫ﺣﻘﻴﻘﻰ‬ ‫ﻓﺮق‬ ‫ام‬ ‫اﻟﺼﺪﻓﻪ‬ ‫اﻟﻰ‬ ‫ﻳﺮﺟﻊ‬ ‫ﻓﺮﻗﺎ‬ ‫ﻣﻌﻴﻦ‬ ‫ﻟﻤﺠﺘﻊ‬ ‫اﻟﻤﻔﺮوﺿﻪ‬‫ﻓﺮق‬ ‫هﻮ‬ ‫هﻞ‬ ‫ﺧﺮ‬
‫اﺧﺘﺒﺎرات‬ ‫ﺑﺎﺳﻢ‬ ‫اﻻﺧﺘﺒﺎرات‬ ‫هﺬﻩ‬ ‫ﺳﻤﻴﺖ‬ ‫وﺑﺬﻟﻚ‬ ‫ﻣﻌﻨﻮى؟‬ ‫ﻏﻴﺮ‬ ‫ﻓﺮق‬ ‫او‬ ‫ﻣﻌﻨﻮى‬‫اﻟﻤﻌﻨﻮﻳﻪ‬Test of
Significant
‫اﻟﻔﺮ‬ ‫ﻣﺜﻞ‬ ‫اﻟﻤﺠﻬﻮﻟﻪ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻌﺎﻟﻢ‬ ‫ﺣﻮل‬ ‫ﺗﺪور‬ ‫ﻗﺪ‬ ‫اﻻﺣﺼﺎﺋﻴﻪ‬ ‫اﻻﺧﺘﺒﺎرات‬‫ﺑﺎﻟﻮﺳﻂ‬ ‫اﻟﻤﺘﻌﻠﻘﺔ‬ ‫وض‬
،‫اﻻرﺗﺒﺎط‬ ‫ﻣﻌﺎﻣﻞ‬ ،‫اﻟﺘﺒﺎﻳﻦ‬ ،‫اﻟﻨﺴﺒﻪ‬ ،‫اﻟﺤﺴﺎﺑﻰ‬...‫اﺳﻢ‬ ‫اﻻﺧﺘﺒﺎرات‬ ‫هﺬﻩ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻄﻠﻖ‬ ‫اﻟﺤﺎﻟﻪ‬ ‫هﺬﻩ‬ ‫وﻓﻰ‬
‫اﻟﻤﻌﻠﻤﻴﻪ‬ ‫اﻻﺧﺘﺒﺎرات‬Parametric Tests
‫ﻗﺪ‬ ‫اﺧﺮى‬ ‫ﺑﺄﺷﻴﺎء‬ ‫ﺗﺘﻌﻠﻖ‬ ‫وﻟﻜﻦ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﺑﻤﻌﺎﻟﻢ‬ ‫ﺗﺘﻌﻠﻖ‬ ‫ﻻ‬ ‫ﻓﺮوﺿﺎ‬ ‫ﺗﻜﻮن‬ ‫وﻗﺪ‬‫ﻣﺜﻞ‬ ‫وﺻﻔﻴﺔ‬ ‫ﺗﻜﻮن‬
‫اﻟﻌ‬ ،‫ﻣﻌﻴﻨﻪ‬ ‫ﻟﻨﻈﺮﻳﻪ‬ ‫ﻣﻌﻴﻨﻪ‬ ‫ﻧﺘﺎﺋﺞ‬ ‫ﺧﻀﻮع‬ ،‫واﻟﺘﺪﺧﻴﻦ‬ ‫اﻟﺘﻌﻠﻴﻢ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬‫اﻟﻌﻴﻨﻴﻦ‬ ‫ﻟﻮن‬ ‫ﺑﻴﻦ‬ ‫ﻼﻗﺔ‬
،‫اﻟﺸﻌﺮ‬ ‫وﻟﻮن‬....‫اﻟﻼﻣﻌﻠﻤﻰ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﺑﺎﺳﻢ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻳﺴﻤﻰ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫هﺬﻩ‬ ‫وﻓﻰ‬Non
Parametric Test
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 5 of 38

6. ‫اﻻﺣﺼﺎﺋﻰ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﺧﻄﻮات‬‫اﻻﺣﺼﺎﺋﻰ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﺧﻄﻮات‬
‫و‬ ‫اآﺜﺮ‬ ‫او‬ ‫ﻋﻴﻨﺘﻴﻦ‬ ‫او‬ ‫واﺣﺪة‬ ‫ﺑﻌﻴﻨﺔ‬ ‫ﻣﺘﻌﻠﻘﺎ‬ ‫ﻳﻜﻮن‬ ‫ﻗﺪ‬ ‫اﻻﺣﺼﺎﺋﻰ‬ ‫اﻻﺧﺘﺒﺎر‬‫او‬ ‫ﻣﻌﻠﻤﻴﺎ‬ ‫اﺧﺘﺒﺎرا‬ ‫ﻳﻜﻮن‬ ‫ﻗﺪ‬
‫ﺧﻄﻮات‬ ‫ﺑﻌﺪة‬ ‫ﻧﻮﻋﻪ‬ ‫آﺎن‬ ‫اى‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻳﻤﺮ‬ ‫ان‬ ‫وﻳﺠﺐ‬ ‫ﻣﻌﻠﻤﻴﺎ‬ ‫ﻏﻴﺮ‬
.1‫ﻓ‬ ‫ﻓﻰ‬ ‫اﻷهﺪاف‬ ‫هﺬﻩ‬ ‫ﺻﻴﺎﻏﻪ‬ ‫اﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﺒﺤﺚ‬ ‫اهﺪاف‬ ‫ﺑﺘﻔﻬﻢ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻳﺒﺪأ‬‫ﻳﺴﻤﻰ‬ ‫اﺣﺪاهﻤﺎ‬ ‫ﺮﺿﻴﻦ‬
‫اﻟﻌﺪم‬ ‫ﻓﺮض‬Null Hypothesis‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫ﻳﺴﻤﻰ‬ ‫واﻷﺧﺮ‬Alternative
Hypothesis
.2‫اﻟﺨﻄﺄ‬ ‫اﺣﺘﻤﺎل‬ ‫ﻳﺤﺪد‬)‫اﻟﺨﻄﺮ‬(‫اﻷول‬ ‫اﻟﻨﻮع‬ ‫ﻣﻦ‬ ‫اﻟﺨﻄﺄ‬ ‫وﻳﻤﺜﻞ‬)‫وهﻮ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫رﻓﺾ‬ ‫اﺣﺘﻤﺎل‬
‫ﺻﺤﻴﺢ‬(Type I Error‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﻪ‬ ‫وﻳﺮﻣﺰ‬α‫ﻳﺴﺎوى‬ ‫وﻏﺎﻟﺒﺎ‬0.05‫أو‬0.01
.3‫اﻟﻌﻴﻨﻪ‬ ‫ﻣﻦ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫وﺗﺠﻤﻴﻊ‬ ‫اﻟﺘﺠﺮﺑﻪ‬ ‫اﺟﺮاء‬ ‫ﻳﺘﻢ‬
.4‫اﻟﻔﺮوض‬ ‫ﺗﺮاﺟﻊ‬Assumptions‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬ ‫ﻋﻦ‬ ‫ﺗﺨﺘﻠﻒ‬ ‫وهﻰ‬ ‫ﻟﻼﺧﺘﺒﺎر‬ ‫اﻟﻼزﻣﻪ‬)
‫اﻟﺒﺪﻳﻞ‬ ‫واﻟﻔﺮض‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬.(
.5‫اﻻﺧﺘﺒ‬ ‫اﺣﺼﺎﺋﻰ‬ ‫ﻳﺴﻤﻰ‬ ‫ﻋﺸﻮاﺋﻰ‬ ‫ﻣﺘﻐﻴﺮ‬ ‫ﻋﻦ‬ ‫ﻧﺒﺤﺚ‬ ‫اﻻﺣﺘﻤﺎﻻت‬ ‫ﻧﻈﺮﻳﺔ‬ ‫اﺳﺘﺨﺪام‬‫ﺎر‬Test
Statistic‫اﻟﻌﻴﻨﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫وﻋﻦ‬Sampling Distribution‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﻟﻬﺬا‬ ‫اﻟﻤﻼﺋﻢ‬
.6‫ﻻﺗﺨ‬ ‫اﻟﻌﻴﻨﻰ‬ ‫واﻟﺘﻮزﻳﻊ‬ ‫واﻟﻤﺠﺘﻤﻊ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺎﺣﻪ‬ ‫اﻟﻤﻌﻠﻮﻣﺎت‬ ‫ﺗﺴﺘﺨﺪم‬‫او‬ ‫ﺑﻘﺒﻮل‬ ‫اﻣﺎ‬ ‫ﻣﻌﻴﻦ‬ ‫ﻗﺮار‬ ‫ﺎذ‬
‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫رﻓﺾ‬.
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 6 of 38

