]Œ^ŠÖ]<Ø’ËÖ ]°ÃÛj¥<êŞ‰çjÚ<°e<íÞ…^Ϲ Comparing the Averages of Two Populations
.1 .6ﻣﻘﺪﻣﺔ .2 .6اﻟﻄﺮق اﻟﻤﻌﻠﻤﻴﺔ :اﺧﺘﺒﺎرات t .1 .2 .6ﻓﺮوض وﺷﺮوط اﺳﺘﺨﺪام اﺧﺘﺒﺎرات t .2 .2 .6اﺧﺘﺒﺎرات tﻓﻲ ﺣﺎﻟﺔ اﻟﻌﻴﻨﺘﻴﻦ اﻟﻤﺮﺗﺒﻄﺘﻴﻦ .3 .2 .6اﺧﺘﺒﺎرات tﻓﻲ ﺣﺎﻟﺔ اﻟﻌﻴﻨﺘﻴﻦ اﻟﻤﺴﺘﻘﻠﺘﻴﻦ .3 .6اﻟﻄﺮق اﻟﻼﻣﻌﻠﻤﻴﺔ .1 .3 .6ﺣﺎﻟﺔ اﻟﻌﻴﻨﺎت اﻟﻤﺮﺗﺒﻄﺔ اﺧﺘﺒﺎرات وﻳﻠﻜﻮآﺴﻦ واﻹﺷﺎرة وﻣﻜﻨﻤﺎر .2 .3 .6ﺣﺎﻟﺔ اﻟﻌﻴﻨﺎت اﻟﻤﺴﺘﻘﻠﺔ :اﺧﺘﺒﺎر ﻣﺎن وﻳﺘﻨﻲ .4 .6ﺗﻄﺒﻴﻘﺎت .1 .4 .6ﺣﺎﻟﺔ اﻻﺧﺘﺒﺎرات اﻟﻤﺘﻌﻠﻘﺔ ﺑﻌﻴﻨﺔ واﺣﺪة .2 .4 .6اﺧﺘﺒﺎر اﻟﻔﺮﺿﻴﺎت اﻟﻤﺘﻌﻠﻘﺔ ﺑﻨﺴﺐ اﻟﺤﺪوث
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
218
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
219
]Œ^ŠÖ]<Ø’ËÖ ]°ÃÛj¥<êŞ‰çjÚ<°e<íÞ…^Ϲ Comparing the averages of two populations .1 .6ﻣﻘﺪﻣﺔ: ﻟﻨﻔﺭﺽ ﺃﻨﻪ ﺘﻡ ﺇﺠﺭﺍﺀ ﺃﺤﺩ ﺍﻟﺘﺠﺎﺭﺏ ﺍﻟﺘﻲ ﺘﻡ ﺒﻬﺎ ﻗﻴﺎﺱ ﻤﺴﺘﻭﻯ ﺇﻨﺠﺎﺯ
ﻤﺠﻤﻭﻋﺘﻴﻥ ﻤﻥ ﺍﻷﻓﺭﺍﺩ ﻟﻤﻬﻤﺔ ﻤﻌﻴﻨﺔ ﺘﺤﺕ ﺘﺄﺜﻴﺭ ﻤﺠﻤﻭﻋﺘﻴﻥ ﻤﺨﺘﻠﻔﺘﻴﻥ ﻤﻥ ﺍﻟﺸﺭﻭﻁ،
ﺃﻭ ﺒﺸﻜل ﺃﺩﻕ ﻓﻲ ﻅل ﺸﺭﻁﻴﻥ ﻤﺨﺘﻠﻔﻴﻥ ﻭﺒﺘﺜﺒﻴﺕ ﺍﻟﺸﺭﻭﻁ ﺍﻷﺨﺭﻯ ،ﻓﻌﻠﻰ ﺴﺒﻴل ﺍﻟﻤﺜﺎل ﻴﻤﻜﻥ ﺃﻥ ﺘﻜﻭﻥ ﻫﺫﻩ ﺍﻟﻤﻬﻤﺔ ﻫﻲ ﺤﻔﻅ ﺴﻭﺭﺓ ﻤﻥ ﺍﻟﻘﺭﺁﻥ ﺍﻟﻜﺭﻴﻡ ﺃﻭ ﻗﺼﻴﺩﺓ
ﺸﻌﺭﻴﺔ ،ﻭﻴﻜﻭﻥ ﺍﻟﻐﺭﺽ ﻤﻥ ﺍﻟﺘﺠﺭﺒﺔ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻫﻭ ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺠﻤﻭﻋﺘﻲ ﺍﻷﻓﺭﺍﺩ ﻤﻥ ﻨﺎﺤﻴﺔ ﻗﺩﺭﺘﻬﻡ ﻋﻠﻰ ﻗﺭﺍﺀﺓ ﺘﻠﻙ ﺍﻟﻘﻁﻌﺔ ﻋﻥ ﻅﻬﺭ ﻗﻠﺏ ﺒﺩﻗﺔ ،ﻋﻠﻤﹰﺎ ﺒﺄﻥ
ﻫﺎﺘﻴﻥ ﺍﻟﻤﺠﻤﻭﻋﺘﻴﻥ ﻤﻥ ﺍﻷﻓﺭﺍﺩ ﻗﺩ ﺘﺩﺭﺒﺘﺎ ﻋﻠﻰ ﺍﻟﺘﺤﻔﻴﻅ ﺒﻁﺭﻴﻘﺘﻴﻥ ﻤﺨﺘﻠﻔﺘﻴﻥ ،ﻭﻋﻨﺩ
ﺍﻟﻨﻅﺭ ﺇﻟﻰ ﺩﺭﺠﺎﺕ ﻜل ﻤﻥ ﺍﻟﻤﺠﻭﻋﺘﻴﻥ ﻓﻲ ﺍﺨﺘﺒﺎﺭ ﺍﻟﺤﻔﻅ ﻓﺈﻨﻨﺎ ﻓﻲ ﺍﻟﻐﺎﻟﺏ ﻭﻤﻥ
ﺍﻟﻁﺒﻴﻌﻲ ﺃﻥ ﻨﺠﺩ ﺃﻥ ﻫﻨﺎﻙ ﺍﺨﺘﻼﻑ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﺩﺭﺠﺎﺕ ﻓﻲ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﻭﻟﻜﻥ ﻫﺫﺍ
ﺍﻻﺨﺘﻼﻑ ﻗﺩ ﻴﻌﻭﺩ ﺇﻟﻰ ﺍﻟﻌﺸﻭﺍﺌﻴﺔ ﻷﻥ ﺍﻟﺘﺠﺭﺒﺔ ﺃﺠﺭﻴﺕ ﻋﻠﻰ ﺃﻓﺭﺍﺩ ﻤﺨﺘﻠﻔﻴﻥ ﺍﺨﺘﻴﺭﻭﺍ
ﺒﻁﺭﻴﻘﺔ ﻋﺸﻭﺍﺌﻴﺔ ،ﻭﻟﺫﻟﻙ ﻓﻨﺤﻥ ﺒﺤﺎﺠﺔ ﺇﻟﻰ ﺍﺨﺘﺒﺎﺭ ﺇﺤﺼﺎﺌﻲ ﻟﻠﺠﺯﻡ ﺒﺄﻥ ﻫﺫﺍ ﺍﻻﺨﺘﻼﻑ ﺤﻘﻴﻘﻴﹰﺎ ﻭﻟﻴﺱ ﻅﺎﻫﺭﻴﹰﺎ ﻭﻴﻌﻭﺩ ﺒﺎﻟﺘﺎﻟﻲ ﺇﻟﻰ ﺍﺨﺘﻼﻑ ﺤﻘﻴﻘﻲ ﺒﻴﻥ ﻁﺭﻴﻘﺘﻲ ﺍﻟﺘﻌﻠﻴﻡ.
ﻭﻴﺴﺘﺨﺩﻡ ﻓﻲ ﻤﺜل ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻓﻲ ﺍﻟﻌﺎﺩﺓ ﺍﺨﺘﺒﺎﺭ tﻻﺨﺘﺒﺎﺭ ﻤﺩﻯ ﻤﻌﻨﻭﻴﺔ )ﺩﻻﻟﺔ(
ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﻴﻥ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﺍﻟﺫﻴﻥ ﺍﺨﺘﻴﺭ ﻤﻨﻬﻤﺎ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﺃﻱ ﻫل ﺘﺩل
ﺍﻟﻤﻌﻁﻴﺎﺕ ﺍﻟﻤﺘﺎﺤﺔ ﻤﻥ ﻫﺫﻩ ﺍﻟﺘﺠﺭﺒﺔ ﻋﻠﻰ ﺃﻨﻪ ﻓﻲ ﺍﻟﺤﺎﻟﺔ )ﺍﻻﻓﺘﺭﺍﻀﻴﺔ( ﻟﻭ ﺘﻡ ﺘﺩﺭﻴﺏ
ﺍﻟﻤﺠﺘﻤﻊ ﺒﺄﺴﺭﻩ ﺒﺄﻱ ﻤﻥ ﺍﻟﻁﺭﻴﻘﺘﻴﻥ ﺴﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻓﺭﻕ ﺒﻴﻥ ﺩﺭﺠﺎﺕ ﻤﻥ ﺘﺩﺭﺒﻭﺍ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻷﻭﻟﻰ ﻋﻥ ﺃﻭﻟﺌﻙ ﺍﻟﺫﻴﻥ ﺘﺩﺭﺒﻭﺍ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﺜﺎﻨﻴﺔ؟ ﺃﻱ ﺃﻥ ﻓﺭﻀﻴﺔ ﻫﺫﻩ
ﺍﻟﺘﺠﺭﺒﺔ ﺴﺘﻜﻭﻥ ﺃﺤﺩ ﺍﻟﻁﺭﻴﻘﺘﻴﻥ ﺃﻓﻀل ﻤﻥ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻷﺨﺭﻯ ﻓﻲ ﻗﺩﺭﺘﻬﺎ ﻋﻠﻰ ﺘﺤﻔﻴﻅ
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
220
ﺍﻷﻓﺭﺍﺩ ﺒﺩﻗﺔ ،ﻭﺭﻏﻡ ﺫﻟﻙ ﻓﺈﻨﻪ ﻓﻲ ﻓﻠﺴﻔﺔ ﺍﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻔﺭﻭﺽ ﺍﻹﺤﺼﺎﺌﻴﺔ ﻋﺎﺩﺓ ﻤﺎ ﺘﻜﻭﻥ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻤﺭﺍﺩ ﺍﺨﺘﺒﺎﺭﻫﺎ ﻟﻴﺴﺕ ﻓﺭﻀﻴﺔ ﺍﻟﺘﺠﺭﺒﺔ ﺒل ﻋﻜﺴﻬﺎ ﻭﺘﺴﻤﻰ ﻓﻲ ﻫﺫﻩ
ﺍﻟﺤﺎﻟﺔ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ Null Hypothesisﻭﻴﺭﻤﺯ ﻟﻬﺎ ﺒﺎﻟﺭﻤﺯ ، H0ﻭﻓﻲ ﻫﺫﺍ
ﺍﻟﻤﺜﺎل ﻴﻤﻜﻥ ﺼﻴﺎﻏﺔ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﻋﻠﻰ ﺃﻨﻬﺎ :ﻻ ﻴﻭﺠﺩ ﻓﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ
ﺍﻟﺩﺭﺠﺎﺕ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﺍﻟﺫﻴﻥ ﺴﺤﺒﺘﺎ ﻤﻨﻬﻤﺎ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﻭﺇﺫﺍ ﺘﻤﻜﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻥ ﺭﻓﺽ
ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﻓﺈﻨﻨﺎ ﺴﻭﻑ ﻨﺴﺘﻨﺘﺞ ﺃﻥ ﻓﺭﻀﻴﺔ ﺍﻟﺘﺠﺭﺒﺔ ﺼﺤﻴﺤﺔ ،ﺃﻱ ﺒﺘﻌﺒﻴﺭ
ﺇﺤﺼﺎﺌﻲ ﺘﻜﻭﻥ ﻤﺎ ﺘﻌﺭﻑ ﺒﺎﻟﻔﺭﻀﻴﺔ ﺍﻟﺒﺩﻴﻠﺔ ﺼﺤﻴﺤﺔ.
