This document discusses statistical hypothesis testing and statistical inferences. It notes that statistical hypothesis testing is one of the most important applications of probability theory in statistics. This allows researchers to make decisions about accepting or rejecting hypotheses based on sample data. The process of decision making through hypothesis testing involves multiple steps, including drawing a representative sample, collecting relevant data, applying statistical rules to test hypotheses, and making a decision based on results. Statistical inferences aim to estimate unknown population parameters through sampling and probability theory plays a key role in this process and in decision making more broadly.

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