7. .1‫و‬ ‫ﻧﻔﺴﻪ‬ ‫اﻟﺒﺎﺣﺚ‬ ‫ﺑﻤﻌﺮﻓﺔ‬ ‫ﺗﺤﺪد‬ ‫اﻟﺴﺎدﺳﻪ‬ ‫واﻟﺨﻄﻮﻩ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﺜﻼﺛﻪ‬ ‫اﻟﺨﻄﻮات‬‫ﺗﺤﺘﺎج‬ ‫ﻻ‬
‫اﺣﺼﺎﺋﻴﻪ‬ ‫ﻟﻤﻌﻠﻮﻣﺎت‬
.2‫ارﺟ‬ ‫ﺑﺪون‬ ‫او‬ ‫ﺑﺎرﺟﺎع‬ ‫اﻟﺴﺤﺐ‬ ‫وهﻰ‬ ‫اﻟﻌﺸﻮاﺋﻴﺔ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻟﺴﺤﺐ‬ ‫ﻃﺮﻳﻘﺘﻴﻦ‬ ‫ﺗﻮﺟﺪ‬‫وﺳﻨﻔﺮض‬ ‫ﺎع‬
‫ﺑﺎرﺟﺎع‬ ‫ﺳﺤﺒﻬﺎ‬ ‫ﺗﻢ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻌﺸﻮاﺋﻴﺔ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻣﻊ‬ ‫ﻧﺘﻌﺎﻣﻞ‬ ‫اﻧﻨﺎ‬.
.3‫ﺗﺘﻌ‬ ‫ﻣﻌﻠﻤﻴﻪ‬ ‫اﺧﺘﺒﺎرات‬ ‫هﻰ‬ ‫اﻟﺪرس‬ ‫هﺬا‬ ‫ﻓﻰ‬ ‫ﻣﻌﻬﺎ‬ ‫ﺳﻨﺘﻌﺎﻣﻞ‬ ‫اﻟﺘﻰ‬ ‫اﻻﺧﺘﺒﺎرات‬‫واﺣﺪﻩ‬ ‫ﺑﻌﻴﻨﺔ‬ ‫ﻠﻖ‬
‫ﻋﻴﻨﺘﻴﻦ‬ ‫واﻳﻀﺎ‬.
.4‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻻﺧﺘﺒﺎرات‬ ‫ﻓﻰ‬ ‫ﻗﺮار‬ ‫ﻻﺗﺨﺎذ‬ ‫ﻃﺮﻳﻘﺘﻴﻦ‬ ‫ﺗﻮﺟﺪ‬
(i)‫اﻟﺠﺪوﻟﻴﻪ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫وﺗﺤﺪد‬ ‫ﺟﺪوﻟﻴﻪ‬ ‫ﺑﻘﻴﻤﺔ‬ ‫وﻣﻘﺎرﻧﺘﻪ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺣﺼﺎء‬ ‫ﺣﺴﺎب‬‫ﻧﻮع‬ ‫ﻋﻠﻰ‬ ‫ﺑﻨﺎء‬
‫واﺣﺪ‬ ‫ﻃﺮف‬ ‫ذو‬ ‫اﻻﺣﺘﺒﺎر‬One Tail Test‫ﻃﺮﻓﻴﻦ‬ ‫ذو‬ ‫أو‬Two Tail Test
(ii)‫اﻻﺣﺘﻤﺎﻟﻴﻪ‬ ‫ﺑﺎﻟﻘﻴﻤﺔ‬ ‫ﻳﺴﻤﻰ‬ ‫ﻣﺎ‬ ‫ﺣﺴﺎب‬P-value‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﺤﺰﻣﺔ‬ ‫ﻓﻰ‬ ‫ﻟﻬﺎ‬ ‫وﻳﺮﻣﺰ‬Sig.‫ﻓﺎذا‬
‫ﺗﻘﺎرن‬ ‫واﺣﺪ‬ ‫ﻃﺮف‬ ‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫آﺎن‬Sig.‫ﺑﺎﻟﻘﻴﻤﺔ‬α‫ﻃﺮﻓﻴﻦ‬ ‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫آﺎن‬ ‫اذا‬ ‫ﻟﻜﻦ‬
‫ﺑﺎﻟﻘﻴﻤﺔ‬ ‫ﺗﻘﺎرن‬α/2
‫اﻟﻤﻼﺣﻈﺎت‬ ‫ﺑﻌﺾ‬‫اﻟﻤﻼﺣﻈﺎت‬ ‫ﺑﻌﺾ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 7 of 38

8. ‫اﻻﺧﺘﺒﺎر‬ ‫اﻧﻮاع‬‫اﻻﺧﺘﺒﺎر‬ ‫اﻧﻮاع‬))‫اﻟﻔﺮوض‬‫اﻟﻔﺮوض‬((‫واﺣﺪﻩ‬ ‫ﻋﻴﻨﻪ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬‫واﺣﺪﻩ‬ ‫ﻋﻴﻨﻪ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬
‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﻤﺠﻬﻮل‬ ‫ﻟﻠﻤﻌﻠﻢ‬ ‫ﻧﺮﻣﺰ‬ ‫ﺳﻮف‬ ‫اﻧﻨﺎ‬ ‫ﺑﻔﺮض‬Θ‫ان‬ ‫اﻟﻘﺎﺋﻞ‬ ‫اﻟﻔﺮض‬ ‫اﺧﺘﺒﺎر‬ ‫وﻧﺮﻳﺪ‬
‫ﺗﺴﺎوى‬ ‫ﻗﻴﻤﺘﻪ‬Θ0‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﺳﻴﻜﻮن‬
‫واﺣﺪ‬ ‫ﻃﺮف‬ ‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﺳﻴﻜﻮن‬
‫ﻃﺮﻓﻴﻦ‬ ‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﺳﻴﻜﻮن‬
00 :: Θ>ΘΘ<Θ aa HorH
00 : Θ=ΘH
0: Θ≠ΘaH
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 8 of 38

9. ‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ((‫اﻟﻔﺮوض‬‫اﻟﻔﺮوض‬))‫اﻻﺧﺘﺒﺎر‬ ‫اﻧﻮاع‬‫اﻻﺧﺘﺒﺎر‬ ‫اﻧﻮاع‬
‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﻤﺠﻬﻮل‬ ‫ﻟﻠﻤﻌﻠﻢ‬ ‫ﻧﺮﻣﺰ‬ ‫ﺳﻮف‬ ‫اﻧﻨﺎ‬ ‫ﺑﻔﺮض‬Θ‫ان‬ ‫اﻟﻘﺎﺋﻞ‬ ‫اﻟﻔﺮض‬ ‫اﺧﺘﺒﺎر‬ ‫وﻧﺮﻳﺪ‬
‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﻳﻪ‬ ‫ﻗﻴﻤﺘﻪ‬‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﺳﻴﻜﻮن‬
‫واﺣﺪ‬ ‫ﻃﺮف‬ ‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﺳﻴﻜﻮن‬
‫ﻃﺮﻓﻴﻦ‬ ‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﺳﻴﻜﻮن‬
2121 :: Θ>ΘΘ<Θ aa HorH
210 : Θ=ΘH
21: Θ≠ΘaH
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 9 of 38

10. ‫اﻻﺧﺘﺒﺎر‬ ‫اﻧﻮاع‬‫اﻻﺧﺘﺒﺎر‬ ‫اﻧﻮاع‬))‫اﻟﻔﺮوض‬‫اﻟﻔﺮوض‬((‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻣﻦ‬ ‫أآﺜﺮ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻣﻦ‬ ‫أآﺜﺮ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬
‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﻤﺠﻬﻮل‬ ‫ﻟﻠﻤﻌﻠﻢ‬ ‫ﻧﺮﻣﺰ‬ ‫ﺳﻮف‬ ‫اﻧﻨﺎ‬ ‫ﺑﻔﺮض‬Θ‫ان‬ ‫اﻟﻘﺎﺋﻞ‬ ‫اﻟﻔﺮض‬ ‫اﺧﺘﺒﺎر‬ ‫وﻧﺮﻳﺪ‬
‫ﻋﺪدهﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﻳﻪ‬ ‫ﻗﻴﻤﺘﻪ‬r‫اﻟﺼﻮرة‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﺳﻴﻜﻮن‬
‫اﻟﺘﺎﻟﻴﺔ‬
‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﺳﻴﻜﻮن‬
‫اﻟﻨ‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﺨﻄﺄ‬ ‫ﻳﺴﻤﻰ‬ ‫ﺑﻤﺎ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻗﻮة‬ ‫ﻗﻴﺎس‬ ‫ﻳﻤﻜﻦ‬ ‫اﻻﺧﺘﺒﺎرات‬ ‫ﺟﻤﻴﻊ‬ ‫ﻓﻰ‬‫اﻟﺜﺎﻧﻰ‬ ‫ﻮع‬
Type II Error‫اﻟﻘﻮﻩ‬ ‫داﻟﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻓﻰ‬ ‫ﺑﺪورﻩ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫واﻟﺬى‬Power
Function
differentareleast twoat:aH
rH Θ==Θ=Θ L210 :
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 10 of 38