ﺇﻥ ﺇﻨﺠﺎﺯ ﺃﻱ ﺍﺨﺘﺒﺎﺭ ﺇﺤﺼﺎﺌﻲ ﻴﺘﻁﻠﺏ ﻤﻌﺭﻓﺔ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ )ﺃﻭ ﻤﺎ ﻴﺴﻤﻰ
ﻫﻨﺎ ﺒﺘﻭﺯﻴﻊ ﺍﻟﻤﻌﺎﻴﻨﺔ( ﻟﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ،ﻭﻫﺫﻩ ﺍﻟﺩﺍﻟﺔ ﻫﻲ ﺍﻟﻘﺎﻋﺩﺓ ﺍﻟﺘﻲ ﻴﺘﻡ ﺤﺴﺎﺒﻬﺎ ﻤﻥ
ﺒﻴﻨﺎﺕ ﺍﻟﻌﻴﻨﺎﺕ ﻭﺘﺭﻓﺽ ﺃﻭ ﺘﻘﺒل ﻋﻠﻰ ﺃﺴﺎﺴﻬﺎ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ، H0ﻭﺘﻌﺭﻑ ﻗﻴﻤﺔ p
ﺍﻟﻤﻌﺭﻭﻓﺔ ﺒﺘﻌﺒﻴﺭ p-valueﻷﻱ ﺩﺍﻟﺔ ﺍﺨﺘﺒﺎﺭ ) tﺃﻭ Fﺃﻭ ﺃﻱ ﺩﺍﻟﺔ ﺃﺨﺭﻯ( ﻋﻠﻰ ﺃﻨﻬﺎ ﺍﺤﺘﻤﺎل ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﻗﻴﻤﺔ ﻜﺒﻴﺭﺓ ﻭﻤﺴﺎﻭﻴﺔ ﻋﻠﻰ ﺍﻷﻗل ﺘﻠﻙ ﺍﻟﻘﻴﻤﺔ ﺍﻟﺘﻲ ﺤﺼﻠﻨﺎ ﻋﻠﻴﻬﺎ
ﺒﺎﻟﻔﻌل ﻤﻥ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻌﻴﻨﺎﺕ ﻭﺫﻟﻙ ﻓﻲ ﺼﺤﺔ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ، H0ﻓﺈﺫﺍ ﻜﺎﻨﺕ ﻗﻴﻤﺔ p-valueﺍﻟﺘﻲ ﺤﺼﻠﻨﺎ ﻋﻠﻴﻬﺎ ﺼﻐﻴﺭﺓ ﻓﺈﻥ ﺫﻟﻙ ﻴﺅﺨﺫ ﻋﻠﻰ ﺃﻨﻪ ﺩﻟﻴل ﻜﺎﻓﻲ ﻟﺭﻓﺽ ﺘﻠﻙ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ، H0ﻭﺫﻟﻙ ﻷﻨﻪ ﻤﻥ ﺍﻟﻤﺴﺘﺒﻌﺩ ﺃﻥ ﻨﺤﺼل ﻋﻠﻰ ﻗﻴﻤﺔ ﻜﺒﻴﺭﺓ ﺒﻬﺫﺍ
ﺍﻟﻘﺩﺭ ﻟﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻨﺘﻴﺠﺔ ﻓﻘﻁ ﻟﻠﻌﺸﻭﺍﺌﻴﺔ ﺇﻻ ﺒﺎﺤﺘﻤﺎل ﻀﺌﻴل ﺠﺩﹰﺍ ،ﻭﻟﺫﻟﻙ ﻓﺈﻨﻨﺎ
ﻨﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻗﻴﻤﺔ p-valueﺼﻐﻴﺭﺓ ﻭﺃﺼﻐﺭ ﻤﻥ ﻗﻴﻤﺔ
ﺍﻓﺘﺭﺍﻀﻴﺔ ﻭﻤﺤﺩﺩﺓ ﺴﻠﻔ ﹰﺎ ﻭﺘﻌﺭﻑ ﺒﻤﺴﺘﻭﻯ ﺍﻟﻤﻌﻨﻭﻴﺔ ﺃﻭ ﻤﺴﺘﻭﻯ ﺍﻟﺩﻻﻟﺔ Significance
، Levelﻭﻓﻲ ﺍﻟﻌﺎﺩﺓ ﺘﺄﺨﺫ ﻗﻴﻤﺔ ﻤﺴﺘﻭﻯ ﺍﻟﻤﻌﻨﻭﻴﺔ ﻋﻠﻰ ﺃﻨﻬﺎ ﻤﺴﺎﻭﻴﺔ 0.05ﺃﻭ 0.01 ﺃﻭ ﻗﻴﻤﺔ ﻤﻘﺎﺭﺒﺔ ﺘﻌﺘﻤﺩ ﻋﻠﻰ ﻤﺩﻯ ﺍﻟﺩﻗﺔ ﺍﻟﻤﻁﻠﻭﺒﺔ ،ﻭﻫﺫﺍ ﻴﺨﺘﻠﻑ ﺤﺴﺏ ﻁﺒﻴﻌﺔ ﺍﻟﻤﺸﻜﻠﺔ ﻤﻭﻀﻭﻉ ﺍﻟﺩﺭﺍﺴﺔ ،ﻭﺒﻬﺫﺍ ﻓﺈﻨﻪ ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻗﻴﻤﺔ p-valueﺃﺼﻐﺭ ﻤﻥ ﻤﺴﺘﻭﻯ
ﺍﻟﻤﻌﻨﻭﻴﺔ ﻓﺈﻨﻪ ﻴﻘﺎل ﺃﻥ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻴﺔ ﺃﻭ ﺫﺍﺕ ﺩﻻﻟﺔ . Significant
ﺇﺫﺍ ﻜﺎﻨﺕ ﻗﻴﻤﺔ p-valueﺃﻜﺒﺭ ﻤﻥ ﻤﺴﺘﻭﻯ ﺍﻟﻤﻌﻨﻭﻴﺔ ﻓﺈﻨﻨﺎ ﻨﻘﺒل ﺍﻟﻔﺭﻀﻴﺔ
ﺍﻟﻌﺩﻤﻴﺔ H0ﺃﻭ ﺒﻤﻌﻨﻰ ﺃﺩﻕ ﻻ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺩﻟﻴل ﻜﺎﻓﻲ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻟﺭﻓﺽ ﺘﻠﻙ
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
221
ﺍﻟﻔﺭﻀﻴﺔ ،ﺃﻱ ﺍﻟﻤﻌﻨﻰ ﺍﻟﺩﻗﻴﻕ ﻟﺫﻟﻙ ﺃﻨﻪ ﻓﺸل ﺍﻻﺨﺘﺒﺎﺭ ﻓﻲ ﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﺃﻭ ﻻ ﻴﻭﺠﺩ ﻫﻨﺎﻙ ﺩﻟﻴل ﻜﺎﻓﻲ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻟﺭﻓﺽ ﺘﻠﻙ ﺍﻟﻔﺭﻀﻴﺔ. ﺨﻼﺼﺔ ﻤﺎ ﺴﺒﻕ ﺃﻥ: .1ﺇﺫﺍ ﻜﺎﻨﺕ ﻗﻴﻤﺔ p-valueﺃﻜﺒﺭ ﻤﻥ 0.05ﻓﺈﻨﻨﺎ ﻨﻘﺒل ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0
ﻭﺘﻜﻭﻥ ﺍﻟﻨﺘﻴﺠﺔ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻏﻴﺭ ﻤﻌﻨﻭﻱ . not significant
.2ﺇﺫﺍ ﻜﺎﻨﺕ ﻗﻴﻤﺔ p-valueﺃﻗل ﻤﻥ 0.05ﻓﺈﻨﻨﺎ ﻨﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ
H0ﻭﺘﻜﻭﻥ ﺍﻟﻨﺘﻴﺠﺔ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ significantﻭﺫﻟﻙ ﺒﻤﺴﺘﻭﻯ
ﻤﻌﻨﻭﻴﺔ .0.05 .3ﺇﺫﺍ ﻜﺎﻨﺕ ﻗﻴﻤﺔ p-valueﺃﻗل ﻤﻥ 0.01ﻓﺈﻨﻨﺎ ﻨﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ
H0ﻭﺘﻜﻭﻥ ﺍﻟﻨﺘﻴﺠﺔ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ significantﻭﺫﻟﻙ ﺒﻤﺴﺘﻭﻯ
ﻤﻌﻨﻭﻴﺔ .0.01
ﻭﻓﻲ ﻫﺫﺍ ﺍﻟﻜﺘﺎﺏ ﺴﻨﻔﺘﺭﺽ ﺃﻥ ﺍﻟﻘﺎﺭﺉ ﻟﺩﻴﻪ ﺒﻌﺽ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﻋﻥ ﺍﺴﺘﺨﺩﺍﻡ
ﺍﺨﺘﺒﺎﺭﺍﺕ ، tﻭﺇﺫﺍ ﻟﻡ ﻴﻜﻥ ﻟﺩﻴﻙ ﺃﻱ ﻤﻌﻠﻭﻤﺎﺕ ﻋﻨﻬﺎ ﺃﻭ ﻟﻤﺯﻴﺩ ﻤﻥ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﻨﻨﺼﺤﻙ ﺒﻘﺭﺍﺀﺓ ﺍﻷﺠﺯﺍﺀ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺘﻠﻙ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻓﻲ ﺃﺤﺩ ﻜﺘﺏ ﺍﻹﺤﺼﺎﺀ ﻭﻤﻨﻬﺎ ﻋﻠﻰ ﺴﺒﻴل
ﺍﻟﻤﺜﺎل ﻜﺘﺎﺏ "ﺍﻹﺤﺼﺎﺀ ﺍﻟﺘﻁﺒﻴﻘﻲ" ﻟﻠﻤﺅﻟﻑ ،ﺍﻟﻁﺒﻌﺔ ﺍﻟﺜﺎﻨﻴﺔ ﻟﻌﺎﻡ ، 2001ﻓﻔﻲ ﺍﻟﻌﻴﻨﺎﺕ
ﺍﻟﻤﺴﺘﻘﻠﺔ ﺘﺤﺴﺏ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ tﻋﻠﻰ ﺃﻨﻬﺎ ﻨﺎﺘﺞ ﻗﺴﻤﺔ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻌﻴﻨﺘﻴﻥ
ﻋﻠﻰ ﺘﻘﺩﻴﺭ ﺍﻟﺨﻁﺄ ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﻭﻓﻲ ﺤﺎﻟﺔ ﻤﺎ ﺇﺫﺍ ﻜﺎﻥ
ﺘﺒﺎﻴﻨﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﻤﺘﺴﺎﻭﻴﻴﻥ ﻓﺈﻨﻪ ﻋﺎﺩﺓ ﻴﻘﺩﺭ ﺍﻟﺘﺒﺎﻴﻥ ﺍﻟﻤﺸﺘﺭﻙ ﻟﻠﻤﺠﺘﻤﻌﻴﻥ ﻤﻥ ﺒﻴﺎﻨﺎﺕ
ﺍﻟﻌﻴﻨﺘﻴﻥ ﺒﺩﻤﺠﻬﻤﺎ ﻤﻌﹰﺎ ،ﻭﻗﻴﻤﺔ p-valueﺍﻟﻤﺼﺎﺤﺒﺔ ﻻﺨﺘﺒﺎﺭ tﺘﻌﺘﻤﺩ ﻋﻠﻰ ﻤﺎ ﻴﻌﺭﻑ ﺒﺩﺭﺠﺎﺕ ﺍﻟﺤﺭﻴﺔ ﻟﻠﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ﻭﺍﻟﺘﻲ ﺒﺩﻭﺭﻫﺎ ﺘﻌﺘﻤﺩ ﻋﻠﻰ ﻋﺩﺩ ﻤﻔﺭﺩﺍﺕ ﺍﻟﻌﻴﻨﺘﻴﻥ.
ﻻ ﺒﺎﻟﻘﻭﺍﺌﻡ ﻭﺍﻷﻭﺍﻤﺭ ﺍﻟﻤﺘﺎﺤﺔ ﻓﻲ ﻨﻅﺎﻡ SPSS ﻭﺸﻜل 1-6ﺃﺩﻨﺎﻩ ﻴﻭﻀﺢ ﺠﺩﻭ ﹰ
ﻭﺫﻟﻙ ﻟﻠﺤﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ ،ﺤﻴﺙ ﻴﻭﻀﺢ ﺍﻟﺼﻔﻴﻥ ﺍﻷﻭل ﻭﺍﻟﺜﺎﻨﻲ ﻓﻲ ﺍﻟﺠﺩﻭل ﺤﺎﻟﺔ ﺍﻟﻔﺭﻭﺽ ﺤﻭل ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ﻟﻠﺒﻴﺎﻨﺎﺕ ﻓﻲ
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
222
ﺤﺎﻻﺕ ﺍﻟﻌﻴﻨﺘﻴﻥ ﺍﻟﻤﺴﺘﻘﻠﺘﻴﻥ ﻭﺍﻟﻌﻴﻨﺘﻴﻥ ﺍﻟﻤﺭﺘﺒﻁﺘﻴﻥ ﺒﻴﻨﻤﺎ ﻴﻭﻀﺢ ﺍﻟﺼﻑ ﺍﻟﺜﺎﻟﺙ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﻤﻨﺎﺴﺒﺔ ﻟﻠﺤﺎﻟﺔ ﻓﻲ ﻨﻅﺎﻡ SPSSﺘﺤﺕ ﻗﺎﺌﻤﺔ ﺍﻹﺤﺼﺎﺀﺍﺕ ) Statisticsﺃﻭ ﺍﻟﺘﺤﻠﻴل
(Analysisﻭﻴﻭﻀﺢ ﺍﻟﺼﻑ ﺍﻟﺭﺍﺒﻊ ﺍﻷﻤﺭ ﺍﻟﻤﻨﺎﺴﺏ ﻓﻲ ﺘﻠﻙ ﺍﻟﻘﺎﺌﻤﺔ.
ﺸﻜل : -6ﻗﻭﺍﺌﻡ ﻭﺃﻭﺍﻤﺭ ﻨﻅﺎﻡ SPSSﻟﻠﺤﺎﻻﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ
ﻋﻨﺩﻤﺎ ﻻ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺃﻱ ﺍﻓﺘﺭﺍﺽ ﺤﻭل
ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻤﻥ ﻤﺠﺘﻤﻌﻴﻥ ﻟﻬﻤﺎ
ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ﻟﻠﺒﻴﺎﻨﺎﺕ
ﺘﻭﺯﻴﻊ ﻁﺒﻴﻌﻲ ﻭﺘﺒﺎﻴﻨﻬﻤﺎ ﻤﺘﺴﺎﻭﻱ
ﺤﺎﻟﺔ ﻋﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ
ﺤﺎﻟﺔ ﻋﻴﻨﺘﻴﻥ ﻤﺴﺘﻘﻠﺘﻴﻥ
Non-Parametric Non-Parametric Tests Tests 2 Paired Samples
2 Independent Samples
ﺤﺎﻟﺔ ﻋﻴﻨﺘﻴﻥ
ﺤﺎﻟﺔ ﺍﻟﻌﻴﻨﺎﺕ
Compare Means
Compare Means
Paired Samples t-test
Independent Samples t-test
ﻤﺭﺘﺒﻁﺘﻴﻥ
ﺍﻟﻤﺴﺘﻘﻠﺔ
ﻭﻴﺒﻴﻥ ﺍﻟﺸﻜل ﺍﻟﺴﺎﺒﻕ ﺃﻥ ﺍﻟﻨﺼﻑ ﺍﻷﻴﺴﺭ ﻤﻥ ﺍﻟﺠﺩﻭل ﻴﺘﻌﻠﻕ ﺒﺎﻻﺨﺘﺒﺎﺭﺍﺕ
ﺍﻟﻤﻌﻠﻤﻴﺔ ) Parametric Testsﺃﻱ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻓﺭﻭﺽ ﺘﺘﻌﻠﻕ ﺒﺎﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ﻟﻠﻤﺠﺘﻤﻌﺎﺕ ﺍﻟﺘﻲ ﺴﺤﺒﺕ ﻤﻨﻬﺎ ﺍﻟﻌﻴﻨﺎﺕ( ﺒﻴﻨﻤﺎ ﻴﺘﻌﻠﻕ ﻨﺼﻑ ﺍﻟﺠﺩﻭل ﺍﻷﻴﻤﻥ
ﺒﺎﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ) Non-Parametric Testsﺃﻱ ﺤﺎﻟﺔ ﻋﺩﻡ ﻭﺠﻭﺩ ﺘﻠﻙ
ﺍﻟﻔﺭﻭﺽ ﺤﻭل ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ﻟﻠﻤﺠﺘﻤﻌﺎﺕ( ،ﻭﻓﻲ ﻜل ﻤﻥ ﺍﻟﻨﻭﻋﻴﻥ ﻫﻨﺎﻙ ﺤﺎﻻﺕ ﻋﻴﻨﺎﺕ ﻤﺴﺘﻘﻠﺔ Independent Samplesﻭﺤﺎﻻﺕ ﻋﻴﻨﺎﺕ ﻤﺭﺘﺒﻁﺔ
Paired
) Samplesﺃﻭ Related Samplesﻓﻲ ﺤﺎﻟﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ( ،ﻭﺴﻭﻑ ﻨﺘﺤﺩﺙ ﻓﻲ ﺍﻷﻗﺴﺎﻡ ﺍﻟﻼﺤﻘﺔ ﻤﻥ ﻫﺫﺍ ﺍﻟﻔﺼل ﻋﻥ ﻜل ﻤﻥ ﻫﺫﻩ ﺍﻟﺤﺎﻻﺕ ﺒﺎﻟﺘﻔﺼﻴل.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
223
.2 .6اﻟﻄﺮق اﻟﻤﻌﻠﻤﻴﺔ :اﺧﺘﺒﺎرات : t Parametric methods : the t-tests: .1 .2 .6ﻓﺮوض وﺷﺮوط اﺳﺘﺨﺪام اﺧﺘﺒﺎرات : t ﺍﻟﻨﻤﻭﺫﺝ ﺍﻻﺤﺘﻤﺎﻟﻲ ﺍﻟﺫﻱ ﺍﺸﺘﻘﺕ ﻤﻨﻪ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻴﻔﺘﺭﺽ ﺃﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺘﻤﺜل
ﻋﻴﻨﺔ ﻋﺸﻭﺍﺌﻴﺔ ﺍﺨﺘﻴﺭﺕ ﻤﻥ ﻤﺠﺘﻤﻊ ﻴﺘﺒﻊ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ ﺒﺘﺒﺎﻴﻥ ﺜﺎﺒﺕ ،ﻭﻟﻜﻥ ﻋﻠﻰ ﺍﻟﺭﻏﻡ ﻤﻥ ﺫﻟﻙ ﺃﺜﺒﺘﺕ ﻁﺭﻕ ﺍﻟﻤﺤﺎﻜﺎﺓ ﺃﻨﻪ ﺤﺘﻰ ﻓﻲ ﺤﺎﻻﺕ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﻲ ﺘﺨﺘﺭﻕ ﻫﺫﺍ
ﺍﻟﺸﺭﻁ ﺍﺨﺘﺭﺍﻕ ﻁﻔﻴﻑ ﻴﻤﻜﻥ ﺃﻴﻀﹰﺎ ﺍﺴﺘﺨﺩﺍﻡ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻭﻟﻜﻥ ﺒﺸﺭﻁ ﺃﻻ ﺘﻜﻭﻥ ﺍﻟﻌﻴﻨﺎﺕ ﺼﻐﻴﺭﺓ ﺍﻟﺤﺠﻡ ﻭﻻ ﺘﺤﺘﻭﻱ ﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﺸﺎﺫﺓ ﺃﻭ ﻤﺘﻁﺭﻓﺔ ﻭﺤﺠﻤﻲ ﺍﻟﻌﻴﻨﺘﻴﻥ
ﻤﺘﺴﺎﻭﻴﻴﻥ ،ﻭﺇﺫﺍ ﺘﺒﻴﻥ ﻤﻥ ﺍﺴﺘﻜﺸﺎﻑ ﺍﻟﺒﻴﺎﻨﺎﺕ )ﺒﺎﻟﻁﺭﻕ ﺍﻟﺘﻲ ﺘﻡ ﺘﻭﻀﻴﺤﻬﺎ ﻓﻲ ﺍﻟﻔﺼﻭل
ﺍﻟﺴﺎﺒﻘﺔ( ﺃﻥ ﻫﻨﺎﻙ ﺍﺨﺘﺭﺍﻕ ﻜﺒﻴﺭ ﻟﺘﻙ ﺍﻟﺸﺭﻭﻁ ﻓﺈﻥ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻟﻥ ﺘﻜﻭﻥ ﻗﻭﻴﺔ ﻓﻲ ﻤﺜل
ﻫﺫﻩ ﺍﻟﺤﺎﻻﺕ ،ﻭﻴﻨﺼﺢ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭﺍﺕ ﻻﻤﻌﻠﻤﻴﺔ ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ
ﺍﻟﺘﻲ ﺴﻴﺘﻡ ﺘﻭﻀﻴﺤﻬﺎ ﻓﻲ ﺍﻟﻘﺴﻡ ﺍﻟﺘﺎﻟﻲ ،ﻭﻓﻲ ﺒﻌﺽ ﺍﻟﺤﺎﻻﺕ ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺍﻟﺘﻐﻠﺏ ﻋﻠﻰ
ﺘﻠﻙ ﺍﻟﻤﺸﻜﻠﺔ ﺒﻤﺠﺭﺩ ﺍﺴﺘﺒﻌﺎﺩ ﺘﻠﻙ ﺍﻟﻘﻴﻡ ﺍﻟﺸﺎﺫﺓ ﻤﻥ ﺍﻟﻘﻴﻡ ﺜﻡ ﺘﻁﺒﻴﻕ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻋﻠﻰ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺘﺒﻘﻴﺔ.
.2 .2 .6اﺧﺘﺒﺎرات tﻓﻲ ﺣﺎﻟﺔ اﻟﻌﻴﻨﺘﻴﻦ اﻟﻤﺮﺗﺒﻄﺘﻴﻦ : The paired samples t-tests : ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻟﺩﻴﻨﺎ ﺘﺠﺭﺒﺔ ﺘﻡ ﺘﻁﺒﻴﻘﻬﺎ ﻋﻠﻰ ﻨﻔﺱ ﺍﻟﻤﻔﺭﺩﺍﺕ ﻤﺭﺘﻴﻥ ﻓﻲ ﻅﺭﻓﻴﻥ ﺃﻭ ﺸﺭﻁﻴﻥ ﻤﺨﺘﻠﻔﻴﻥ ﻓﺈﻥ ﺍﻟﻘﻴﺎﺴﺎﺕ ﺍﻟﻤﺄﺨﻭﺫﺓ ﻓﻲ ﺍﻟﺤﺎﻟﺘﻴﻥ ﺴﺘﻨﺘﺞ ﻋﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ
Paired samplesﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﺤﻴﺙ ﺃﻥ ﺍﻟﺘﺠﺭﺒﺔ ﺘﻜﺭﺭﺕ ﻋﻠﻰ ﻨﻔﺱ ﺍﻟﻤﻔﺭﺩﺍﺕ ﻓﺈﻥ ﺤﺠﻤﻲ ﺍﻟﻌﻴﻨﺘﻴﻥ ﺴﻴﻜﻭﻥ ﺜﺎﺒﺕ ﻭﺴﻴﻘﺎﺒل ﻜل ﻗﻴﻤﺔ ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﻗﻴﻤﺔ ﻟﻨﻔﺱ ﺍﻟﻤﻔﺭﺩﺓ
ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ،ﻜﺫﻟﻙ ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺃﻥ ﺘﻜﻭﻥ ﺍﻟﻌﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ ﺇﺫﺍ ﻁﺒﻘﺕ ﺍﻟﺘﺠﺭﺒﺔ
ﻋﻠﻰ ﺃﺯﻭﺍﺝ ﻟﻬﺎ ﻨﻔﺱ ﺍﻟﺨﺼﺎﺌﺹ ﻤﻥ ﺍﻟﻤﻔﺭﺩﺍﺕ ﺃﻭ ﺘﺭﺒﻁ ﺒﻴﻨﻬﻤﺎ ﻋﻼﻗﺔ ﻤﺎ ﻜﺄﻥ ﻴﻜﻭﻥ ﺍﻟﻤﻔﺭﺩﺍﺕ ﻋﺒﺎﺭﺓ ﻋﻥ ﺃﺯﻭﺍﺝ ﻤﻥ ﺍﻷﺨﻭﺓ ﺍﻟﺘﻭﺍﺌﻡ ﺃﻭ ﺍﻟﺯﻭﺝ ﻭﺯﻭﺠﺘﻪ ﻭﻤﺎ ﺇﻟﻰ ﺫﻟﻙ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
224
ﻭﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻟﺩﻴﻨﺎ ﻋﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ ﺒﻬﺫﺍ ﺍﻟﺸﻜل ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ t
ﺍﻟﺨﺎﺹ ﺒﺎﻟﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired samples t-testﻭﺫﻟﻙ ﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻴﺔ ﺍﻟﻔﺭﻕ
ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﺍﻟﺫﻴﻥ ﺴﺤﺒﺘﺎ ﻤﻨﻬﻤﺎ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﻴﻤﻜﻥ ﺍﻟﻭﺼﻭل
ﺇﻟﻴﻪ ﻤﻥ ﺨﻼل ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ) Analysisﺃﻭ ﺍﻹﺤﺼﺎﺀ Statisticsﻓﻲ ﺇﺼﺩﺍﺭ (8.0 ﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﻭﺍﺨﺘﻴﺎﺭ ﺃﻤﺭ ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ Compare meansﻤﻥ ﺘﻠﻙ ﺍﻟﻘﺎﺌﻤﺔ ،ﻭﻟﻜﻥ ﻫﺫﺍ ﻓﻲ ﺍﻟﺒﺩﺍﻴﺔ ﻴﺴﺘﺩﻋﻲ ﺘﺠﻬﻴﺯ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻟﻜﻲ ﺘﻜﻭﻥ ﻤﺨﺯﻨﺔ ﺒﺎﻟﺼﻭﺭﺓ ﺍﻟﺘﺎﻟﻴﺔ :
ﻟﻨﻔﺭﺽ ﺃﻨﻪ ﺘﻡ ﺇﺠﺭﺍﺀ ﺘﺠﺭﺒﺔ ﻋﻠﻰ ﻋﻴﻨﺔ ﻤﻜﻭﻨﺔ ﻤﻥ ﻋﺸﺭﺓ ﻤﻥ ﺍﻷﻁﻔﺎل ﺒﻬﺩﻑ
ﺍﺨﺘﺒﺎﺭ ﻓﺭﻀﻴﺔ ﺃﻥ ﻤﻭﻀﻊ ﺍﻟﻜﻠﻤﺔ ﺴﻭﺍﺀ ﻋﻠﻰ ﻴﻤﻴﻥ ﺃﻭ ﻋﻠﻰ ﻴﺴﺎﺭ ﺸﺎﺸﺔ ﺍﻟﺤﺎﺴﻭﺏ ﻟﻪ
ﺘﺄﺜﻴﺭ ﻋﻠﻰ ﻗﺩﺭﺓ ﺍﻷﻁﻔﺎل ﻋﻠﻰ ﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ﻓﻲ ﺍﻟﺸﺎﺸﺔ ،ﻭﺃﻋﻁﻲ ﻜل ﻤﻥ ﺍﻷﻁﻔﺎل ﺍﻟﻌﺸﺭﺓ ﻋﺩﺩﹰﺍ ﻤﺘﺴﺎﻭﻴﹰﺎ ﻤﻥ ﺍﻟﻜﻠﻤﺎﺕ ﻋﻠﻰ ﻜل ﻤﻥ ﻴﻤﻴﻥ ﻭﻴﺴﺎﺭ ﺸﺎﺸﺔ ﺍﻟﺤﺎﺴﻭﺏ ،ﻭﺘﻡ
ﻗﻴﺎﺱ ﺍﻟﻭﻗﺕ ﺍﻟﻼﺯﻡ ﻟﻸﻁﻔﺎل ﻟﺘﻤﻴﻴﺯ ﺘﻠﻙ ﺍﻟﻜﻠﻤﺎﺕ ﺒﺄﻋﺸﺎﺭ ﺍﻟﺜﺎﻨﻴﺔ ﻭﺇﻋﻁﺎﺀ ﻜل ﻤﻨﻬﻡ
ﺩﺭﺠﺔ ﻟﻠﻴﻤﻴﻥ ﻭﺩﺭﺠﺔ ﻟﻠﻴﺴﺎﺭ ﻋﻠﻰ ﺃﺴﺎﺱ ﺃﻨﻬﺎ ﻭﺴﻴﻁ ﺍﻟﻔﺘﺭﺍﺕ ﺍﻟﺯﻤﻨﻴﺔ ﺍﻟﻤﺴﺘﻐﺭﻗﺔ ﻤﻥ
ﻜل ﻁﻔل ﻟﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ،ﻓﺘﻜﻭﻥ ﻟﺩﻴﻨﺎ ﻤﺘﻐﻴﺭﻴﻥ ﻜل ﻤﺘﻐﻴﺭ ﻤﻜﻭﻥ ﻤﻥ 10ﻗﻴﻡ
)ﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﺭﻗﻡ ﺍﻟﻁﻔل( ،ﻭﻻﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ tﺍﻟﺨﺎﺹ ﺒﺎﻟﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired
samples t-testﻭﺫﻟﻙ ﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻴﺔ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﺩﺭﺠﺎﺕ ﻓﻲ ﻤﺠﺘﻤﻌﻲ ﺍﻷﻁﻔﺎل ﺍﻟﺫﻴﻥ ﻴﺘﻌﺭﻀﻭﻥ ﻻﺨﺘﺒﺎﺭ ﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ﻋﻠﻰ ﻜل ﻤﻥ ﻴﻤﻴﻥ ﻭﻴﺴﺎﺭ ﺸﺎﺸﺔ
ﺍﻟﺤﺎﺴﻭﺏ ﻻﺒﺩ ﻤﻥ ﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﻟﻠﺤﺎﺴﻭﺏ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data Editor
ﻓﻲ ﻨﻅﺎﻡ SPSSﻋﻠﻰ ﺸﻜل ﻤﺘﻐﻴﺭﻴﻥ )ﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﻤﺘﻐﻴﺭ ﻟﻠﺭﻗﻡ ﺍﻟﻤﺴﻠﺴل( ﻟﺘﻅﻬﺭ ﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻋﻠﻰ ﺍﻟﺸﺎﺸﺔ ﻜﻤﺎ ﻓﻲ ﺸﻜل 2-6ﺃﺩﻨﺎﻩ .
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
225
ﺸﻜل : 2-6ﺼﻭﺭﺓ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻜﻤﺎ ﺩﺨﻠﺕ ﻟﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﻨﻅﺎﻡ . SPSS Paired data: Median word recognition time in milliseconds for words in the left and right visual fields. Subject
Right Field
Left Field
304
323
1
493
512
2
2
491
502
3
3
365
385
4
4
426
453
3
5
320
343
6
6
523
543
7
7
442
440
8
8
580
682
9
9
564
590
10
10
10
10
10
N
1
Total
ﻭﻟﺘﻔﺤﺹ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻗﺒل ﺇﺠﺭﺍﺀ ﺍﺨﺘﺒﺎﺭ tﺍﻟﻤﻨﺎﺴﺏ ﻴﺤﺴﻥ ﺘﻤﺜﻴل ﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ
ﻫﻨﺩﺴﻴﹰﺎ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ،ﻭﻴﻤﻜﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻟﻬﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ
ﻤﻥ ﺨﻼل ﺃﻤﺭ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatter..ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ ﻜﻤﺎ ﺘﻡ
ﺘﻭﻀﻴﺤﻪ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺴﺎﺒﻕ ﻟﻨﺼل ﺇﻟﻰ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻓﻲ ﺸﻜل 3-6ﺃﺩﻨﺎﻩ .
ﻭﻤﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﻴﺘﻀﺢ ﺃﻨﻪ ﻻ ﻴﻭﺠﺩ ﺃﻱ ﻗﻴﻡ ﻴﻤﻜﻥ ﺃﻥ ﺘﺼﻨﻑ ﻋﻠﻰ ﺃﻨﻬﺎ ﺸﺎﺫﺓ
، outlierﻭﻴﺠﺏ ﺍﻟﻤﻼﺤﻅﺔ ﻫﻨﺎ ﺃﻥ ﻭﺠﻭﺩ ﺃﺤﺩ ﺍﻟﻘﻴﻡ ﻤﻥ ﺒﻴﻥ ﻗﻴﻡ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﻌﺸﺭﺓ
ﺸﺎﺫﺓ ﻴﻤﻜﻥ ﺃﻥ ﻴﻜﻭﻥ ﻟﻪ ﺘﺄﺜﻴﺭ ﺴﻴﺊ ﻋﻠﻰ ﻨﺘﻴﺠﺔ ﺍﻻﺨﺘﺒﺎﺭ ،ﻓﻬﺫﻩ ﺍﻟﻘﻴﻤﺔ ﺴﻭﻑ ﺘﺠﻌل ﺍﻟﺘﺒﺎﻴﻥ ﻜﺒﻴﺭ ﻭﺒﺎﻟﺘﺎﻟﻲ ﺴﻭﻑ ﺘﺠﻌل ﻗﻴﻤﺔ ﻤﻘﺎﻡ ﺩﺍﻟﺔ tﻜﺒﻴﺭﺓ ،ﺃﻱ ﺃﻨﻬﺎ ﺴﻭﻑ ﺘﺠﻌل
ﺍﻟﺩﺍﻟﺔ ﺼﻐﻴﺭﺓ ،ﻭﻫﺫﺍ ﺴﻭﻑ ﻴﻘﻠل ﻤﻥ ﺍﺤﺘﻤﺎل ﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ،ﺃﻱ ﺃﻨﻪ ﺴﻭﻑ ﻴﻘﻠل ﻤﻥ ﻓﺭﺼﺔ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺍﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
226
ﺸﻜل : 3-6ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻟﻤﺘﻐﻴﺭﻱ ﻭﺴﻴﻁ ﺍﻟﻭﻗﺕ ﻟﻼﺯﻡ ﻟﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ﻋﻠﻰ ﻴﺴﺎﺭ ﻭﻋﻠﻰ ﻴﻤﻴﻥ ﺍﻟﺸﺎﺸﺔ ﻟﻌﺸﺭﺓ ﻤﻥ ﺍﻷﻁﻔﺎل ﺍﻟﺫﻴﻥ ﺘﻌﺭﻀﻭﺍ ﻟﻠﺘﺠﺭﺒﺔ
Median word recognition times in millisecond for words in the left and rightvisual fields Left Field
700
600
500
400
300 600
500
400
300
200
Right Field
ﻋﻨﺩ ﻭﺠﻭﺩ ﺃﻱ ﻤﻥ ﺍﻟﻘﻴﻡ ﺍﻟﺸﺎﺫﺓ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﺈﻥ ﺍﻟﻤﺴﺘﺨﺩﻡ ﻴﻤﻜﻨﻪ ﺃﻥ ﻴﺨﺘﺎﺭ ﺇﻤﺎ
ﺍﺴﺘﺒﻌﺎﺩ ﺘﻠﻙ ﺍﻟﻘﻴﻤﺔ ﻤﻥ ﺒﻴﻥ ﺍﻟﻘﻴﻡ )ﻭﻫﺫﺍ ﺍﻟﺨﻴﺎﺭ ﻏﻴﺭ ﻤﺤﺒﺫ ﺨﺎﺼﺔ ﻓﻲ ﺍﻟﻌﻴﻨﺎﺕ
ﺍﻟﺼﻐﻴﺭﺓ ﺒﻬﺫﺍ ﺍﻟﺤﺠﻡ( ﺃﻭ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ ﺁﺨﺭ ﻻ ﻤﻌﻠﻤﻲ ﻤﺜل ﺍﺨﺘﺒﺎﺭ ﺍﻹﺸﺎﺭﺓ Sign
testﺃﻭ ﺍﺨﺘﺒﺎﺭ ﻭﻴﻠﻜﻭﻜﺴﻥ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ، Wilcoxon matched pairs test
ﻓﻬﺫﻴﻥ ﺍﻻﺨﺘﺒﺎﺭﻴﻥ ﺃﻜﺜﺭ ﻗﺩﺭﺓ ﻋﻠﻰ ﺘﺠﻨﺏ ﺁﺜﺎﺭ ﺍﻟﻘﻴﻡ ﺍﻟﻤﺘﻁﺭﻓﺔ ﻋﻠﻰ ﻨﺘﻴﺠﺔ ﺍﻻﺨﺘﺒﺎﺭ،
ﻭﻟﻜﻥ ﻓﻲ ﺤﺎﻟﺔ ﻋﺩﻡ ﻭﺠﻭﺩ ﺃﻱ ﻤﻭﺍﻨﻊ ﻤﻥ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ tﻓﺈﻨﻪ ﻴﻔﻀل ﺍﺴﺘﺨﺩﺍﻤﻪ،
ﺤﻴﺙ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﻌﻠﻤﻴﺔ ﺩﺍﺌﻤﹰﺎ ﻟﻬﺎ ﻗﻭﺓ ﺍﺨﺘﺒﺎﺭ ﺃﻜﺒﺭ ﻤﻥ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
227
ﻭﻴﻤﻜﻥ ﺘﻨﻔﻴﺫ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﺒﺈﺠﺭﺍﺀ ﺍﻟﺨﻁﻭﺍﺕ ﺍﻟﺘﺎﻟﻴﺔ: • ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ) Analyzeﺃﻭ Statisticsﻓﻲ ﺇﺼﺩﺍﺭ (8.0 ﺍﺨﺘﺭ ﺃﻤﺭ ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ Compare Meansﻭﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺠﺎﻨﺒﻴﺔ
ﺍﺨﺘﺭ ﺃﻤﺭ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired-Samples T Testﻜﻤﺎ ﻓﻲ
ﺍﻟﺸﻜل 4-6ﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired-Samples T
، Testﻭﺘﺒﺩﻭ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻗﺩ ﺘﻤﺕ ﺘﻌﺒﺌﺔ ﺒﻴﺎﻨﺎﺘﻬﺎ ﻓﻲ ﺸﻜل 5-6ﺃﺩﻨﺎﻩ.
ﺸﻜل : 4-6ﻁﺭﻴﻘﺔ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﻤﻥ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ
ﺸﻜل : 5-6ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ .Paired-Samples T Test
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
•
228
ﻤﺒﺩﺌﻴ ﹰﺎ ﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired-Samples T Test
ﻭﺘﻜﻭﻥ ﻓﺎﺭﻏﺔ ﻤﻥ ﺍﻟﻤﻌﻁﻴﺎﺕ ﻭﺴﻭﻑ ﺘﻅﻬﺭ ﺃﺴﻤﺎﺀ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﻁﻠﻭﺒﺔ Left
fieldﻭ Right fieldﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻋﻠﻰ ﻴﺴﺎﺭ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ،ﻓﻘﻡ ﺒﺎﺨﺘﻴﺎﺭ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻷﻭل ﻭﺍﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺘﺤﻜﻡ Ctrlﻭﺍﺒﻕ ﻀﺎﻏﻁﹰﺎ ﻋﻠﻴﻪ
ﺇﻟﻰ ﺃﻥ ﺘﺨﺘﺎﺭ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺜﺎﻨﻲ ﻭﻴﺘﻡ ﺘﺤﺩﻴﺩ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ،ﺴﻴﺘﻡ ﻋﻨﺩﻫﺎ ﺇﻀﺎﺀﺓ ﺍﻟﺴﻬﻡ
ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﻤﻨﻰ
ﻹﺯﺍﺤﺔ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺇﻟﻰ ﺍﻟﻴﻤﻴﻥ ﻟﻴﺴﺘﻘﺭﺍ ﻤﺘﻘﺎﺒﻼﻥ ﻓﻲ
ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﺒﻬﻤﺎ ﺘﺤﺕ ﻋﻨﻭﺍﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺍﻟﻤﺭﺘﺒﻁﻴﻥ Paired Variables
ﻜﻤﺎ ﻫﻭ ﻤﻭﻀﺢ ﻓﻲ ﺍﻟﺸﻜل .5-6
• ﺍﻀﻐﻁ ﻋﻠﻰ ﻤﺭﺒﻊ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﻼﺴﺘﻤﺭﺍﺭ ﻓﻲ ﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ،ﻭﺴﺘﻅﻬﺭ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻤﺤﺭﺭ ﺍﻟﻨﺘﺎﺌﺞ ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل 6-6ﺃﺩﻨﺎﻩ.
ﻭﺤﻴﺙ ﺃﻨﻪ ﻴﻤﻜﻥ ﺇﺠﺭﺍﺀ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired-Samples T
Testﻋﻠﻰ ﻤﺠﻤﻭﻋﺔ ﻜﺒﻴﺭﺓ ﻤﻥ ﺃﺯﻭﺍﺝ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺃﻤﺭ ﻭﺍﺤﺩ ﻭﻤﻥ ﻨﻔﺱ ﺍﻟﻨﺎﻓﺫﺓ ﺍﻟﺴﺎﺒﻘﺔ ﻓﺈﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻻﺒﺩ ﺃﻥ ﺘﻭﻀﺢ ﻨﺘﺎﺌﺞ ﺍﻟﺘﻁﺒﻴﻕ ﻋﻠﻰ ﻜل ﺯﻭﺝ Pairﻋﻠﻰ
ﺤﺩﻩ ﻓﻲ ﻜل ﺠﺩﻭل ﻤﻥ ﺠﺩﺍﻭل ﺍﻟﻨﺘﺎﺌﺞ ،ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻻ ﻴﻭﺠﺩ ﺴﻭﻯ ﺯﻭﺝ ﻭﺍﺤﺩ ﻤﻥ
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ،ﻟﺫﻟﻙ ﻓﺈﻥ ﺍﻟﺠﺩﻭل ﺍﻷﻭل ﻓﻲ ﺍﻟﻨﺘﺎﺌﺞ
Paired Sample
Statisticsﻴﻭﻀﺢ ﻤﺠﻤﻭﻋﺔ ﺍﻹﺤﺼﺎﺀﺍﺕ ﺍﻟﺘﻲ ﺘﺘﻌﻠﻕ ﺒﻜل ﻤﺘﻐﻴﺭ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻋﻠﻰ ﺤﺩﻩ ،ﺒﻴﻨﻤﺎ ﻴﻭﻀﺢ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ Paired Samples Correlationsﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻭﻜﺫﻟﻙ ﻗﻴﻤﺔ p-valueﺍﻟﻨﺎﺘﺠﺔ ﻋﻥ ﺍﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ
ﺍﻟﻘﺎﺌﻠﺔ ﺒﻌﺩﻡ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺃﻱ ﺇﺫﺍ ﻜﺎﻨﺕ ﻫﺫﻩ ﺍﻟﻘﻴﻤﺔ ﺼﻐﻴﺭﺓ ﻓﺈﻥ ﻫﺫﻩ
ﺍﻟﻔﺭﻀﻴﺔ ﺴﺘﺭﻓﺽ ﺃﻱ ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﻤﺎ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻭﺘﻜﻭﻥ ﻓﻲ ﺍﻟﻌﺎﺩﺓ ﻗﻴﻤﺔ
ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﻜﺒﻴﺭﺓ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ،ﻭﻴﻭﻀﺢ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻟﺙ ﻭﺍﻷﺨﻴﺭ ﻓﻲ ﻜﺸﻑ
ﺍﻟﻨﺘﺎﺌﺞ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired-Samples Testﺍﻟﺨﺼﺎﺌﺹ ﺍﻻﺤﺘﻤﺎﻟﻴﺔ
ﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻌﻴﻨﺘﻴﻥ Paired Differencesﻭﻫﻲ 95%ﻓﺘﺭﺓ ﺜﻘﺔ ﻟﻠﻔﺭﻕ ﺒﻴﻥ
ﺍﻟﻤﺘﻭﺴﻁﻴﻥ ﻭﻜﺫﻟﻙ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ tﻭﻋﺩﺩ ﺩﺭﺠﺎﺕ ﺤﺭﻴﺘﻬﺎ dfﻭﻗﻴﻤﺔ p-value
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
229
ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﻬﺎ ﻭﺫﻟﻙ ﻋﻠﻰ ﺍﻓﺘﺭﺍﺽ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﺜﻨﺎﺌﻲ ﺍﻟﻁﺭﻑ ، 2-tailedﺒﻤﻌﻨﻰ ﺃﻥ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﺒﺩﻴﻠﺔ ﺘﺭﻓﺽ ﻓﻲ ﺍﻟﺤﺎﻟﺘﻴﻥ ﺴﻭﺍﺀ ﻜﺎﻥ ﻤﺘﻭﺴﻁ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻷﻭل ﺃﻜﺒﺭ ﻤﻥ ﻤﺘﻭﺴﻁ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺜﺎﻨﻲ ﺃﻭ ﻜﺎﻥ ﺃﺼﻐﺭ ﻤﻨﻪ ،ﻭﻴﻠﺯﻡ ﺃﻥ ﻴﻜﻭﻥ ﺍﻻﺨﺘﺒﺎﺭ ﺃﺤﺎﺩﻱ ﺍﻟﻁﺭﻑ
1-tailedﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﺍﻫﺘﻤﺎﻤﻨﺎ ﻋﻠﻰ ﺃﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻷﻭل ﺃﺼﻐﺭ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺜﺎﻨﻲ ﺒﺎﻟﺘﺤﺩﻴﺩ ﺃﻭ ﺃﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺜﺎﻨﻲ ﺃﺼﻐﺭ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻷﻭل ﻭﻟﻴﺱ ﺃﻱ ﻤﻥ ﺍﻟﺤﺎﻟﺘﻴﻥ.
ﺸﻜل : 6-6ﻜﺸﻑ ﻨﺘﺎﺌﺞ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﺘﺠﺭﺒﺔ ﻋﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ Listings of the results of Paired-Samples T Test Paired Samples Statistics Std. Error Mean
Std. Deviation
Mean
N
35.45
112.09
10
477.30
Left Field
30.70
97.09
10
450.80
Right Field
Pair 1
Paired Samples Correlations Correlation
Sig.