11. ‫ت‬ ‫اﺧﺘﺒﺎر‬‫ت‬ ‫اﺧﺘﺒﺎر‬T TestT Test
‫ﺗﻮزﻳﻊ‬ ‫واﻟﻤﺴﻤﻰ‬ ‫اﻻﺣﺘﻤﺎﻟﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻪ‬ ‫اﻟﺤﺎﻟﻪ‬ ‫هﺬﻩ‬ ‫ﻓﻰ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺣﺼﺎء‬T(T
Distribution)‫ت‬ ‫ﺑﺎﺧﺘﺒﺎر‬ ‫اﻻﺧﺘﺒﺎر‬ ‫هﺬا‬ ‫ﻳﺴﻤﻰ‬ ‫ﻟﺬا‬T‫ﻋﻨﺪﻣﺎ‬ ‫ت‬ ‫اﺣﺘﺒﺎر‬ ‫وﻳﺴﺘﺨﺪم‬
‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻳﻜﻮن‬)‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫او‬(‫واﻟﺘﺒﺎﻳﻦ‬ ‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬)‫اﻟﺘﺒﺎﻳﻨﺎت‬(‫ﻏﻴﺮ‬
‫اﻟﻌﻴﻨﻪ‬ ‫ﺣﺠﻢ‬ ‫واﻳﻀﺎ‬ ‫ﻣﻌﻠﻮم‬)‫اﻟﻌﻴﻨﺎت‬(‫ﻣﻦ‬ ‫أﻗﻞ‬30‫ﻋﻦ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﺣﺠﻢ‬ ‫زاد‬ ‫اذا‬ ‫ﻟﻜﻦ‬30
‫ﻣﻌﻠ‬ ‫اﺧﺘﺒﺎر‬ ‫وهﻮ‬ ‫اﻟﻤﻌﻴﺎرى‬ ‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻷﺣﺼﺎء‬ ‫ﻳﻜﻮن‬ ‫ﺳﻮف‬‫ﻤﻰ‬.
‫واﺧﺘﺒﺎر‬T‫وهﻰ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﻗﺒﻞ‬ ‫ﺗﻮاﻓﺮهﺎ‬ ‫ﻳﺠﺐ‬ ‫ﺷﺮوط‬ ‫ﻋﺪة‬ ‫ﻋﻠﻰ‬ ‫ﻳﺘﻮﻗﻒ‬
.1‫وهﺬ‬ ‫اﻷﻗﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺑﻔﺘﺮﻩ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺑﻬﺎ‬ ‫اﻟﻤﻘﺎﺳﻪ‬ ‫اﻟﻘﻴﺎس‬ ‫وﺣﺪة‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻳﺠﺐ‬‫ان‬ ‫ﻳﻌﻨﻰ‬ ‫ا‬
‫ﻣﺴﺘﻤﺮﻩ‬ ‫ﻟﻤﺘﻐﻴﺮات‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻳﺠﺐ‬ ‫اﻟﺒﻴﺎﻧﺎت‬.‫او‬ ‫اﺳﻤﻴﻪ‬ ‫اﻟﻘﻴﺎس‬ ‫وﺣﺪة‬ ‫آﺎﻧﺖ‬ ‫ﻓﺎذا‬
‫اﻻﺧﺘﺒﺎر‬ ‫ﻳﻄﺒﻖ‬ ‫ﻓﻼ‬ ‫ﺗﺮﺗﻴﺒﻴﻪ‬
.2‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﻦ‬ ‫ﻋﺸﻮاﺋﻴﺎ‬ ‫ﻣﺨﺘﺎرة‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻳﺠﺐ‬ ‫اﻟﻌﻴﻨﺔ‬
.3‫اﻟ‬ ‫ﺣﺴﺐ‬ ‫ﺗﺘﻮزع‬ ‫ان‬ ‫ﻳﺠﺐ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻓﻰ‬ ‫اﻟﺪاﺧﻠﻪ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫او‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﺑﻴﺎﻧﺎت‬‫ﺘﻮزﻳﻊ‬
‫اﻟﻄﺒﻴﻌﻰ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 11 of 38

12. ‫ﻳ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺸﺮط‬ ‫ﻟﻜﻦ‬ ‫ﻣﻨﻬﻤﺎ‬ ‫اﻟﺒﺎﺣﺚ‬ ‫ﻳﺘﺤﻘﻖ‬ ‫ان‬ ‫ﻳﺠﺐ‬ ‫واﻟﺜﺎﻧﻰ‬ ‫اﻷول‬ ‫اﻟﺸﺮط‬‫ﻤﻜﻦ‬
‫اﻷﻣﺮ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻪ‬ ‫اﻟﺘﺤﻘﻖ‬Frequencies‫اﻷﻣﺮ‬ ‫أو‬Explore‫ﺗﻢ‬ ‫آﻤﺎ‬
‫ﺳﺎﺑﻘﺎ‬
‫اﺧﺘﺒﺎرات‬ ‫ﻻﺳﺘﺨﺪاﻣﺎت‬ ‫واﻟﺘﻮﺿﻴﺢ‬ ‫ﺑﺎﻟﺸﺮح‬ ‫هﻨﺎ‬ ‫ﻧﻬﺘﻢ‬ ‫وﺳﻮف‬T‫واﻟﺬى‬
‫ﻣﻨﻬﺎ‬ ‫اﻻﺧﺘﺒﺎرات‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻓﻰ‬ ‫ﻳﺴﺘﺨﺪم‬:
.1‫ﻣﺠﺘﻤﻊ‬ ‫ﻣﺘﻮﺳﻂ‬ ‫ﻳﺴﺎوى‬ ‫واﺣﺪﻩ‬ ‫ﻋﻴﻨﻪ‬ ‫ﻣﺘﻮﺳﻂ‬ ‫هﻞ‬.
.2‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬ ‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻣﺘﻮﺳﻂ‬ ‫اﺧﺘﺒﺎر‬Independent Samples‫وﻳﻜﻮن‬
‫ﻻ؟‬ ‫ام‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻧﻔﺲ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺤﻮﺑﺘﺎن‬ ‫اﻟﻌﻴﻨﺘﻴﻦ‬ ‫هﻞ‬ ‫اﺧﺘﺒﺎر‬ ‫اﻟﻤﻄﻠﻮب‬
.3‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬ ‫ﻏﻴﺮ‬ ‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻣﺘﻮﺳﻄﻰ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮق‬ ‫اﺧﺘﺒﺎر‬.
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 12 of 38

13. SPSS for Beginners: Lesson 6SPSS for Beginners: Lesson 6
‫واﺣﺪة‬ ‫ﻟﻌﻴﻨﺔ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻻﺧﺘﺒﺎرات‬‫واﺣﺪة‬ ‫ﻟﻌﻴﻨﺔ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻻﺧﺘﺒﺎرات‬
One Sample TestOne Sample Test
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 13 of 38

14. ‫ﻣﻦ‬ ‫ﻋﻴﻨﺔ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ان‬ ‫ﺑﻔﺮض‬20‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﻟﺪﻳﻨﺎ‬ ‫وآﺎﻧﺖ‬ ‫ﺑﺎﻟﻜﻠﻴﻮﺟﺮام‬ ‫ﺷﺨﺺ‬ ‫آﻞ‬ ‫وزن‬ ‫ﻗﻴﺎس‬ ‫وﺗﻢ‬ ‫ﺷﺨﺺ‬
‫اﻟﺘﺎﻟﻴﺔ‬:
65 75 80 120 110 90 60 100 90 70 165 100 90 80 70 75 85
55 130 100
‫اﻟﻌﺪﻣﻰ‬ ‫اﻟﻔﺮض‬ ‫اﺧﺘﺒﺎر‬ ‫ﻧﺮﻳﺪ‬ ‫اﻧﻨﺎ‬ ‫ﺑﻔﺮض‬:‫ﻳﺴﺎوى‬ ‫اﻟﻌﻴﻨﻪ‬ ‫ﻣﻨﻪ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻓﻰ‬ ‫اﻟﻮزن‬ ‫ﻣﺘﻮﺳﻂ‬
100‫آﺠﻢ‬
‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬:‫ﻳﺴﺎوى‬ ‫ﻻ‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻣﺘﻮﺳﻂ‬100‫آﺠﻢ‬
‫اﻟﺤﻞ‬‫اﻟﺤﻞ‬::
‫اوﻻ‬:‫وﻟﻴﻜﻦ‬ ‫ﻣﻠﻒ‬ ‫ى‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫هﺬﻩ‬ ‫ﺑﻮﺿﻊ‬weight.sav
‫ﺛﺎﻧﻴﺎ‬:‫ﺑﺎﺳﺘﺨ‬ ‫وذﻟﻚ‬ ‫ﻻ‬ ‫ام‬ ‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﺗﺘﺒﻊ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫هﺬﻩ‬ ‫هﻞ‬ ‫اﺧﺘﺒﺎر‬ ‫ﻳﺠﺐ‬‫اﻷﻣﺮ‬ ‫ﺪام‬Frequencies
‫أو‬Explore‫ﺳﺒﻖ‬ ‫آﻤﺎ‬
Tests of Normality
.158 20 .200* .913 20 .072weight
Statistic df Sig. Statistic df Sig.
Kolmogorov-Smirnov
a
Shapiro-Wilk
This is a lower bound of the true significance.*.
Lilliefors Significance Correctiona.
‫اﺧﺘﺒﺎر‬ ‫ﻣﻦ‬Test of Normality‫ان‬ ‫ﻧﺠﺪ‬
‫ﻗﻴﻤﺔ‬Sig.‫ﻣﻦ‬ ‫اآﺒﺮ‬0.05‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬
‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ان‬ ‫وهﻮ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬
‫اﻟﻄﺒﻴﻌﻰ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 14 of 38

15. ‫ان‬ ‫ﻧﺠﺪ‬ ‫اﻟﺒﻴﺎﻧﻰ‬ ‫اﻟﺮﺳﻢ‬ ‫ﻣﻦ‬
‫ﺣﻮل‬ ‫ﺗﺘﺮآﺰ‬ ‫اﻟﺒﻴﺎﻧﺎت‬
‫ﻓﺎﻧﻬﺎ‬ ‫ﻟﺬا‬ ‫اﻟﻤﺴﺘﻘﻴﻢ‬ ‫اﻟﺨﻂ‬
‫ﻟﻠﺘﻮزﻳﻊ‬ ‫ﺗﺒﻌﺎ‬ ‫ﺗﺘﻮزع‬
‫اﻟﻄﺒﻴﻌﻰ‬
‫ﺛﺎﻟﺜﺎ‬:‫اﻟﻌﻴﻨﻪ‬ ‫ﺣﺠﻢ‬ ‫ان‬ ‫ﺑﻤﺎ‬20‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫اى‬30‫هﻮ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺣﺼﺎء‬ ‫ﻓﺎن‬ ‫ﻟﺬا‬T‫ﺳﻮف‬ ‫اﻧﻨﺎ‬ ‫ﺑﻤﻌﻨﻰ‬
‫اﺧﺘﺒﺎر‬ ‫ﻧﺴﺘﺨﺪم‬T‫آﺎﻟﺘﺎﻟﻰ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫وﺳﻨﺠﺮى‬
1-‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 15 of 38

16. ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬Null Hypothesis‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻟﻪ‬ ‫ﺳﻴﻜﻮن‬:
‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬Alternative Hypothesis‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻟﻪ‬ ‫ﺳﻴﻜﻮن‬:
‫هﻮ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺣﺼﺎء‬
‫اﺣ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻳﻤﻜﻦ‬ ‫ﻟﻠﻌﻴﻨﻪ‬ ‫اﻟﻤﻌﻴﺎرى‬ ‫واﻻﻧﺤﺮاف‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫وﺑﺘﻌﻴﻦ‬‫اﻻﺧﺘﺒﺎر‬ ‫ﺼﺎء‬
T
‫ﺗﻮزﻳﻊ‬ ‫ﺟﺪول‬ ‫وﻣﻦ‬T‫ﻓﺎذا‬ ‫اﻟﺤﺮﺟﻪ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻳﻤﻜﻦ‬
‫آﺎﻧﺖ‬|T|‫اذا‬ ‫ﻟﻜﻦ‬ ‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﻧﻘﺒﻞ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﺮﻓﺾ‬ ‫اﻟﺤﺮﺟﺔ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ﻣﻦ‬ ‫أآﺒﺮ‬
‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﻧﺮﻓﺾ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫أﻗﻞ‬ ‫آﺎﻧﺖ‬
100:0 =μH
100:0 ≠μH
nS
X
T
/
0μ−
=
)2/,1(2/ αα −= ntt
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 16 of 38

17. ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫هﺬا‬ ‫اﺟﺮاء‬ ‫وﻳﻤﻜﻦ‬
‫ﺣﺰﻣﺔ‬SPSS‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﺑﺴﻬﻮﻟﻪ‬:
1-‫ﻣﻠﻒ‬ ‫ﻓﻰ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺑﺘﺨﺰﻳﻦ‬Weight.sav
2-‫ﻗﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Analyze‫ﻧﺨﺘﺎر‬Compare
Means
3-‫ﻧﺨﺘﺎر‬ ‫اﻟﻔﺮﻋﻴﻪ‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫ﻣﻦ‬One
Sample T Test
4-‫ﺑﻌﻨﻮان‬ ‫ﺟﺪﻳﺪﻩ‬ ‫ﺷﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬One-
Sample T test‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﻧﻨﻘﻞ‬
Weight‫ﻟﻘﺎﺋﻤﺔ‬Test Variable(s)
5-‫اﻟﻤﺴﺘﻄﻴﻞ‬ ‫ﻓﻰ‬Test Value:‫ﻗﻴﻤﺔ‬ ‫ﻧﻜﺘﺐ‬
‫وهﻰ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬100
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 17 of 38

18. 6-‫اﻷﻣﺮ‬ ‫ﻧﺨﺘﺎر‬Options‫ﺟﺪﻳﺪﻩ‬ ‫ﺷﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬
‫ﺑﻌﻨﻮان‬One- Sample T Test:
Options‫ﺧﺎﻧﺔ‬ ‫ﻓﻰ‬ ‫اﻧﻪ‬ ‫ﻻﺣﻆ‬Confidence
interval‫اﻟﻘﻴﻤﺔ‬95%‫ﻣﺴﺘﻮى‬ ‫ان‬ ‫ﺑﻤﻌﻨﻰ‬
‫اﻟﻤﻌﻨﻮﻳﻪ‬α=0.05‫ﻧﺨﺘﺎر‬ ‫ﺛﻢ‬ ‫ﺗﻐﻴﺮهﺎ‬ ‫وﻳﻤﻜﻦ‬
Continue‫ﻧﻀﻐﻂ‬ ‫ﺛﻢ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫ﻟﻠﺸﺎﺷﺔ‬ ‫ﻧﻌﻮد‬Ok
7-‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻈﻬﺮ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 18 of 38

19. ‫اﻷول‬ ‫اﻟﺠﺪول‬‫اﻷول‬ ‫اﻟﺠﺪول‬::
‫ﺑﻌﻨﻮان‬One-Sample Statistics‫واﻟﻮﺳﻂ‬ ‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﺣﺎﻻت‬ ‫ﻋﺪد‬ ‫وﻋﺮض‬
‫اﻟﺤﺴﺎﺑﻰ‬ ‫ﻟﻠﻮﺳﻂ‬ ‫اﻟﺘﻘﺪﻳﺮ‬ ‫وﺧﻄﺄ‬ ‫اﻟﻤﻌﻴﺎر‬ ‫واﻻﻧﺤﺮاف‬ ‫اﻟﺤﺴﺎﺑﻰ‬.
‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺠﺪول‬‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺠﺪول‬::
‫ﺑﻌﻨﻮان‬One-Sample Test‫وﻋﺮض‬‫ﻋﻠﻰ‬ ‫اﻟﺠﺪول‬ ‫ﻳﺤﺘﻮى‬ ‫ﺣﻴﺚ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ﻧﺘﻴﺠﻪ‬
.1‫اﻟﺠﺪول‬ ‫اﻋﻠﻰ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬Test Value = 100
.2‫اﻟﻤﺘﻐﻴﺮ‬ ‫واﺳﻢ‬
.3‫اﻻﺧﺘﺒﺎر‬ ‫اﺣﺼﺎء‬ ‫ﻗﻴﻤﻪ‬T= -1.621
.4‫اﻟﺤﺮﻳﺔ‬ ‫درﺟﺔ‬n-1 = 19
.5‫اﻻﺣﺘﻤﺎﻟﻴﺔ‬ ‫اﻟﻘﻴﻤﺔ‬P-value‫وهﻰ‬Sig. = 0.121
.6‫اﻟﻌﺪﻣﻰ‬ ‫اﻟﻔﺮض‬ ‫وﻗﻴﻤﺔ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫وﺳﻂ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮق‬Mean Difference
.795%‫اﻟﻌﻴﻨﺔ‬ ‫ﻣﻨﻪ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫ﻟﻮﺳﻂ‬ ‫ﺛﻘﺔ‬ ‫ﻓﺘﺮة‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 19 of 38

20. ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺑﻨﺎء‬ ‫ﻗﺮار‬ ‫اﺗﺨﺎذ‬ ‫ﻳﻤﻜﻦ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺠﺪول‬ ‫ﻣﻦ‬Sig.=0.121‫ذو‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ان‬ ‫ﺣﻴﺚ‬
‫ﺑﺎﻟﻘﻴﻤﺔ‬ ‫ﻧﻘﺎرﻧﻬﺎ‬ ‫ﺳﻮف‬ ‫ﻓﺎﻧﻨﺎ‬ ‫ﻃﺮﻓﻴﻦ‬α/2 =0.025‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬ ‫اآﺒﺮ‬ ‫وهﻰ‬.
‫اﻻﺧﺘﺒﺎر‬ ‫ﻷﺣﺼﺎء‬ ‫اﻟﻤﻮﺟﺒﻪ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫ان‬ ‫ﻟﻠﻤﺴﺘﺨﺪم‬ ‫ﻳﻤﻜﻦ‬|T|‫اﻟﺤﺮﺟﺔ‬ ‫ﺑﺎﻟﻘﻴﻤﺔ‬ ‫وﻣﻘﺎرﻧﺘﻬﺎ‬
‫ﺟﺪول‬ ‫ﻣﻦ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻧﺤﺼﻞ‬ ‫واﻟﺘﻰ‬T‫ﻣﻌﻨﻮﻳﻪ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻋﻨﺪ‬α/2 =0.025‫ﺣﺮﻳﺔ‬ ‫ودرﺟﺔ‬
n-1 = 19
‫ان‬ ‫اﻟﻤﻼﺣﻆ‬ ‫وﻣﻦ‬
‫ﻓﺎن‬ ‫وﺑﺎﻟﺘﺎﻟﻰ‬
‫ﻳﺴﺎ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﻣﻨﻪ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫اﻟﻤﺠﺘﻤﻊ‬ ‫وﺳﻂ‬ ‫ان‬ ‫وهﻮ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬‫وى‬100‫آﺠﻢ‬
‫ﻧﺴﺘﺨﺪم‬ ‫ان‬ ‫اﻟﺤﺰﻣﺔ‬ ‫ﻣﻊ‬ ‫اﻟﺘﻌﺎﻣﻞ‬ ‫ﻋﻨﺪ‬ ‫داﺋﻤﺎ‬ ‫وﻳﻔﻀﻞ‬Sig.‫اﺣﺼﺎء‬ ‫اﻟﻘﺮاروﻟﻴﺴﺖ‬ ‫ﻻﺗﺨﺎذ‬
‫اﻻﺧﺘﺒﺎر‬
621.1||,262.2)19,025.0(2/ === Tttα
2/|| αtT <
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 20 of 38