.975
.000
N Left Field & Right Field
10
Pair 1
Paired Samples Test
Paired Differences 95% Confidence Interval of the Difference
Sig. )(2-tailed
df
.015
9
t 3.013
Upper
Lower
Std. Error Mean
Std. Deviatio n
Mean
46.40
6.60
8.80
27.81
26.50
Left FieldRight Field
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
230
ﻴﻭﻀﺢ ﺸﻜل 6-6ﻨﺘﺎﺌﺞ ﺘﻁﺒﻴﻕ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired-
Samples T Testﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﻤﺜﺎﻟﻨﺎ ﺍﻟﺫﻱ ﻴﺘﻌﻠﻕ ﺒﺎﺨﺘﺒﺎﺭ ﻓﺭﻀﻴﺔ ﺃﻥ ﻤﻭﻀﻊ ﺍﻟﻜﻠﻤﺔ
ﺴﻭﺍﺀ ﻋﻠﻰ ﻴﻤﻴﻥ ﺃﻭ ﻋﻠﻰ ﻴﺴﺎﺭ ﺸﺎﺸﺔ ﺍﻟﺤﺎﺴﻭﺏ ﻟﻪ ﺘﺄﺜﻴﺭ ﻋﻠﻰ ﻗﺩﺭﺓ ﺍﻷﻁﻔﺎل ﻋﻠﻰ ﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ﻓﻲ ﺍﻟﺸﺎﺸﺔ ﺤﻴﺙ ﺘﻅﻬﺭ ﺒﻴﺎﻨﺎﺕ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻓﻲ ﺸﻜل ،2-6ﻭﻴﺒﻴﻥ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻓﻲ ﺍﻟﺸﻜل ﺃﻥ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻤﺴﺎﻭﻴﹰﺎ 0.975ﻭﻫﻲ
ﻗﻴﻤﺔ ﻤﻌﻨﻭﻴﺔ ﺇﻟﻰ ﺩﺭﺠﺔ ﻜﺒﻴﺭﺓ ﺒﺎﻟﻨﻅﺭ ﺇﻟﻰ ﻗﻴﻤﺔ p-valueﺍﻟﺘﻲ ﺘﻘﺘﺭﺏ ﻤﻥ ﺍﻟﺼﻔﺭ ﺃﻱ ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﻗﻭﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻤﻭﻀﻊ ﺍﻟﺩﺭﺍﺴﺔ ،ﻜﻤﺎ ﻴﺒﻴﻥ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻟﺙ ﻓﻲ
ﺍﻟﺸﻜل ﺃﻥ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ t-valueﻫﻲ 3.013ﻭﻟﻬﺎ 9ﺩﺭﺠﺎﺕ ﺤﺭﻴﺔ ﻭﺃﻥ ﻗﻴﻤﺔ
p-valueﻤﺴﺎﻭﻴﺔ ،0.015ﺃﻱ ﺃﻨﻨﺎ ﻨﺴﺘﻁﻴﻊ ﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﺃﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻤﺘﺴﺎﻭﻴﻴﻥ ﺒﻤﺴﺘﻭﻯ ﻤﻌﻨﻭﻴﺔ ) 0.05ﻷﻥ ﻗﻴﻤﺔ p-valueﺃﻗل ﻤﻥ ،(0.05 ﻭﺒﺫﻟﻙ ﻨﺴﺘﻨﺘﺞ ﺃﻥ ﻫﻨﺎﻙ ﻓﺭﻕ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﻴﻥ ،ﺃﻱ ﺃﻥ ﻫﻨﺎﻙ ﺘﺄﺜﻴﺭ ﻟﻤﻭﻗﻊ ﺍﻟﻜﻠﻤﺎﺕ
ﻋﻠﻰ ﻴﻤﻴﻥ ﺃﻭ ﻋﻠﻰ ﻴﺴﺎﺭ ﺍﻟﺸﺎﺸﺔ ﻋﻠﻰ ﻗﺩﺭﺓ ﺍﻷﻁﻔﺎل ﻋﻠﻰ ﺘﻤﻴﻴﺯ ﺘﻠﻙ ﺍﻟﻜﻠﻤﺎﺕ.
ﻭﻴﻭﻀﺢ ﺃﻴﻀﹰﺎ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻟﺙ ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺸﻜل 6-6ﺘﻘﺩﻴﺭ ﻟﻔﺘﺭﺓ 95%ﺜﻘﺔ ﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ 95% Confidence Interval for the
، Differenceﺤﺙ ﻴﻭﺠﺩ ﻓﻲ ﻤﻔﺎﻫﻴﻡ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ﻁﺭﻴﻘﺘﻴﻥ ﻟﻠﺘﻘﺩﻴﺭ ﻭﻫﻤﺎ:
.1ﺍﻟﺘﻘﺩﻴﺭ ﺒﻨﻘﻁﺔ : Point estimatesﻭﻫﻭ ﻋﺒﺎﺭﺓ ﻋﻥ ﺘﻘﺩﻴﺭ ﻟﻠﻘﻴﻤﺔ ﺍﻟﻤﺠﻬﻭﻟﺔ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ ﻜﻜل ﺒﻘﻴﻤﺔ ﻭﺤﻴﺩﺓ ﻭﺫﻟﻙ ﻤﻥ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻌﻴﻨﺔ.
.2ﺍﻟﺘﻘﺩﻴﺭ ﺒﻔﺘﺭﺓ ﺜﻘﺔ : Confidence interval estimatesﻭﻫﻲ ﻋﺒﺎﺭﺓ ﻋﻥ ﻓﺘﺭﺓ ﺘﻘﻊ ﺒﻬﺎ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﺠﻬﻭﻟﺔ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ ﻭﺒﺩﺭﺠﺔ ﺜﻘﺔ ﻤﺤﺩﺩﺓ.
ﻭﺘﺒﻴﻥ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺍﻟﺠﺩﻭل ﺃﻥ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﻴﻥ ﻟﻥ ﻴﻘل ﻋﻥ 6.60ﻭﻟﻥ
ﻴﺯﻴﺩ ﻋﻥ 46.40ﻭﺫﻟﻙ ﺒﺩﺭﺠﺔ ﺜﻘﺔ ،95%ﻭﺤﻴﺙ ﺃﻥ ﻫﺫﻩ ﺍﻟﻔﺘﺭﺓ ﻻ ﺘﺤﺘﻭﻱ ﻋﻠﻰ
ﻗﻴﻤﺔ ﺍﻟﻔﺭﻕ ﻓﻲ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﻭﻫﻲ ﺍﻟﺼﻔﺭ ﻓﺈﻥ ﻫﺫﺍ ﻴﻌﺘﺒﺭ ﻤﺅﺸﺭ ﻋﻠﻰ ﺭﻓﻀﻬﺎ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
231
.3 .2 .6اﺧﺘﺒﺎرات tﻓﻲ ﺣﺎﻟﺔ اﻟﻌﻴﻨﺘﻴﻦ اﻟﻤﺴﺘﻘﻠﺘﻴﻦ : The independent samples t-tests : ﻤﻥ ﺃﺠل ﺘﻁﺒﻴﻕ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﺴﻭﻑ ﻨﺴﺘﺨﺩﻡ ﻨﻔﺱ ﺒﻴﺎﻨﺎﺕ
ﺍﻟﺘﺠﺭﺒﺔ ﻓﻲ ﺍﻟﻤﺜﺎل ﺍﻟﺴﺎﺒﻕ ﻭﻟﻜﻥ ﺴﻨﻔﺘﺭﺽ ﺃﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻨﺎﺘﺠﺔ ﻋﻥ ﺘﺠﺭﺒﺔ ﺘﻡ ﺘﻁﺒﻴﻘﻬﺎ
ﻋﻠﻰ ﻋﻴﻨﺘﻴﻥ ﻤﺴﺘﻘﻠﺘﻴﻥ ﻤﻥ ﺍﻷﻁﻔﺎل ﻭﺤﺠﻡ ﻜل ﻤﻨﻬﺎ 10ﺃﻁﻔﺎل ﻭﺘﻡ ﻋﺭﺽ ﺍﻟﻜﻠﻤﺎﺕ ﻟﻸﻁﻔﺎل ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﻋﻠﻰ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺭﻯ ﻤﻥ ﺸﺎﺸﺔ ﺍﻟﺤﺎﺴﻭﺏ ﻭﻟﻸﻁﻔﺎل ﻓﻲ
ﺍﻟﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ﻋﻠﻰ ﺍﻟﺠﻬﺔ ﺍﻟﻴﻤﻨﻰ ﻤﻨﻬﺎ ،ﻭﺤﺼﻠﻨﺎ ﻋﻠﻰ ﻤﻘﺎﻴﻴﺱ ﻟﻭﺴﻴﻁ ﺍﻟﻭﻗﺕ ﺍﻟﻼﺯﻡ ﻟﻜل ﻁﻔل ﻤﻥ ﺒﻴﻥ ﺍﻟﻌﺸﺭﻴﻥ ﻁﻔل ﻟﺘﺤﺩﻴﺩ ﺍﻟﻜﻠﻤﺎﺕ ،ﻭﻟﻐﺭﺽ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭﺍﺕ t
ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﻻﺒﺩ ﻤﻥ ﺇﻋﺎﺩﺓ ﺘﺭﺘﻴﺏ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺒﺤﻴﺙ ﻴﻜﻭﻥ ﻤﺘﻐﻴﺭ ﻭﺴﻴﻁ ﺍﻟﻭﻗﺕ ﺍﻟﻼﺯﻡ ﻟﻸﻁﻔﺎل ﻟﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ﻓﻲ ﻋﻤﻭﺩ ﻭﺍﺤﺩ ﻤﻥ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻭﻟﺘﺤﺩﻴﺩ ﺍﻟﻌﻴﻨﺔ
ﺍﻟﺘﻲ ﻴﻨﺘﻤﻲ ﺇﻟﻴﻬﺎ ﻜل ﻁﻔل ﻻﺒﺩ ﻤﻥ ﺃﻥ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭ ﺘﺼﻨﻴﻑ ﻴﻭﻀﺢ ﺭﻗﻡ ﺍﻟﻌﻴﻨﺔ، ﻭﺒﺫﻟﻙ ﻓﺈﻥ ﻨﻔﺱ ﺍﻟﻘﻴﻡ ﺍﻟﺘﻲ ﻅﻬﺭﺕ ﻓﻲ ﺸﻜل 2-6ﺍﻟﺴﺎﺒﻕ ﺃﻋﻴﺩ ﺘﺭﺘﻴﺒﻬﺎ ﺒﺎﺴﺘﺨﺩﺍﻡ
ﺃﻭﺍﻤﺭ ﻗﺎﺌﻤﺔ ﺍﻟﺘﻌﺩﻴل Editﻓﻲ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data Editorﻟﺘﻅﻬﺭ ﺍﻵﻥ ﻜﻤﺎ ﻓﻲ
ﺸﻜل 10-6ﺃﺩﻨﺎﻩ.
ﻭﻋﻨﺩﻤﺎ ﻴﺘﻡ ﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺒﺎﻟﺸﻜل ﺍﻟﻨﺎﺴﺏ ﺍﻟﻤﺫﻜﻭﺭ ﺃﻋﻼﻩ ﻭﺤﻔﻅﻬﺎ ﻓﻲ ﻤﻠﻑ
ﻴﻤﻜﻥ ﺇﺠﺭﺍﺀ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﻋﻠﻰ ﺍﻟﻌﻤﻭﺩ ﺍﻟﺫﻱ ﻴﺤﺘﻭﻱ ﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻤﺘﻐﻴﺭ ﻟﻠﻌﻴﻨﺘﻴﻥ ﻭﻤﻌﺭﻑ ﺭﻗﻡ ﺍﻟﻌﻴﻨﺔ ﺍﻟﺘﻲ ﺘﻨﺘﻤﻲ ﺇﻟﻴﻬﺎ ﻜل ﻤﺸﺎﻫﺩﺓ ﻓﻲ ﻤﺘﻐﻴﺭ ﺘﺼﻨﻴﻑ ﻜﻤﺎ ﻴﻠﻲ :
• ﻤﻥ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻭﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ Analyzeﻜﻤﺎ ﻓﻲ
ﺸﻜل ) 7-6ﺃﻭ Statisticsﻓﻲ ﺇﺼﺩﺍﺭ (8.0ﻨﺨﺘﺎﺭ ﻗﺎﺌﻤﺔ ﺃﻤﺭ ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ
ﺍﻟﻤﺘﻭﺴﻁﺎﺕ Compare Meansﻭﻤﻨﻬﺎ ﻨﺨﺘﺎﺭ ﺃﻤﺭ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ
Independent Samples T Testﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Independent Samples T Testﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل 8-6ﺃﺩﻨﺎﻩ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
232
ﺸﻜل : 7-6ﺸﺎﺸﺔ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻤﻭﻀﺤ ﹰﺎ ﻋﻠﻴﻬﺎ ﺃﻤﺭ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ Independent-Samples T Testﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﺎﺕ
ﺸﻜل : 8-6ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ .Independent-Samples T Test
•
ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ ﺍﻟﺴﺎﺒﻘﺔ ﻴﻤﻜﻥ ﺘﺤﺩﻴﺩ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ )ﺃﻭ ﻤﺘﻐﻴﺭ ﺍﻻﺨﺘﺒﺎﺭ( Test
) Variable(sﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺭﻯ ﻤﻥ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻫﻭ ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﻭﺴﻴﻁ ﺍﻟﻭﻗﺕ ﺍﻟﻼﺯﻡ ﻟﺘﺤﺩﻴﺩ ﺍﻟﻜﻠﻤﺎﺕ ﻟﻠﻁﻔل Recognition Timeﻭﻤﻥ
ﺜﻡ ﺇﺯﺍﺤﺘﻪ ﺇﻟﻰ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﺒﺎﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﺎﺒﻌﺔ ﻋﻠﻰ ﺍﻟﻴﻤﻴﻥ ﺒﻭﺍﺴﻁﺔ ﺍﻟﺴﻬﻡ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
233
• ﺒﺎﻟﻤﺜل ﻴﻤﻜﻥ ﺘﺤﺩﻴﺩ ﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ Grouping Variableﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺭﻯ ﻤﻥ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻫﻭ ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﺠﻬﺔ ﺍﻟﺸﺎﺸﺔ Left-
Right Identifierﻭﻤﻥ ﺜﻡ ﺇﺯﺍﺤﺘﻪ ﺇﻟﻰ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﺒﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﺼﻨﻴﻑ
ﻋﻠﻰ ﻴﻤﻴﻥ ﻭﺃﺴﻔل ﺍﻟﻨﺎﻓﺫﺓ ﺒﻭﺍﺴﻁﺔ ﺍﻟﺴﻬﻡ ،ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺴﻴﻅﻬﺭ ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ) lftrghtﻭﻟﻴﺱ ﺩﻟﻴﻠﻪ( ﻓﻲ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﻭﺘﻘﺎﺒﻠﻪ ﻋﻼﻤﺎﺕ ﺍﻻﺴﺘﻔﻬﺎﻡ ؟ ؟ ﻜﻤﺎ
ﻓﻲ ﺍﻟﺸﻜل 8-6ﺃﻋﻼﻩ.
• ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻻﺒﺩ ﻤﻥ ﺘﻌﺭﻴﻑ ﻗﻴﻡ ﺍﻟﻤﺠﻤﻭﻋﺎﺕ )ﺍﻟﻌﻴﻨﺎﺕ( ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺘﻐﻴﺭ ﻭﺫﻟﻙ ﺒﺎﻟﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺤﻭﺍﺭ ﺘﻌﺭﻴﻑ ﺍﻟﻤﺠﻤﻭﻋﺎﺕ Define
Groupsﺍﻟﻤﻘﺎﺒل ﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ ﻭﻓﺘﺢ ﻨﺎﻓﺫﺓ ﺘﻌﺭﻴﻑ ﻤﺠﻤﻭﻋﺎﺕ ﺍﻟﻌﻴﻨﺎﺕ
Define Groupsﻟﻭﻀﺢ ﺩﻟﻴل ﻜل ﻤﻥ ﺍﻟﻌﻴﻨﺘﻴﻥ ﻜﻤﺎ ﻓﻲ ﺸﻜل ،9-6ﻭﻓﻲ
ﻤﺜﺎﻟﻨﺎ ﻓﻘﺩ ﺘﻡ ﺘﻌﺭﻴﻑ ﺩﻟﻴل ﺍﻟﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﺒﺎﻟﺭﻗﻡ 1ﻭﺍﻟﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ﺒﺎﻟﺭﻗﻡ 2ﻓﻲ
ﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ ﻭﻫﻭ ﺠﻬﺔ ﺍﻟﺸﺎﺸﺔ . Left-Right Identifier
ﺸﻜل : 9-6ﻨﺎﻓﺫﺓ ﺘﻌﺭﻴﻑ ﻤﺠﻤﻭﻋﺎﺕ ﺍﻟﻌﻴﻨﺎﺕ Define Groupsﻓﻲ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ .Independent-Samples T Test
• ﻴﺘﻡ ﺇﻋﻁﺎﺀ ﺩﻟﻴل ﺍﻟﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﺃﻤﺎﻡ Group 1ﻭﺩﻟﻴل ﺍﻟﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ﺃﻤﺎﻡ
Group 2ﻓﻲ ﺘﻠﻙ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻤﻥ ﺜﻡ ﻴﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻻﺴﺘﻤﺭﺍﺭ Continue
ﻟﻴﻅﻬﺭ ﺍﻟﺭﻗﻤﻴﻥ 1ﻭ 2ﺃﻤﺎﻡ ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﻓﻲ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ) Independent Samples T Testﺸﻜل . (8-6
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
•
234
ﺍﻵﻥ ﻓﻲ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Independent Samples T
Testﻓﻲ ﺍﻟﺸﻜل 8-6ﻴﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺘﻨﻔﻴﺫ OKﻹﻨﻬﺎﺀ ﺍﻟﻤﻬﻤﺔ ﻭﺘﻨﻔﻴﺫ
ﺃﻤﺭ ﺇﺠﺭﺍﺀ ﺍﻻﺨﺘﺒﺎﺭ ﺍﻟﻤﻁﻠﻭﺏ.
ﻭﻴﻭﻀﺢ ﺸﻜل 10-6ﻗﻴﻡ ﺍﻟﻌﻴﻨﺘﻴﻥ ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﺍﻟﺴﺎﺒﻕ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﺘﻲ ﻴﺘﻁﻠﺒﻬﺎ
ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Independent Samples T Testﻓﻲ ﻨﻅﺎﻡ SPSSﻟﺘﻨﻔﻴﺫ
ﻫﺫﺍ ﺍﻷﻤﺭ ﻋﻠﻴﻬﺎ ﻭﻴﻭﻀﺢ ﺸﻜل 11-6ﻨﺘﺎﺌﺞ ﺘﻨﻔﻴﺫ ﻫﺫﺍ ﺍﻷﻤﺭ ﻋﻠﻰ ﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ. ﺸﻜل : 10-6ﺠﺩﻭل ﻴﺒﻴﻥ ﻗﻴﻡ ﺍﻟﻌﻴﻨﺘﻴﻥ ﻟﻠﺘﻤﻜﻥ ﻤﻥ ﺍﺴﺘﺨﺩﺍﻤﻬﺎ ﻓﻲ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ .Independent-Samples T Test Case Summaries Left Right Indicator
Recognition Time
1
323
1
1
512
2
1
502
3
1
385
4
1
453
5
1
343
6
1
543
7
1
440
8
1
682
9
1
590
10
2
304
11
2
493
12
2
491
13
2
365
14
2
426
15
2
320
16
2
523
17
2
442
18
2
580
19
2
564
20
20
20
N
Total
( ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ6)
235
ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔt ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻤﺤﺭﺭ ﺍﻟﻨﺘﺎﺌﺞ ﻤﻥ ﺘﻁﺒﻴﻕ ﺃﻤﺭ ﺍﺨﺘﺒﺎﺭ: 11-6 ﺸﻜل .9-6 ﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻓﻲ ﺸﻜلIndependent-Samples T Test T-Test Group Statistics
Left Right Indicator Recognition Time
N
Mean
Std. Deviation
Std. Error Mean
1
10
477.30
112.09
35.45
2
10
450.80
97.09
30.70
Independent Samples Test Levene's Test for Equality of Variances
Recognition Equal variances Time assumed Equal variances not assumed
t-test for Equality of Means
F
Sig.
t
.132
.721
.565
df
Sig. Mean (2-taile Differ d) ence
95% Confidence Interval of the Difference
Std. Error Differ ence Lower Upper
18
.579 26.50 46.89 -72.02 125.0
.565 17.64
.579 26.50 46.89 -72.16 125.2
ﻭﺘﺒﺩﺃ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺠﺩﻭل ﻴﺒﻴﻥ ﺒﻌﺽ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ ﻟﻜل ﻋﻴﻨﺔ ﻋﻠﻰ ﻓﻲ ﻜل ﻋﻴﻨﺔ ﻭﺍﻟﻭﺴﻁN ﻭﻫﺫﻩ ﺍﻟﻤﻘﺎﻴﻴﺱ ﻫﻲ ﻋﺩﺩ ﺍﻟﻘﻴﻡ، Group Statistics ﺤﺩﻩ
ﻭﺍﻟﺨﻁﺄ ﺍﻟﻤﻌﻴﺎﺭﻱStandard Deviation ﻭﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱMean ﺍﻟﺤﺴﺎﺒﻲ
ﻭﻴﺘﻀﺢ ﺃﻥ ﺍﻟﻭﺴﻁ، Standard Error of the Mean ﻟﻠﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ ﻟﻜل ﻋﻴﻨﺔ ﺃﻱ ﺃﻥ ﺍﻟﻭﺴﻁﻴﻥ، 450.8 ﻭﻟﻠﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ﻫﻭ477.3 ﺍﻟﺤﺴﺎﺒﻲ ﻟﻠﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﻫﻭ ﻭﻟﻜﻥ ﻫل ﺍﻻﺨﺘﻼﻑ ﻤﻌﻨﻭﻱ؟،ﻤﺨﺘﻠﻔﺎﻥ
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
236
ﻭﻴﻭﻀﺢ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻓﻲ ﺍﻟﺸﻜل ﻨﺘﺎﺌﺞ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Independent Samples T Testﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﻭﻫﺫﺍ ﺍﻟﺠﺩﻭل ﻴﺠﻴﺏ ﻋﻠﻰ
ﺍﻷﺴﺌﻠﺔ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﻨﺘﻴﺠﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻭﺫﻟﻙ ﻋﻥ ﻁﺭﻴﻕ ﺘﻜﻭﻴﻥ ﺠﺩﻭل ﻟﻭﻀﻊ ﻗﻴﻡ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ tﻭ ﻗﻴﻤﺔ p-valueﺍﻟﻤﺼﺎﺤﺒﺔ ﻟﻬﺎ ﻭﻜﺫﻟﻙ 95%ﻓﺘﺭﺓ ﺜﻘﺔ ﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﺍﻟﺫﻴﻥ ﺴﺤﺒﺘﺎ ﻤﻨﻬﻤﺎ ﺍﻟﻌﻴﻨﺘﻴﻥ 95% Confidence Interval for
the Differenceﻭﺫﻟﻙ ﻓﻲ ﺤﺎﻟﺘﻲ ﺍﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ ﺘﺒﺎﻴﻨﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﻭﺍﻓﺘﺭﺍﺽ ﻋﺩﻡ ﺘﺴﺎﻭﻱ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ .
ﻭﺍﻟﻤﺅﺸﺭ ﻋﻠﻰ ﺃﻱ ﺤﺎﻟﺔ ﻴﺠﺏ ﺍﺴﺘﺨﺩﺍﻤﻬﺎ ﻤﻥ ﺒﻴﻥ ﺍﻟﺤﺎﻟﺘﻴﻥ ﺍﻟﺴﺎﺒﻘﺘﻲ ﺍﻟﺫﻜﺭ
ﻴﻜﻤﻥ ﻓﻲ ﺍﺨﺘﺒﺎﺭ ﻟﻴﻔﻴﻥ ﻟﻠﺘﺠﺎﻨﺱ ، Levene’s Test for Equality of variances
ﻓﺈﺫﺍ ﻜﺎﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻏﻴﺭ ﻤﻌﻨﻭﻱ ) (p>0.05ﻓﻴﻜﻭﻥ ﺍﻻﻓﺘﺭﺍﺽ ﺃﻥ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ ﻤﺘﺴﺎﻭﻴﻴﻥ ﻻ ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﺈﻨﻪ ﻴﺅﺨﺫ ﺒﺎﻟﺤﺎﻟﺔ ﺍﻷﻭﻟﻰ ﻭﻴﻨﻅﺭ ﻟﻠﺴﻁﺭ ﺍﻷﻭل ﻤﻥ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻤﻘﺒﻭ ﹰ
ﺍﻟﺠﺩﻭل ،ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﺒﻨﺎﺀ ﻋﻠﻰ ﺍﺨﺘﺒﺎﺭ ﻟﻴﻔﻴﻥ ﻟﻠﺘﺠﺎﻨﺱ ﻴﻜﻭﻥ :
• ﺇﺫﺍ ﻜﺎﻨﺕ p>0.05ﻓﺈﻨﻪ ﻻ ﻴﻭﺠﺩ ﻤﺎ ﻴﺩل ﻋﻠﻰ ﺃﻥ ﻫﻨﺎﻙ ﺍﻨﺘﻬﺎﻙ ﻻﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ tﺍﻟﻤﺒﻨﻲ ﻋﻠﻰ ﺃﺴﺎﺱ
ﺍﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ ﺘﺒﺎﻴﻨﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ . Equal variances assumed
• ﺇﺫﺍ ﻜﺎﻨﺕ p<0.05ﻓﺈﻨﻪ ﻴﻭﺠﺩ ﺩﻟﻴل ﻜﺎﻓﻲ ﻋﻠﻰ ﺃﻥ ﻫﻨﺎﻙ ﺍﻨﺘﻬﺎﻙ ﻻﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ
ﺍﻟﺘﺒﺎﻴﻨﻴﻥ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ﻭﺒﺎﻟﺘﺎﻟﻲ ﻴﺴﺘﺨﺩﻡ ﺍﺨﺘﺒﺎﺭ tﺍﻟﻤﺒﻨﻲ ﻋﻠﻰ ﺃﺴﺎﺱ ﺍﻓﺘﺭﺍﺽ ﻋﺩﻡ
ﺘﺴﺎﻭﻱ ﺘﺒﺎﻴﻨﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ Equal variances not assumedﻭﻴﺘﻡ ﺘﻘﺩﻴﺭ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ ﻜل
ﻋﻠﻰ ﺤﺩﻩ .
ﻭﻴﻤﻜﻥ ﺍﻵﻥ ﻟﻠﻤﺴﺘﺨﺩﻡ ﺍﻟﻤﻼﺤﻅﺔ ﺒﺎﻟﻨﻅﺭ ﺇﻟﻰ ﻻﺌﺤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺍﻟﺸﻜل 11-6
ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﺍﻟﺴﺎﺒﻕ ﺃﻥ ﻜل ﻤﻥ ﻗﻴﻤﺘﻲ tﻭﻗﻴﻤﺘﻲ p-valuesﻤﺘﻘﺎﺭﺒﺘﻴﻥ ﻓﻲ ﻜل ﻤﻥ ﺤﺎﻟﺘﻲ ﺍﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ Equal variances assumedﻭﺍﻓﺘﺭﺍﺽ ﻋﺩﻡ ﺘﺴﺎﻭﻱ ﻼ ﻤﺘﺴﺎﻭﻴﻴﻥ ،ﻭﻟﻜﻥ ﻟﻥ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ Equal variances not assumedﻭﺫﻟﻙ ﻷﻨﻬﻤﺎ ﻓﻌ ﹰ
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
237
ﺘﻜﻭﻥ ﺍﻟﺤﺎﻟﺔ ﻜﺫﻟﻙ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺩﻟﻴل ﻜﺎﻓﻲ ﻋﻠﻰ ﺃﻥ ﻫﻨﺎﻙ ﺍﻨﺘﻬﺎﻙ ﻻﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ ،ﻓﺴﻭﻑ ﺘﻜﻭﻥ ﺍﻟﻨﺘﺎﺌﺞ ﻤﺨﺘﻠﻔﺔ ﻓﻲ ﺍﻟﺤﺎﻟﺘﻴﻥ ،ﻭﺴﻭﻑ
ﻴﺅﺨﺫ ﺒﻨﺘﻴﺠﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻓﻲ ﻅل ﺍﻻﻓﺘﺭﺍﺽ ﺒﻌﺩﻡ ﺘﺴﺎﻭﻱ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ ،ﺃﻱ ﺒﻨﺘﺎﺌﺞ ﺍﻟﺴﻁﺭ ﺍﻟﺜﺎﻨﻲ . Equal variances not assumed
ﻓﻔﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻴﺘﻀﺢ ﺃﻥ ﺍﺨﺘﺒﺎﺭ ﻟﻴﻔﻴﻥ Levene’s Test for Equality of
variancesﻏﻴﺭ ﻤﻌﻨﻭﻱ ) (p>0.05ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﺈﻥ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ﺍﻟﻤﻨﺎﺴﺒﺔ ﻻﺒﺩ
ﻭﺃﻥ ﺘﺤﺴﺏ ﻓﻲ ﻅل ﺍﻓﺘﺭﺍﺽ ﺘﺴﺎﻭﻱ ﺍﻟﺘﺒﺎﻴﻨﻴﻥ )(Equal variances assumed
ﻭﺒﺎﺴﺘﺨﺩﺍﻡ ﺘﻘﺩﻴﺭ ﺍﻟﺘﺒﺎﻴﻥ ﺍﻟﻤﺘﺠﻤﻊ ) Pooled Varianceﻓﻲ ﺍﻟﻭﺍﻗﻊ ﻓﻲ ﻤﺜل ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ
ﺘﻜﻭﻥ ﺍﻟﻨﺘﻴﺠﺘﻴﻥ ﻤﺘﺸﺎﺒﻬﺘﻴﻥ( ،ﻭﺒﻘﻴﻤﺔ p-valueﻤﺴﺎﻭﻴﺔ 0.579ﻨﺴﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﻴﻥ ﻏﻴﺭ ﻤﻌﻨﻭﻱ ،ﺃﻱ ﺃﻥ ﺍﻟﻨﺘﻴﺠﺔ ﺘﻜﻭﻥ :
.ﻏﻴﺭ ﻤﻌﻨﻭﻱ t = 0.565 ; df = 18 ; Not significant
ﻭﺍﻟﻨﺘﻴﺠﺔ ﺍﻷﺨﻴﺭﺓ ﻤﻥ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﺘﺅﻜﺩ ﺍﻟﻨﺘﻴﺠﺔ ﺍﻟﺴﺎﺒﻘﺔ ،ﺤﻴﺙ ﺃﻥ 95%
ﻓﺘﺭﺓ ﺜﻘﺔ ﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ 95% Confidence Interval of the
Difference Between Meansﻫﻲ ) 125.0ﻭ ، (-72.02ﻭﻫﻲ ﺘﺤﺘﻭﻱ ﺒﺩﺍﺨﻠﻬﺎ ﻋﻠﻰ ﻗﻴﻤﺔ ﺍﻟﻔﺭﻕ ﻓﻲ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﻭﻫﻭ ﺍﻟﺼﻔﺭ ،ﻭﻟﻭ ﻜﺎﻥ ﺤﺩﻱ ﺍﻟﺜﻘﺔ ﺍﻟﺴﺎﺒﻘﻴﻥ ﻤﻭﺠﺒﻴﻥ ﻓﺴﻭﻑ ﺘﻜﻭﻥ ﺍﻟﻨﺘﻴﺠﺔ ﻓﻲ ﺘﻠﻙ ﺍﻟﺤﺎﻟﺔ ﺍﻻﻓﺘﺭﺍﻀﻴﺔ ﻫﻲ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ
ﻤﻌﻨﻭﻱ .