21. SPSS for Beginners: Lesson 6SPSS for Beginners: Lesson 6
‫اﺧﺘﺒﺎرﻋﻴﻨﺘﻴﻦ‬‫اﺧﺘﺒﺎرﻋﻴﻨﺘﻴﻦ‬‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 21 of 38

22. ‫اﻟﻌﻴﻨﺘﻴﻦ‬ ‫آﻼ‬ ‫ﻓﻰ‬ ‫ﻣﻌﻴﻦ‬ ‫ﺑﻤﺘﻐﻴﺮ‬ ‫وﻧﻬﺘﻢ‬ ‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬ ‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ان‬ ‫ﺑﻔﺮض‬‫ﻓﻰ‬ ‫وﻧﺮﻏﺐ‬
‫اﻟﻮﺳﻂ‬ ‫ﻧﻔﺲ‬ ‫ﻟﻬﻤﺎ‬ ‫اﻟﻌﻴﻨﺘﻴﻦ‬ ‫ﻣﻨﻬﻤﺎ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﻣﺘﻮﺳﻄﻰ‬ ‫ان‬ ‫اﺧﺘﺒﺎر‬‫ام‬ ‫اﻟﺤﺴﺎﺑﻰ‬
‫آﺎﻟﺘﺎﻟﻰ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬ ‫ﺗﺼﺎغ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬ ‫ﻻ‬:
.1‫ﻃﺮﻓﻴﻦ‬ ‫ذو‬ ‫اﺧﺘﺒﺎر‬
.2‫واﺣﺪ‬ ‫ﻃﺮف‬ ‫ذو‬ ‫اﺧﺘﺒﺎر‬
‫اﻟﺸﺮوط‬ ‫ﺑﻌﺾ‬ ‫ﺗﻮاﻓﺮ‬ ‫ﻳﺠﺐ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫هﺬا‬ ‫وﻻﺟﺮاء‬
211210 :,: μμμμ ≠= HH
211210
211210
211210
:,:or
:,:or
)(:,:
μμμμ
μμμμ
μμμμ
≤>
≥<
><=
HH
HH
HH
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 22 of 38

23. ‫ﺗﻮاﻓﺮهﺎ‬ ‫اﻟﻼزم‬ ‫اﻟﺸﺮوط‬
.1‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫اﻟﻤﺴﺤﻮﺑﻪ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﺣﺠﻢ‬30‫اﺧﺘﺒﺎر‬ ‫اﺳﺘﺨﺪام‬ ‫ﻻﻣﻜﺎﻧﻴﻪ‬T‫ﻣﻦ‬ ‫اآﺒﺮ‬ ‫آﺎﻧﺖ‬ ‫اذا‬ ‫ﻟﻜﻦ‬30
‫ﻧﺴﺘﺨﺪم‬ ‫ﺳﻮف‬Z
.2‫ﻣﺴﺘﻘﻠﻪ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻳﺠﺐ‬
.3‫ﻣﺘﺠﺎﻧﺴﻪ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻣﻨﻬﺎ‬ ‫اﻟﻤﺴﺤﻮب‬ ‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻳﺠﺐ‬
.4‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻳﺠﺐ‬
‫واﻟﺮ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺸﺮﻃﻴﻦ‬ ‫ﻟﻜﻦ‬ ‫اﻟﺒﺎﺣﺚ‬ ‫ﻣﻨﻬﻤﺎ‬ ‫ﻳﺘﺄآﺪ‬ ‫واﻟﺜﺎﻧﻰ‬ ‫اﻷول‬ ‫اﻟﺸﺮﻃﻴﻦ‬‫ﻣﻨﻬﻤﺎ‬ ‫اﻟﺘﺎآﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫اﺑﻊ‬
‫ﺣﺰﻣﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬SPSS
‫اﻷﻣﺮ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ﺳﺎﺑﻘﺎ‬ ‫اﺟﺮاﺋﻪ‬ ‫ﺗﻢ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﻃﺒﻴﻌﻴﺔ‬ ‫اﺧﺘﺒﺎر‬Explore‫واﻷﻣﺮ‬Frequencies
‫اﻻ‬ ‫اﻟﻔﺮوض‬ ‫وﺳﺘﻜﻮن‬ ‫ﻣﺘﺴﺎوى‬ ‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﺗﺒﺎﻳﻦ‬ ‫ان‬ ‫وﻳﻌﻨﻰ‬ ‫اﻟﺘﺠﺎﻧﺲ‬ ‫اﺧﺘﺒﺎر‬‫اﻟﺸﻜﻞ‬ ‫ﻟﻬﺎ‬ ‫ﺣﺼﺎﺋﻴﺔ‬
‫اﻟﺘﺎﻟﻰ‬
‫ا‬ ‫ﻓﻰ‬ ‫ﻧﺴﺘﻤﺮ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬ ‫ﺗﺠﺎﻧﺲ‬ ‫هﻨﺎك‬ ‫ان‬ ‫ﻳﻌﻨﻰ‬ ‫ﻓﻬﺬا‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻗﺒﻮل‬ ‫ﺗﻢ‬ ‫اذا‬‫ﺗﻢ‬ ‫اذا‬ ‫اﻣﺎ‬ ‫ﻻﺧﺘﺒﺎر‬
‫اﻻﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﻳﺠﻮز‬ ‫ﻻ‬ ‫ﻟﺬا‬ ‫ﺗﺠﺎﻧﺲ‬ ‫وﺟﻮد‬ ‫ﻋﺪم‬ ‫ﻓﻴﻌﻨﻰ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫رﻓﺾ‬.
2
2
2
11
2
2
2
10 :,: σσσσ ≠= HH
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 23 of 38

24. ‫ﺗﻤﺮﻳﻦ‬‫ﺗﻤﺮﻳﻦ‬::
‫اﻻﺣﺼﺎء‬ ‫ﻣﻘﺮر‬ ‫ﻓﻰ‬ ‫درﺟﺎﺗﻬﻢ‬ ‫ﺗﺴﺠﻴﻞ‬ ‫وﺗﻢ‬ ‫اﻟﻄﻼب‬ ‫ﻣﻦ‬ ‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ان‬ ‫ﺑﻔﺮض‬‫آﺎﻟﺘﺎﻟﻰ‬
‫ﻻ؟‬ ‫ام‬ ‫ﻟﻠﻤﺠﻤﻮﻋﺘﻴﻦ‬ ‫اﻟﺘﺤﺼﻴﻞ‬ ‫ﻣﺴﺘﻮى‬ ‫ﺑﻴﻦ‬ ‫ﻓﺮق‬ ‫هﻨﺎك‬ ‫هﻞ‬ ‫ﻣﻌﺮﻓﺔ‬ ‫واﻟﻤﻄﻠﻮب‬
‫اﻟﺤﻞ‬‫اﻟﺤﻞ‬::
1-‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﺣﺠﻢ‬ ‫ان‬ ‫اﻟﻮاﺿﺢ‬ ‫ﻣﻦ‬30
2-‫ﻣﺴﺘﻘﻠﻪ‬ ‫اﻟﻌﻴﻨﺎت‬
3-‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻻ‬ ‫ام‬ ‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫هﻞ‬ ‫اﺧﺘﺒﺎر‬ ‫ﻳﺠﺐ‬
‫ﻳﺴﻤﻰ‬ ‫اﺣﺪاهﻤﺎ‬ ‫ﻣﺘﻐﻴﺮﻳﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺑﺎدﺧﺎل‬ ‫ﺳﻨﻘﻮم‬Factor‫واﻷﺧﺮ‬Data‫ﺣﻴﺚ‬
‫ﺗﺤﺘﻮى‬data‫واﻟﻤﺘﻐﻴﺮ‬ ‫اﻟﻌﻴﻨﺘﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﻘﺮاءات‬ ‫ﻋﻠﻰ‬factor‫اﻟﺮﻗﻢ‬ ‫ﻳﺤﺘﻮى‬1‫آﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﻓﻰ‬ ‫اﻟﻘﻴﻤﺔ‬data‫واﻟﺮﻗﻢ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﻣﻦ‬2،‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫آﺎﻧﺖ‬ ‫اذا‬
‫آﺎﻟﺘﺎﻟﻰ‬
17
10
10
13
3
15
8
14
19
14
16101519Sample 2
1720Sample 1
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 24 of 38

25. ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ ‫اﺧﺘﺒﺎر‬ ‫ﻻﺟﺮاء‬data‫ﻧﻘﻮم‬ ‫ﺳﻮف‬
‫اﻟﺘﺎﻟﻴﺘﻴﻦ‬ ‫ﺑﺎﻟﺨﻄﻮﺗﻴﻦ‬:
‫اﻻوﻟﻰ‬ ‫اﻟﺨﻄﻮﻩ‬:
1-‫ﻗﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Data‫ﻧﺨﺘﺎر‬Split File
2-‫ﻧﺨﺘﺎر‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬Compare groups‫وﻧﻨﻘﻞ‬
‫اﻟﻤﺘﻐﻴﺮ‬Factor‫ﻟﺨﺎﻧﺔ‬Groups Based on
3-‫ﻧﺨﺘﺎر‬Ok‫ﺗﺒﻌﺎ‬ ‫ﻟﻤﺠﻤﻮﻋﺘﻴﻦ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺗﻘﺴﻴﻢ‬ ‫ﺳﻴﺘﻢ‬
‫ﻟﻠﻤﺘﻐﻴﺮ‬Factor‫ﻇﺎهﺮى‬ ‫ﻏﻴﺮ‬ ‫ﺗﻘﺴﻴﻢ‬ ‫وهﻮ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 25 of 38

26. ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺨﻄﻮﻩ‬:
1-‫ﻗﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Analyze‫ﻧﺨﺘﺎر‬Descriptive Statistics‫ﻧﻀﻐﻂ‬ ‫ﺛﻢ‬Explore
2-‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﻧﻨﻘﻞ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬Data‫ﻟﺨﺎﻧﺔ‬Dependent List‫وﻧﻨﻘﻞ‬
‫اﻟﻤﺘﻐﻴﺮ‬Factor‫ﻟﺨﺎﻧﺔ‬Factor List
3-‫ﻧﺨﺘﺎر‬Plots‫اﻻﺧﺘﻴﺎر‬ ‫ﻧﺤﺪد‬ ‫ﺛﻢ‬Normality plots with tests‫ﻧﺨﺘﺎر‬ ‫ﺳﻮ‬
Continue‫ﻧﺨﺘﺎر‬ ‫ﺛﻢ‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫ﻟﻠﺸﺎﺷﺔ‬ ‫ﻧﻌﻮد‬Ok‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻈﻬﺮ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 26 of 38

27. ‫ﺟﺪول‬ ‫ﻣﻦ‬ ‫ﻧﺠﺪ‬Tests of Normality
‫ﻗﻴﻤﺔ‬ ‫أن‬Sig.‫اآﺒﺮ‬ ‫اﻟﺤﺎﻻت‬ ‫ﺟﻤﻴﻊ‬ ‫ﻓﻰ‬
‫ﻣﻦ‬0.05‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬
‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ان‬ ‫اﻟﻘﺎﺋﻞ‬
‫اﻟﺒﻴﺎﻧﻰ‬ ‫اﻟﺮﺳﻢ‬ ‫ﻣﻦ‬ ‫اﻳﻀﺎ‬ ‫ذﻟﻚ‬ ‫وﻳﺘﻀﺢ‬
‫اﻟﺘﺎﻟﻰ‬
Tests of Normality
.178 .197
.968 .915
7 9
7 9
.200* .200*
.883 .354
Data
Data
Data
Data
Data
Data
Kolmogorov-Smirnova
Shapiro-Wilk
Kolmogorov-Smirnova
Shapiro-Wilk
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
1.00 2.00
Factor
This is a lower bound of the true significance.*.
Lilliefors Significance Correctiona.
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 27 of 38

28. ‫اﻟﻤﻠﻒ‬ ‫ﻟﺒﻴﺎﻧﺎت‬ ‫اﻟﺘﻘﺴﻴﻢ‬ ‫اﻟﻐﺎء‬ ‫ﻳﺠﺐ‬indp_samples‫اﺧﺮى‬ ‫ﻋﻤﻠﻴﻪ‬ ‫اى‬ ‫اﺟﺮاء‬ ‫ﻗﺒﻞ‬
‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﻋﻠﻰ‬.
4-‫ﻣﺘﺠﺎﻧﺴﻪ؟‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﻣﻨﻬﺎ‬ ‫اﻟﻤﺨﺘﺎر‬ ‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫هﻞ‬
1-‫ﻗﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Analyze‫ﻧﺨﺘﺎر‬Compare Means
2-‫ﻧﺨﺘﺎر‬ ‫اﻟﻤﻨﺴﺪﻟﻪ‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Independent Sample T Test
3-‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﻧﻨﻘﻞ‬Data‫ﻟﺨﺎﻧﺔ‬Test variable(s)
4-‫اﻟﻤﺘﻐﻴﺮ‬ ‫ﻧﻨﻘﻞ‬Factor‫ﻟﺨﺎﻧﺔ‬Grouping Variable:
5-‫ﻋﻠﻰ‬ ‫ﻧﻀﻐﻂ‬Define Groups‫اﻟﻤﺠﻤﻮﻋﺎت‬ ‫ﻟﺘﺤﺪﻳﺪ‬
6-‫اﻟﺮﻗﻢ‬ ‫ﺗﻜﺘﺐ‬ ‫ﺟﺪﻳﺪة‬ ‫ﺷﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬1‫اﻷوﻟﻰ‬ ‫ﻟﻠﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻤﻴﺰ‬
‫واﻟﺮﻗﻢ‬2‫ﻧﺨﺘﺎر‬ ‫ﺛﻢ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫ﻟﻠﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻤﻴﺰ‬Continue
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 28 of 38

29. 7-‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻀﻐﻂ‬Option‫اﻟﺜﻘﺔ‬ ‫ﻓﺘﺮة‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﻴﻬﺎ‬ ‫ﻧﺤﺪد‬ ‫ﺟﺪﻳﺪة‬ ‫ﺷﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬ ‫ﺳﻮف‬(1-
α)100%‫ﺑﺎﺳﺘﻤﺮار‬ ‫وﺳﺘﻜﻮن‬95%‫اﻟﻤﻌﻨﻮﻳﻪ‬ ‫ﻣﺴﺘﻮى‬ ‫ان‬ ‫اى‬α =0.05
‫اﻟﻤﻔﻘﻮدة‬ ‫اﻟﻘﻴﻢ‬ ‫ﻣﻊ‬ ‫اﻟﺘﻌﺎﻣﻞ‬ ‫آﻴﻔﻴﺔ‬ ‫واﻳﻀﺎ‬.
8-‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻀﻐﻂ‬Continue‫ﺛﻢ‬Ok‫اﻟﺘﺎﻟﻴﻪ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻈﻬﺮ‬
‫اﻷول‬ ‫اﻟﺠﺪول‬:
‫اﻟﻤﻌﻴﺎرى‬ ‫واﻟﺨﻄﺄ‬ ‫اﻟﻤﻌﻴﺎرى‬ ‫واﻻﻧﺤﺮاف‬ ‫واﻟﻮﺳﻂ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫ﺣﺠﻢ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬‫ﻋﻴﻨﻪ‬ ‫ﻟﻜﻞ‬
Group Statistics
7 14.7143 3.14718 1.18952
9 13.0000 5.52268 1.84089
Factor
1.00
2.00
Data
N Mean Std. Deviation
Std. Error
Mean
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 29 of 38

30. ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺠﺪول‬:‫واﺧﺘﺒﺎر‬ ‫اﻟﺘﺠﺎﻧﺲ‬ ‫اﺧﺘﺒﺎرى‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬T
.1‫اﻟﻤﺘﻐﻴﺮ‬ ‫اﺳﻢ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻷول‬ ‫اﻟﻌﻤﻮد‬Data
.2‫ﻗﻴﻤﺔ‬ ‫ان‬ ‫وﺣﻴﺚ‬ ‫اﻟﺘﺠﺎﻧﺲ‬ ‫اﺧﺘﺒﺎر‬ ‫ﻻﺟﺮاء‬ ‫ﻳﺴﺎرا‬ ‫واﻟﺜﺎﻟﺚ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻌﻤﻮد‬Sig. = 0.053‫ﻓﻬﻰ‬
‫ﻣﻦ‬ ‫اآﺒﺮ‬0.05‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫وهﻮﺗﺠﺎﻧﺲ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬
.3‫اﺧﺘﺒﺎر‬ ‫ﻻﺟﺮاء‬ ‫واﻟﺴﺎدس‬ ‫واﻟﺨﺎﻣﺲ‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﻌﻤﻮد‬T‫ﻧﻬﺘﻢ‬ ‫ﺳﻮف‬ ‫ﻣﺘﺠﺎﻧﺴﻪ‬ ‫اﻟﻤﺠﺘﻤﻌﺎت‬ ‫ان‬ ‫وﺣﻴﺚ‬
‫اﻟﺴﺎدس‬ ‫اﻟﻌﻤﻮد‬ ‫وﻣﻦ‬ ‫اﻷول‬ ‫ﺑﺎﻟﺼﻒ‬Sig. = 0.477‫ﻣﻦ‬ ‫اآﺒﺮ‬ ‫وهﻰ‬0.025‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬
‫ﻣﺴﺘﻮى‬ ‫ﺑﻴﻦ‬ ‫ﻓﺮق‬ ‫ﻳﻮﺟﺪ‬ ‫ﻻ‬ ‫أى‬ ‫ﻣﺘﺴﺎوى‬ ‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫وﺳﻄﻰ‬ ‫ان‬ ‫وهﻮ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬‫ﻓﻰ‬ ‫اﻟﻄﻼب‬
‫اﻟﻤﺠﻤﻮﻋﺘﻴﻦ‬.
.4‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﻣﺘﻮﺳﻄﻰ‬ ‫ﺑﻴﻦ‬ ‫ﻟﻠﻔﺮق‬ ‫اﻟﺜﻘﺔ‬ ‫ﻓﺘﺮة‬ ‫ﺗﻘﺪم‬ ‫اﻻﺧﻴﺮة‬ ‫اﻻﻋﻤﺪﻩ‬.
Independent Samples Test
4.481 .053 .731 14 .477 1.71429 2.34614 -3.31768 6.74626
.782 13.043 .448 1.71429 2.19177 -3.01915 6.44772
Equal variances
assumed
Equal variances
not assumed
Data
F Sig.
Levene's Test for
Equality of Variances
t df Sig. (2-tailed)
Mean
Difference
Std. Error
Difference Lower Upper
95% Confidence
Interval of the
Difference
t-test for Equality of Means
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 30 of 38