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
238
.3 .6اﻟﻄﺮق اﻟﻼﻣﻌﻠﻤﻴﺔ Nonparametric Methods : ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺍﻨﺘﻬﺎﻜﺎﺕ ﻜﺒﻴﺭﺓ ﻟﻠﻔﺭﻭﺽ ﺍﻟﻭﺍﺠﺏ ﺘﻭﺍﻓﺭﻫﺎ ﻹﻤﻜﺎﻨﻴﺔ
ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻓﻲ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﺈﻥ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻟﻥ ﺘﻅل ﺼﺎﻟﺤﺔ
ﺍﻻﺴﺘﺨﺩﺍﻡ ﻟﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﺘﻜﻭﻥ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻫﻲ ﺃﺤﺩ
ﺍﻟﺒﺩﺍﺌل ﺍﻟﻤﻁﺭﻭﺤﺔ ﻟﻠﺨﺭﻭﺝ ﻤﻥ ﻫﺫﻩ ﺍﻟﻤﺸﻜﻠﺔ ،ﻭﺭﻏﻡ ﺫﻟﻙ ﻓﺈﻨﻪ ﻻ ﻴﺠﺏ ﺍﺴﺘﺨﺩﺍﻡ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻓﻲ ﻜل ﺍﻟﺤﺎﻻﺕ ﺘﻠﻘﺎﺌﻴﹰﺎ ،ﻭﺫﻟﻙ ﻷﻨﻪ ﺇﺫﺍ ﺘﻭﺍﻓﺭﺕ ﺍﻟﻅﺭﻭﻑ
ﺍﻟﻤﻼﺌﻤﺔ ﻻﺴﺘﺨﺩﺍﻡ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﻌﻠﻤﻴﺔ ﻤﺜل ﺍﺨﺘﺒﺎﺭﺍﺕ tﻓﺈﻥ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﺍﻟﻤﻨﺎﻅﺭﺓ ﻟﻬﺎ ﺴﻭﻑ ﺘﻜﻭﻥ ﺃﻗل ﻗﻭﺓ ﻤﻨﻬﺎ ﻓﻲ ﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ
ﺨﺎﻁﺌﺔ ﺒﺎﻟﻔﻌل ،ﻭﻟﺫﻟﻙ ﻓﺈﻨﻪ ﻴﺤﺴﻥ ﺩﺍﺌﻤﹰﺎ ﺍﻟﻤﺤﺎﻭﻟﺔ ﻓﻲ ﺍﺴﺘﺨﺩﺍﻡ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﻌﻠﻤﻴﺔ
ﻓﻲ ﺍﻟﺒﺩﺍﻴﺔ ﺜﻡ ﺍﻟﺘﻔﻜﻴﺭ ﻓﻲ ﺍﺴﺘﺨﺩﺍﻡ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﺇﺫﺍ ﺜﺒﺕ ﺃﻥ ﻫﻨﺎﻙ ﺍﻨﺘﻬﺎﻜﺎﺕ ﺨﻁﻴﺭﺓ ﻟﻠﻔﺭﻭﺽ ﺍﻟﻤﺒﻨﻲ ﻋﻠﻰ ﺃﺴﺎﺴﻬﺎ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﻌﻠﻤﻴﺔ ﺍﻟﻤﻨﺎﺴﺒﺔ .
ﻭﻴﺤﺘﻭﻱ ﻨﻅﺎﻡ SPSSﻋﻠﻰ ﻤﺠﻤﻭﻋﺔ ﻜﺒﻴﺭﺓ ﻤﻥ ﺃﻭﺍﻤﺭ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ
ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ Nonparametric Testsﻭﺫﻟﻙ ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ،ﻭﺘﻌﺘﺒﺭ ﺍﺨﺘﺒﺎﺭﺍﺕ ﺍﻹﺸﺎﺭﺓ Signﻭﻭﻴﻠﻜﻭﻜﺴﻥ
Wilcoxonﻭﻤﻜﻨﻤﺎﺭ McNemarﺍﺨﺘﺒﺎﺭﺍﺕ ﻻﻤﻌﻠﻤﻴﺔ ﻤﻨﺎﻅﺭﺓ ﻻﺨﺘﺒﺎﺭ tﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ،Paired Samples T Testﺒﻴﻨﻤﺎ ﻴﻌﺘﺒﺭ ﺍﺨﺘﺒﺎﺭ ﻤﺎﻥ
ﻭﻴﺘﻨﻲ Mann-Whitneyﺍﺨﺘﺒﺎﺭﹰﺍ ﻤﻨﺎﻅﺭﹰﺍ ﻻﺨﺘﺒﺎﺭ tﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ ﻓﻲ ﺤﺎﻟﺔ
ﺍﻟﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ . Independent Samples T Test
ﻭﺘﺴﺘﺨﺩﻡ ﻤﻌﻅﻡ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻓﻲ ﺤﺴﺎﺒﻬﺎ ﻤﻘﺎﻴﻴﺱ ﺇﺤﺼﺎﺌﻴﺔ ﻤﺜل
ﺍﻟﻭﺴﻴﻁ Medianﻭﺍﻟﺘﻲ ﻻ ﺘﺘﺄﺜﺭ ﺒﺎﻟﻘﻴﻡ ﺍﻟﻤﺘﻁﺭﻓﺔ ﻭﺍﻟﺸﺎﺫﺓ ﻭﻜﺫﻟﻙ ﺒﺎﻟﺘﻭﺍﺀ ﺘﻭﺯﻴﻊ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﻓﻲ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﺘﺎﻟﻴﺔ ﺴﺘﻨﺹ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﻋﻠﻰ ﻋﺩﻡ ﻭﺠﻭﺩ ﻓﺭﻕ
ﻤﻌﻨﻭﻱ ﺒﻴﻥ ﻭﺴﻴﻁﻲ ﺍﻟﻤﺠﺘﻤﻌﻴﻥ )ﻭﻟﻴﺱ ﻤﺘﻭﺴﻁﻴﻬﻤﺎ ﺍﻟﺤﺴﺎﺒﻴﻴﻥ(.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
239
.1 .3 .6ﺣﺎﻟﺔ اﻟﻌﻴﻨﺎت اﻟﻤﺮﺗﺒﻄﺔ : اﺧﺘﺒﺎرات وﻳﻠﻜﻮآﺴﻦ واﻹﺷﺎرة وﻣﻜﻨﻤﺎر : Related samples: Wilcoxon, Sign and McNemar tests : ﻭﻟﺘﻭﻀﻴﺢ ﻜﻴﻔﻴﺔ ﺍﺴﺘﺨﺩﺍﻡ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺴﻭﻑ ﻨﺴﺘﺨﺩﻡ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﻲ ﺘﻡ
ﺍﺴﺘﺨﺩﺍﻤﻬﺎ ﻓﻲ ﺤﺎﻟﺔ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﻓﻲ ﺸﻜل ،2-6ﻭﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ
ﻤﻠﻑ ﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻤﻔﺘﻭﺤﹰﺎ ﻓﻲ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data Editorﻓﺈﻨﻪ ﻴﻤﻜﻨﻨﺎ ﺇﺠﺭﺍﺀ ﺃﻱ
ﻤﻥ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻜﻤﺎ ﻴﻠﻲ:
• ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ Nonparametric Testsﻭﻤﻨﻬﺎ ﺃﻤﺭ ﺍﻟﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ
Related
Samplesﻜﻤﺎ ﻓﻲ ﺸﻜل 12-6ﺃﺩﻨﺎﻩ .
ﺸﻜل : 12-6ﻁﺭﻴﻘﺔ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺃﻤﺭ ﺍﻟﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Related Samplesﻓﻲ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ Nonparametric Tests
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
240
• ﺒﺎﺨﺘﻴﺎﺭﻙ ﺫﻟﻙ ﺍﻷﻤﺭ ﺴﻭﻑ ﺘﺤﺼل ﻋﻠﻰ ﻨﺎﻓﺫﺓ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ )ﻜﻤﺎ ﻓﻲ ﺸﻜل ،(13-6ﻭﻴﻤﻜﻥ ﻤﻥ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﺇﺠﺭﺍﺀ ﺃﻱ ﻤﻥ ﺃﻭ ﺠﻤﻴﻊ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺒﻨﻔﺱ ﺍﻷﻤﺭ.
• ﻗﻡ ﺒﺘﺤﺩﻴﺩ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺍﻟﻤﺭﺍﺩ ﺍﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻕ ﺒﻴﻥ ﻭﺴﻴﻁﻴﻬﻤﺎ ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
ﻓﻲ ﺍﻟﺠﺯﺀ ﺍﻷﻴﺴﺭ ﻤﻥ ﺍﻟﻨﺎﻓﺫﺓ ﺜﻡ ﺘﺤﻭﻴﻠﻬﻤﺎ ﺇﻟﻰ ﻗﺎﺌﻤﺔ ﺃﺯﻭﺍﺝ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
Test
Pair(s) Listﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﻤﻨﻰ ﻤﻥ ﺍﻟﻨﺎﻓﺫﺓ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﺴﻬﻡ ﺍﻟﺫﻱ ﻴﺘﻭﺴﻁ ﺍﻟﻤﺭﺒﻌﻴﻥ.
• ﺍﺨﺘﺭ ﺃﻱ ﻤﻥ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﻁﻠﻭﺏ ﺇﺠﺭﺍﺀﻫﺎ ﻤﻥ ﺒﻴﻥ ﺍﻟﺜﻼﺜﺔ ﺍﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﺫﻜﻭﺭﺓ ،ﻭﻴﺠﺩﺭ ﺒﺎﻟﺫﻜﺭ ﻫﻨﺎ ﺃﻥ ﺍﺨﺘﺒﺎﺭ ﻤﻜﻨﻤﺎﺭ ﻤﻨﺎﺴﺏ ﻓﻘﻁ ﻟﻠﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻭﺼﻔﻴﺔ
ﺍﻟﺘﻲ ﺘﺄﺨﺫ ﻗﻴﻤﺘﻴﻥ ﻓﻘﻁ ) 0ﻭ dichotomous qualitative variables (1ﻭﺘﻌﺒﺭﺍﻥ ﻋﻥ ﻗﻴﻤﺘﻴﻥ ﻓﻘﻁ ﻴﻤﻜﻥ ﺃﻥ ﻴﺄﺨﺫﻫﻤﺎ ﺍﻟﻤﺘﻐﻴﺭ ﻤﺜل ﻤﻭﺍﻓﻕ ﻭﻏﻴﺭ ﻤﻭﺍﻓﻕ ﺃﻭ ﻨﻌﻡ ﻭﻻ ﺃﻭ
ﺸﻔﻲ ﻤﻥ ﺍﻟﻤﺭﺽ ﻭﻟﻡ ﻴﺸﻔﻰ ﺃﻭ ﻁﻌﻡ ﻭﻟﻡ ﻴﻁﻌﻡ ﻭﻫﻜﺫﺍ ...ﻭﻟﺫﻟﻙ ﻓﺈﻥ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﻏﻴﺭ ﻤﻨﺎﺴﺏ ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﻭﺴﻨﺨﺘﺎﺭ ﻓﻘﻁ ﺍﻻﺨﺘﺒﺎﺭﻴﻥ ﺍﻵﺨﺭﻴﻥ.
• ﺍﺨﺘﺭ ﺍﻵﻥ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﻭﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺍﻟﻨﺘﺎﺌﺞ )ﺸﻜل .(14-6 ﺸﻜل : 13-6ﻨﺎﻓﺫﺓ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Two-Related Samples Tests in Nonparametric Tests
( ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ6)
241
ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻤﻥ ﺇﺠﺭﺍﺀ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ: 14-6 ﺸﻜل Wilcoxon Signed Ranks Test Ranks Mean Rank
N Right Field Left Field
Sum of Ranks
Negative Ranks
9
a
6.00
54.00
Positive Ranks
1
b
1.00
1.00
Ties
0
c
Total
10
a. Right Field < Left Field b. Right Field > Left Field c. Left Field = Right Field
Test Statistics b Right Field - Left Field Z
-2.705
Asymp. Sig. (2-tailed)
a
.007
a. Based on positive ranks. b. Wilcoxon Signed Ranks Test
Sign Test Frequencies N Right Field - Left Field
Negative Differences a
9
Positive Differences b
1
Ties c
0
Total
10
a. Right Field < Left Field b. Right Field > Left Field c. Left Field = Right Field Test Statistics b Right Field - Left Field Exact Sig. (2-tailed)
a. Binomial distribution used. b. Sign Test
a
.021
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
242
ﻼ ﻤﻥ ﺍﻻﺨﺘﺒﺎﺭﻴﻥ ﻓﻲ ﺸﻜل ﺍﻟﻨﺘﺎﺌﺞ )ﺸﻜل (14-6ﻓﻲ ﻗﺴﻤﻴﻥ ﻭﺘﻅﻬﺭ ﻨﺘﺎﺌﺞ ﻜ ﹰ ﻤﺴﺘﻘﻠﻴﻥ ،ﻓﺎﻟﻘﺴﻡ ﺍﻷﻭل ﻴﺘﻌﻠﻕ ﺒﺎﺨﺘﺒﺎﺭ ﻭﻴﻠﻜﻭﻜﺴﻥ ﺘﺤﺕ ﺍﺴﻡ Wilcoxon Signed
Ranks Testﻭﺫﻟﻙ ﻷﻨﻪ ﻴﺤﺴﺏ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺇﺸﺎﺭﺍﺕ ﺍﻟﻔﺭﻭﻕ ﺒﻴﻥ ﺭﺘﺏ ﻗﻴﻡ ﺍﻟﻌﻴﻨﺘﻴﻥ
ﻭﻟﻴﺱ ﻗﻴﻡ ﺍﻟﻌﻴﻨﺘﻴﻥ ﺫﺍﺘﻬﻤﺎ ،ﻓﺎﻟﺠﺩﻭل ﺍﻷﻭل ﻴﺒﻴﻥ ﻤﺠﻤﻭﻉ ﻜل ﻤﻥ ﺭﺘﺏ ﺍﻟﻔﺭﻭﻕ ﺫﺍﺕ ﺍﻹﺸﺎﺭﺍﺕ ﺍﻟﻤﻭﺠﺒﺔ ﻭﻜﺫﻟﻙ ﺫﺍﺕ ﺍﻹﺸﺎﺭﺍﺕ ﺍﻟﺴﺎﻟﺒﺔ ﻭﺫﺍﺕ ﺍﻟﻔﺭﻭﻕ ﺍﻟﻤﺴﺎﻭﻴﺔ ﻟﻠﺼﻔﺭ،
ﻭﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻴﺒﻴﻥ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻭﻜﺫﻟﻙ ﻗﻴﻤﺔ p-valueﺍﻟﻤﺼﺎﺤﺒﺔ ﻟﻬﺎ ،ﻭﻓﻲ ﻤﺜﺎﻟﻨﺎ ﻫﺫﺍ ﻴﺘﻀﺢ ﺃﻥ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻤﺴﺎﻭﻴﺔ -2.705ﻭﻗﻴﻤﺔ p-valueﻤﺴﺎﻭﻴﺔ
0.007ﻤﻤﺎ ﻴﺩل ﻋﻠﻰ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ ،ﺍﻷﻤﺭ ﺍﻟﺫﻱ ﻴﺅﻜﺩ ﺍﻟﻨﺘﻴﺠﺔ ﺒﺄﻥ ﻫﻨﺎﻙ ﻓﺭﻕ
ﻤﻌﻨﻭﻱ ﻓﻲ ﻗﺩﺭﺓ ﺍﻷﻁﻔﺎل ﻋﻠﻰ ﺘﻤﻴﻴﺯ ﺍﻟﻜﻠﻤﺎﺕ ﺒﻴﻥ ﺠﻬﺘﻲ ﺸﺎﺸﺔ ﺍﻟﺤﺎﺴﻭﺏ ،ﻭﻴﻤﻜﻥ
ﺘﻠﺨﻴﺹ ﻫﺫﻩ ﺍﻟﻨﺘﻴﺠﺔ ﻜﻤﺎ ﻴﻠﻲ: ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ
p < 0.01 ; Significant
; Z = -2.705
ﻭﻋﻠﻰ ﺍﻟﺭﻏﻡ ﻤﻥ ﺃﻥ ﺍﺨﺘﺒﺎﺭ ﻭﻴﻠﻜﻭﻜﺴﻥ ﻟﻡ ﻴﻔﺘﺭﺽ ﺃﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺘﺘﺒﻊ ﺍﻟﺘﻭﺯﻴﻊ
ﺍﻻﺤﺘﻤﺎﻟﻲ ﺍﻟﻁﺒﻴﻌﻲ ﻭﻻ ﻴﻔﺘﺭﺽ ﻜﺫﻟﻙ ﺃﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻟﻬﺎ ﺘﺒﺎﻴﻥ ﺜﺎﺒﺕ ﺇﻻ ﺃﻨﻪ ﻴﻔﺘﺭﺽ ﺃﻥ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻌﻴﻨﺘﻴﻥ ﻟﻬﻤﺎ ﻨﻔﺱ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ﺃﻱ ﺃﻨﻬﻤﺎ ﺴﺤﺒﺘﺎ ﻤﻥ ﻤﺠﺘﻤﻌﻴﻥ ﻟﻬﻤﺎ ﻨﻔﺱ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ ،ﻭﺃﻫﻡ ﻤﺎ ﻓﻲ ﺍﻷﻤﺭ ﺃﻥ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﻻ ﻴﺘﺄﺜﺭ ﻜﺜﻴﺭﹰﺍ ﺒﺎﻟﻘﻴﻡ
ﺍﻟﻤﺘﻁﺭﻓﺔ ﺃﻭ ﺍﻟﺸﺎﺫﺓ ﻨﻅﺭﹰﺍ ﻷﻨﻪ ﻴﻌﺘﻤﺩ ﻓﻲ ﺤﺴﺎﺒﻪ ﻋﻠﻰ ﺭﺘﺏ ﺍﻟﻘﻴﻡ ﻭﻟﻴﺱ ﺍﻟﻘﻴﻡ ﺫﺍﺘﻬﺎ.