31. SPSS for Beginners: Lesson 6SPSS for Beginners: Lesson 6
‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬ ‫ﻏﻴﺮ‬ ‫اﺧﺘﺒﺎرﻋﻴﻨﺘﻴﻦ‬‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬ ‫ﻏﻴﺮ‬ ‫اﺧﺘﺒﺎرﻋﻴﻨﺘﻴﻦ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 31 of 38

32. ‫ﻣﺴﺘﻘﻠﺘﻴﻦ‬ ‫ﻏﻴﺮ‬ ‫ﻋﻴﻨﺘﻴﻦ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ﻳﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫ذﻟﻚ‬ ‫ﻳﺴﺘﺨﺪم‬
،‫ﻗﺮاﺋﺘﻴﻦ‬ ‫اﻟﻌﻴﻨﻪ‬ ‫ﻣﻔﺮدات‬ ‫ﻣﻦ‬ ‫ﻣﻔﺮدﻩ‬ ‫وﻟﻜﻞ‬ ‫واﺣﺪﻩ‬ ‫ﻋﻴﻨﺔ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ان‬ ‫ﺑﻤﻌﻨﻰ‬‫ﺗﻤﺜﻞ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻘﺮاءﻩ‬
‫اﻟﺜﺎﻧﻴﻪ‬ ‫اﻟﻌﻴﻨﺔ‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫واﻟﻘﺮاءﻩ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻌﻴﻨﺔ‬.
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺸﺮوط‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫اﻻﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﻗﺒﻞ‬ ‫وﻳﺠﺐ‬
1-‫ﻣﺴﺘﻘﻠﻪ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﻴﻨﺎت‬
2-‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫اﻟﻤﻔﺮدات‬ ‫ﻋﺪد‬30
3-‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﻌﻴﻨﺎت‬
‫ﻣﻦ‬ ‫اآﺒﺮ‬ ‫اﻟﻤﻔﺮدات‬ ‫ﻋﺪد‬ ‫آﺎن‬ ‫اذا‬30‫اﻟﺜﺎﻟﺚ‬ ‫ﺑﺎﻟﺸﺮط‬ ‫ﻧﻬﺘﻢ‬ ‫ﻟﻦ‬ ‫ﻓﺎﻧﻨﺎ‬.
‫ﺗﻤﺮﻳﻦ‬‫ﺗﻤﺮﻳﻦ‬::
‫ﻣﻦ‬ ‫ﻣﻜﻮﻧﻪ‬ ‫ﻋﻴﻨﻪ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ان‬ ‫ﺑﻔﺮض‬10‫ﺑﻌﺪ‬ ‫ﺛﻢ‬ ‫اﻟﻌﻴﻨﻪ‬ ‫ﻓﻰ‬ ‫ﺷﺨﺺ‬ ‫ﻟﻜﻞ‬ ‫اﻟﺪم‬ ‫ﺿﻐﻂ‬ ‫ﻗﻴﺎس‬ ‫ﺗﻢ‬ ‫اﺷﺨﺎص‬
‫ﺛﺎﻧﻴﺔ‬ ‫ﻣﺮﻩ‬ ‫اﻟﺪم‬ ‫ﺿﻐﻂ‬ ‫ﻗﻴﺎس‬ ‫ﺗﻢ‬ ‫زﻣﻨﻴﻪ‬ ‫ﻓﺘﺮة‬‫آﺎﻟﺘﺎﻟﻰ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫وآﺎﻧﺖ‬ ‫اﻷﺷﺨﺎص‬ ‫ﻟﻨﻔﺲ‬
140110120110110130150130140120After
150120110135145140130150140130Before
10987654321Id
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 32 of 38

33. ‫اﻟﺰﻣﻨﻴﻪ‬ ‫اﻟﻔﺘﺮة‬ ‫ﺗﻠﻚ‬ ‫وﺑﻌﺪ‬ ‫ﻗﺒﻞ‬ ‫اﻟﺪم‬ ‫ﺿﻐﻂ‬ ‫ﺑﻴﻦ‬ ‫ﻣﻌﻨﻮى‬ ‫ﻓﺮق‬ ‫ﻳﻮﺟﺪ‬ ‫هﻞ‬.
‫اﻟﺤﻞ‬:‫اﻟﺘﺎﻟﻴﻪ‬ ‫اﻻﺣﺼﺎﺋﻴﺔ‬ ‫اﻟﻔﺮوض‬ ‫اﺧﺘﺒﺎر‬ ‫ﻳﺠﺐ‬ ‫اﻟﺴﺆال‬ ‫هﺬا‬ ‫ﻋﻠﻰ‬ ‫ﻟﻸﺟﺎﺑﻪ‬
‫ﻣﺘﻐﻴﺮﻳﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫وﺑﺈدﺧﺎل‬Before‫واﻟﻤﺘﻐﻴﺮ‬ ‫اﻟﺰﻣﻨﻴﻪ‬ ‫اﻟﻔﺘﺮﻩ‬ ‫ﻗﺒﻞ‬ ‫ﻟﻠﻘﺮاءات‬After
‫اﻟﺰﻣﻨﻴﻪ‬ ‫اﻟﻔﺘﺮﻩ‬ ‫ﺑﻌﺪ‬ ‫ﻟﻠﻘﺮاءات‬.‫اﻟﺸﺮوط‬ ‫ﺑﻌﺾ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﺛﻢ‬
1-‫اﻟ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻘﺮاءات‬ ‫ﻣﺠﺘﻤﻊ‬ ‫ﻣﻦ‬ ‫ﻋﻴﻨﻪ‬ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺰﻣﻨﻴﻪ‬ ‫اﻟﻔﺘﺮﻩ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻘﺮاءات‬‫ﺗﻠﻚ‬ ‫ﺑﻌﺪ‬ ‫واﻟﻘﺮاءات‬ ‫ﻔﺘﺮة‬
‫اﻟ‬ ‫وﺗﻠﻚ‬ ‫اﻟﺰﻣﻨﻴﺔ‬ ‫اﻟﻔﺘﺮة‬ ‫ﺑﻌﺪ‬ ‫اﻟﻘﺮاءات‬ ‫ﻣﺠﺘﻤﻊ‬ ‫ﻣﻦ‬ ‫اﺧﺮى‬ ‫ﻋﻴﻨﻪ‬ ‫هﻰ‬ ‫اﻟﻔﺘﺮﻩ‬‫ﻣﺴﺘﻘﻠﻪ‬ ‫ﻏﻴﺮ‬ ‫ﻌﻴﻨﺎت‬
‫اﻷﺷﺨﺎص‬ ‫ﻟﻨﻔﺲ‬ ‫ﻷﻧﻬﺎ‬.
2-‫اﻟﻌﻴﻨﺎت‬ ‫ﺣﺠﻢ‬10‫ﻣﻦ‬ ‫أﻗﻞ‬30
3-‫ﻻ؟‬ ‫ام‬ ‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﻌﻴﻨﺎت‬ ‫هﻞ‬ ‫اﺧﺘﺒﺎر‬ ‫ﻳﻤﻜﻦ‬
‫ﻗﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Analyze‫ﻧﺨﺘﺎر‬Descriptive Statistics‫ﻧﺨﺘﺎر‬ ‫ﺛﻢ‬Explore
‫اﻟﻤﺘﻐﻴﺮات‬ ‫ﻧﻨﻘﻞ‬Before‫واﻳﻀﺎ‬After‫ﻟﺨﺎﻧﻪ‬Dependent List
AfterBeforeddd HH μμμμμ −=≠= ,0:,0: 10
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 33 of 38

34. ‫ﻋﻠﻰ‬ ‫وﺑﺎﻟﻀﻐﻂ‬Plots‫اﻻﺧﺘﻴﺎر‬ ‫وﺑﺘﺤﺪﻳﺪ‬Normality plots with tests‫اﻟﺘﺎﻟﻴﻪ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻈﻬﺮ‬ ‫ﺳﻮف‬
‫ﺑﻌﻨﻮان‬ ‫ﺟﺪول‬Tests of Normality‫ﻧﻔﺲ‬ ‫ﻋﻠﻰ‬ ‫وﻧﺤﺼﻞ‬ ‫اﻟﻄﺒﻴﻌﻰ‬ ‫اﻟﺘﻮزﻳﻊ‬ ‫ﻟﻬﺎ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ان‬ ‫ﻧﺠﺪ‬ ‫وﻣﻨﻪ‬
‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺒﻴﺎﻧﻰ‬ ‫اﻟﺮﺳﻢ‬ ‫ﻣﻦ‬ ‫اﻟﻨﺘﻴﺠﻪ‬
Tests of Normality
.151 10 .200* .936 10 .505
.168 10 .200* .908 10 .268
Before
After
Statistic df Sig. Statistic df Sig.
Kolmogorov-Smirnov
a
Shapiro-Wilk
This is a lower bound of the true significance.*.
Lilliefors Significance Correctiona.
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 34 of 38

35. ‫اﺧﺘﺒﺎر‬ ‫اﺟﺮاء‬ ‫ﻧﺴﺘﻄﻴﻊ‬ ‫ﺳﺒﻖ‬ ‫ﻣﻤﺎ‬T‫ﻳﻠﻰ‬ ‫آﻤﺎ‬:
.1‫ﻗﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Analyze‫ﻧﺨﺘﺎر‬Compare Means
.2‫ﻧﺨﺘﺎر‬ ‫اﻟﻤﻨﺴﺪﻟﻪ‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫ﻣﻦ‬Paired Samples t
Test
.3‫ﺑﻌﻨﻮان‬ ‫ﺟﺪﻳﺪﻩ‬ ‫ﺷﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬Paired Samples T
Test‫اﻟﻤﺘﻐﻴﺮﻳﻦ‬ ‫ﻧﻨﻘﻞ‬After, Before‫ﻣﻌﺎ‬
‫ﻟﻘﺎﺋﻤﺔ‬Paired Variables
.4‫اﻻﺧﺘﻴﺎر‬ ‫ﻋﻠﻰ‬ ‫ﻧﻀﻐﻂ‬Option‫ﻓﻴﻬﺎ‬ ‫ﻧﺤﺪد‬ ‫ﺷﺎﺷﺔ‬ ‫ﺗﻈﻬﺮ‬
‫اﻟﻤﻔﻘﻮدﻩ‬ ‫اﻟﻘﻴﻢ‬ ‫ﻣﻊ‬ ‫اﻟﺘﻌﺎﻣﻞ‬ ‫وآﻴﻔﻴﺔ‬ ‫اﻟﻤﻌﻨﻮﻳﻪ‬ ‫ﻣﺴﺘﻮى‬.
.5‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻀﻐﻂ‬Continue‫اﻟﺴﺎﺑﻘﻪ‬ ‫ﻟﻠﺸﺎﺷﺔ‬ ‫ﻧﻌﻮد‬
‫ﻧﺨﺘﺎر‬Ok‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻈﻬﺮ‬
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 35 of 38

36. ‫اﻟﻨﺘﺎﺋﺞ‬‫اﻟﻨﺘﺎﺋﺞ‬OutputOutput
‫اﻷول‬ ‫اﻟﺠﺪول‬‫اﻷول‬ ‫اﻟﺠﺪول‬:‫ﺑﻌﻨﻮان‬Paired Samples Statistics
‫اﻟﻤ‬ ‫واﻟﺨﻄﺄ‬ ‫اﻟﻤﻌﻴﺎرى‬ ‫واﻻﻧﺤﺮاف‬ ‫اﻟﻘﻴﻢ‬ ‫وﻋﺪد‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬‫ﻋﻴﻨﻪ‬ ‫ﻟﻜﻞ‬ ‫ﻌﻴﺎرى‬
‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺠﺪول‬‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺠﺪول‬:‫ﺑﻌﻨﻮان‬Paired Samples Correlations
‫ﻗﻴﻤﺔ‬ ‫واﻳﻀﺎ‬ ‫اﻟﻤﺘﻐﻴﺮﻳﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻻرﺗﺒﺎط‬ ‫وﻣﻌﺎﻣﻞ‬ ‫اﻟﻘﻴﻢ‬ ‫ﻋﺪد‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬Sig. =0.398‫ﻣﻌﻨﻮﻳﻪ‬ ‫ﻻﺧﺘﺒﺎر‬
‫ﻣﻦ‬ ‫اآﺒﺮ‬ ‫وﻗﻴﻤﺘﻬﺎ‬ ‫اﻻرﺗﺒﺎط‬ ‫ﻣﻌﺎﻣﻞ‬0.05‫ﺑﻴﻦ‬ ‫ارﺗﺒﺎط‬ ‫وﺟﻮد‬ ‫ﻋﺪم‬ ‫وهﻮ‬ ‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬ ‫ﻟﺬا‬
‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﻋﻨﺎﺻﺮ‬)‫ﻟﻼرﺗﺒﺎط‬ ‫ﻣﻌﻨﻮﻳﺔ‬ ‫ﻳﻮﺟﺪ‬ ‫ﻻ‬.(
Paired Samples Statistics
135.0000 10 12.90994 4.08248
126.0000 10 14.29841 4.52155
Before
After
Pair
1
Mean N Std. Deviation
Std. Error
Mean
Paired Samples Correlations
10 .301 .398Before & AfterPair 1
N Correlation Sig.
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 36 of 38

37. ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺠﺪول‬‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺠﺪول‬:‫ﺑﻌﻨﻮان‬Paired Samples Test
.1‫اﻟﻘﺮاءات‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮق‬ ‫وهﻮ‬ ‫اﻟﺠﺪﻳﺪ‬ ‫اﻟﻤﺘﻐﻴﺮ‬ ‫اﺳﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻷول‬ ‫اﻟﻌﻤﻮد‬ ‫ﻳﺤﺘﻮى‬‫اﻟﺰﻣﻨﻴﻪ‬ ‫اﻟﻔﺘﺮة‬ ‫وﺑﻌﺪ‬ ‫ﻗﺒﻞ‬
(d=Before-After)
.2‫اﻟﻘﺮاءات‬ ‫ﺑﻴﻦ‬ ‫ﻟﻠﻔﺮوق‬ ‫اﻟﺤﺴﺎﺑﻰ‬ ‫اﻟﻮﺳﻂ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻌﻤﻮد‬ ‫ﻳﺤﺘﻮى‬
.3‫ﻗﺒﻞ‬ ‫اﻟﻘﺮاءات‬ ‫ﺑﻴﻦ‬ ‫ﻟﻠﻔﺮوق‬ ‫اﻟﻤﻌﻴﺎر‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﻌﻤﻮد‬‫اﻟﺰﻣﻨﻴﻪ‬ ‫اﻟﻔﺘﺮﻩ‬ ‫وﺑﻌﺪ‬
.4‫ﻟﻠﻔﺮوق‬ ‫اﻟﻤﻌﻴﺎرى‬ ‫اﻟﺨﻄﺎ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﻌﻤﻮد‬
.5‫ﻓﺘﺮة‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻟﺨﺎﻣﺲ‬ ‫اﻟﻌﻤﻮد‬95%‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﻣﺘﻮﺳﻄﻰ‬ ‫ﺑﻴﻦ‬ ‫ﻟﻠﻔﺮق‬ ‫ﺛﻘﻪ‬
.6‫اﻻﺧﺘﺒﺎر‬ ‫اﺣﺼﺎء‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻟﺴﺎدس‬ ‫اﻟﻌﻤﻮد‬T‫اﻟﺴﺎﺑﻊ‬ ‫اﻟﻌﻤﻮد‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻳﺔ‬ ‫ودرﺟﺔ‬
(n-1=9)
.7‫ﻋﻠﻰ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻻﺧﻴﺮ‬ ‫اﻟﻌﻤﻮد‬Sig. = 0.111‫ﻻﺧﺘﺒﺎر‬T‫ﻣﻦ‬ ‫اآﺒﺮ‬ ‫وهﻰ‬α/2=0.025‫ﻟﺬا‬
‫اﻟﻌﺪم‬ ‫ﻓﺮض‬ ‫ﻧﻘﺒﻞ‬ ‫ﺳﻮف‬:‫اﻟﺒﺪﻳﻞ‬ ‫اﻟﻔﺮض‬ ‫وﻧﺮﻓﺾ‬ ‫ﻣﺘﺴﺎوى‬ ‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬ ‫ﻣﺘﻮﺳﻄﻰ‬ ‫اﻧﻪ‬:‫ﻣﺘﻮﺳﻄﻰ‬
‫ﻣﺨﺘﻠﻒ‬ ‫اﻟﻤﺠﺘﻤﻌﻴﻦ‬.
Paired Samples Test
9.00000 16.12452 5.09902 -2.53478 20.53478 1.765 9 .111Before - AfterPair 1
Mean Std. Deviation
Std. Error
Mean Lower Upper
95% Confidence
Interval of the
Difference
Paired Differences
t df Sig. (2-tailed)
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 37 of 38

38. ‫وﺑﺮآﺎﺗﻪ‬ ‫اﷲ‬ ‫ورﺣﻤﺔ‬ ‫ﻋﻠﻴﻜﻢ‬ ‫اﻟﺴﻼم‬‫وﺑﺮآﺎﺗﻪ‬ ‫اﷲ‬ ‫ورﺣﻤﺔ‬ ‫ﻋﻠﻴﻜﻢ‬ ‫اﻟﺴﻼم‬
Dr. A. MustafaDr. A. Mustafa
amelsayed@mans.edu.egamelsayed@mans.edu.eg
Lesson 006. By Dr. Abdelfatah Mustafa. Math. Department, Faculty of Science, Mnasoura University, Egypt. Page 38 of 38