ﻭﺭﻏﻡ ﺃﻥ ﺍﺨﺘﺒﺎﺭ ﺍﻹﺸﺎﺭﺓ ﻟﻪ ﻨﻔﺱ ﻤﺯﺍﻴﺎ ﺍﺨﺘﺒﺎﺭ ﻭﻴﻠﻜﻭﻜﺴﻥ ﻓﻬﻭ ﺃﻴﻀﹰﺎ ﻴﻌﺘﺒﺭ
ﺃﻜﺜﺭ ﻗﻭﺓ ﻤﻨﻪ ﻤﻥ ﻨﺎﺤﻴﺔ ﺘﺄﺜﺭﻩ ﺒﺎﻟﻘﻴﻡ ﺍﻟﻤﺘﻁﺭﻓﺔ ﻭﺍﻟﺸﺎﺫﺓ ،ﻭﺍﻟﻘﺴﻡ ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﺍﻟﻨﺘﺎﺌﺞ
ﻴﻌﻁﻲ ﻨﺘﺎﺌﺞ ﺘﻁﺒﻴﻕ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ،ﻓﺎﻟﺠﺩﻭل ﺍﻟﺜﺎﻟﺙ ﻓﻲ ﺍﻟﺸﻜل ﻴﺘﻌﻠﻕ ﺒﻌﺩﺩ ﺇﺸﺎﺭﺍﺕ ﺍﻟﻔﺭﻭﻕ ﺒﻴﻥ ﻗﻴﻡ ﺍﻟﻌﻴﻨﺘﻴﻥ ﺍﻟﻤﻭﺠﺒﺔ ﻭﺍﻟﺴﺎﻟﺒﺔ ﻭﺍﻟﺼﻔﺭﻴﺔ ،ﺒﻴﻨﻤﺎ ﻴﻌﻁﻲ ﺍﻟﺠﺩﻭل ﺍﻟﺭﺍﺒﻊ
ﻗﻴﻤﺔ p-valueﺍﻟﺘﻲ ﺘﺘﻌﻠﻕ ﺒﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ ﻭﻫﻲ ﻋﺩﺩ ﺍﻹﺸﺎﺭﺍﺕ ﺍﻟﻤﻭﺠﺒﺔ ﻟﻠﻔﺭﻭﻕ
)ﻭﻫﺫﻩ ﺘﺘﺒﻊ ﺘﻭﺯﻴﻊ ﺫﺍﺕ ﺍﻟﺤﺩﻴﻥ( ﻭﺘﺩل ﻫﺫﻩ ﺍﻟﻨﺘﻴﺠﺔ ﻋﻠﻰ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ ﻋﻨﺩ ﻤﺴﺘﻭﻯ ﻤﻌﻨﻭﻴﺔ ﺃﻗل ﻤﻥ ) 0.05ﺤﻴﺕ ﺃﻥ .(p=0.021<0.05
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
243
.2 .3 .6ﺣﺎﻟﺔ اﻟﻌﻴﻨﺎت اﻟﻤﺴﺘﻘﻠﺔ :اﺧﺘﺒﺎر ﻣﺎن وﻳﺘﻨﻲ : Independent samples: Mann-Whitney test : ﻭﻟﺘﻭﻀﻴﺢ ﻜﻴﻔﻴﺔ ﺍﺴﺘﺨﺩﺍﻡ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﺴﻭﻑ ﻨﺴﺘﺨﺩﻡ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﻲ ﺘﻡ
ﺍﺴﺘﺨﺩﺍﻤﻬﺎ ﻓﻲ ﺤﺎﻟﺔ ﺍﺨﺘﺒﺎﺭﺍﺕ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ ﻓﻲ ﺸﻜل ،10-6ﻭﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ
ﻤﻠﻑ ﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻤﻔﺘﻭﺤﹰﺎ ﻓﻲ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data Editorﻓﺈﻨﻪ ﻴﻤﻜﻨﻨﺎ ﺇﺠﺭﺍﺀ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﻜﻤﺎ ﻴﻠﻲ:
• ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ
ﺍﻟﻼﻤﻌﻠﻤﻴﺔ Nonparametric Testsﻭﻤﻨﻬﺎ ﺃﻤﺭ ﺍﻟﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ Independent Samplesﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﻌﻴﻨﺘﻴﻥ ﻤﺴﺘﻘﻠﺘﻴﻥTwo-Independent-
Samples Testsﻜﻤﺎ ﻓﻲ ﺸﻜل 15-6ﺃﺩﻨﺎﻩ .
ﺸﻜل : 15-6ﻨﺎﻓﺫﺓ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻟﻠﻌﻴﻨﺘﻴﻥ ﺍﻟﻤﺴﺘﻘﻠﺘﻴﻥ Two-Independent Samples Tests in Nonparametric Tests
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
244
• ﺍﺨﺘﺭ ﺍﺨﺘﺒﺎﺭ ﻤﺎﻥ ﻭﻴﺘﻨﻲ Mann-Whitney Uﻤﻥ ﺒﻴﻥ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻷﺭﺒﻌﺔ ﺍﻟﻤﺫﻜﻭﺭﺓ ﻓﻲ ﺃﺴﻔل ﺍﻟﻨﺎﻓﺫﺓ ﺤﻴﺙ ﺃﻨﻪ ﺍﻻﺨﺘﺒﺎﺭ ﺍﻟﻭﺤﻴﺩ ﺍﻟﻤﻼﺌﻡ ﻟﻠﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻭﺴﻴﻁﻲ
ﻤﺠﺘﻤﻌﻴﻥ ﻤﻥ ﺒﻴﻥ ﺘﻠﻙ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ،ﻭﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻤﻨﺎﺴﺒﺔ ﻷﻫﺩﺍﻑ ﺃﺨﺭﻯ ﻭﻟﻴﺱ
ﻟﻬﺫﺍ ﺍﻟﻬﺩﻑ ﺒﺎﻟﺘﺤﺩﻴﺩ.
• ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ ﺍﻟﺴﺎﺒﻘﺔ ﻴﺘﻡ ﺘﺤﺩﻴﺩ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺎﺒﻊ )ﺃﻭ ﻤﺘﻐﻴﺭ ﺍﻻﺨﺘﺒﺎﺭ(
Test
Variable Listﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺭﻯ ﻤﻥ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻫﻭ ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﻭﺴﻴﻁ ﺍﻟﻭﻗﺕ ﺍﻟﻼﺯﻡ ﻟﺘﺤﺩﻴﺩ ﺍﻟﻜﻠﻤﺎﺕ ﻟﻠﻁﻔل Recognition Timeﻭﻤﻥ ﺜﻡ ﺇﺯﺍﺤﺘﻪ
ﺇﻟﻰ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﺒﺎﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﺎﺒﻌﺔ ﻋﻠﻰ ﺍﻟﻴﻤﻴﻥ ﺒﻭﺍﺴﻁﺔ ﺍﻟﺴﻬﻡ. • ﻜﺫﻟﻙ ﻴﺘﻡ ﺘﺤﺩﻴﺩ ﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ Grouping Variableﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
ﻓﻲ ﺍﻟﺠﻬﺔ ﺍﻟﻴﺴﺭﻯ ﻤﻥ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻫﻭ ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﺠﻬﺔ ﺍﻟﺸﺎﺸﺔ Left-Right Identifier
ﻭﻤﻥ ﺜﻡ ﺇﺯﺍﺤﺘﻪ ﺇﻟﻰ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﺒﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﺼﻨﻴﻑ ﻋﻠﻰ ﻴﻤﻴﻥ ﻭﺃﺴﻔل ﺍﻟﻨﺎﻓﺫﺓ
ﺒﻭﺍﺴﻁﺔ ﺍﻟﺴﻬﻡ ،ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺴﻴﻅﻬﺭ ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ) lftrghtﻭﻟﻴﺱ ﺩﻟﻴﻠﻪ( ﻓﻲ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﻭﺘﻘﺎﺒﻠﻪ ﻋﻼﻤﺎﺕ ﺍﻻﺴﺘﻔﻬﺎﻡ ؟ ؟ ،ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻻﺒﺩ ﻤﻥ ﺘﻌﺭﻴﻑ
ﻗﻴﻡ ﺍﻟﻤﺠﻤﻭﻋﺎﺕ )ﺍﻟﻌﻴﻨﺎﺕ( ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺘﻐﻴﺭ ﻭﺫﻟﻙ ﺒﺎﻟﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺤﻭﺍﺭ
ﺘﻌﺭﻴﻑ ﺍﻟﻤﺠﻤﻭﻋﺎﺕ Define Groupsﺍﻟﻤﻘﺎﺒل ﻟﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ ﻭﻓﺘﺢ ﻨﺎﻓﺫﺓ ﺘﻌﺭﻴﻑ ﻤﺠﻤﻭﻋﺎﺕ ﺍﻟﻌﻴﻨﺎﺕ Define Groupsﻟﻭﻀﺢ ﺩﻟﻴل ﻜل ﻤﻥ ﺍﻟﻌﻴﻨﺘﻴﻥ ،ﻭﻓﻲ ﻤﺜﺎﻟﻨﺎ ﻓﻘﺩ
ﺘﻡ ﺘﻌﺭﻴﻑ ﺩﻟﻴل ﺍﻟﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﺒﺎﻟﺭﻗﻡ 1ﻭﺍﻟﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ﺒﺎﻟﺭﻗﻡ 2ﻓﻲ ﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ ﻭﻫﻭ ﺠﻬﺔ ﺍﻟﺸﺎﺸﺔ . Left-Right Identifier
•
ﻴﺘﻡ ﺇﻋﻁﺎﺀ ﺩﻟﻴل ﺍﻟﻌﻴﻨﺔ ﺍﻷﻭﻟﻰ ﺃﻤﺎﻡ Group 1ﻭﺩﻟﻴل ﺍﻟﻌﻴﻨﺔ ﺍﻟﺜﺎﻨﻴﺔ ﺃﻤﺎﻡ Group
2ﻓﻲ ﺘﻠﻙ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻤﻥ ﺜﻡ ﻴﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻻﺴﺘﻤﺭﺍﺭ Continueﻓﻴﻅﻬﺭ ﺍﻟﺭﻗﻤﻴﻥ 1ﻭ 2ﺃﻤﺎﻡ ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﻓﻲ ﻨﺎﻓﺫﺓ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻟﻌﻴﻨﺘﻴﻥ ﻤﺴﺘﻘﻠﺘﻴﻥ Two-
Independent-Samples Testsﻜﻤﺎ ﻓﻲ ﺸﻜل 15-6ﺃﻋﻼﻩ.
( ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ6)
245
Two-Independent- ﺍﻵﻥ ﻓﻲ ﻨﺎﻓﺫﺓ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﻌﻴﻨﺘﻴﻥ ﻤﺴﺘﻘﻠﺘﻴﻥ
•
ﻹﻨﻬﺎﺀOK ﻴﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺘﻨﻔﻴﺫ15-6 ﻜﻤﺎ ﻓﻲ ﺸﻜلSamples Tests
.ﺍﻟﻤﻬﻤﺔ ﻭﺘﻨﻔﻴﺫ ﺃﻤﺭ ﺇﺠﺭﺍﺀ ﺍﻻﺨﺘﺒﺎﺭ ﺍﻟﻤﻁﻠﻭﺏ
.(16-6 ﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﻭﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺍﻟﻨﺘﺎﺌﺞ )ﺸﻜلOK • ﺍﺨﺘﺭ ﺍﻵﻥ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ Mann-Whitney Test ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻤﻥ ﺘﻨﻔﻴﺫ ﺃﻤﺭ ﺍﺨﺘﺒﺎﺭ ﻤﺎﻥ ﻭﻴﺘﻨﻲ: 16-6 ﺸﻜل ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻟﻠﻌﻴﻨﺘﻴﻥ ﺍﻟﻤﺴﺘﻘﻠﺘﻴﻥ NPar Tests Mann-Whitney Test
Ranks Left Right Indicator Recognition Time
Mean Rank
N
Sum of Ranks
1
10
11.30
113.00
2
10
9.70
97.00
Total
20
Test Statisticsb Recognition Time Mann-Whitney U
42.000
Wilcoxon W
97.000
Z
-.605
Asymp. Sig. (2-tailed)
.545
Exact Sig. [2*(1-tailed Sig.)]
.579
a
a. Not corrected for ties. b. Grouping Variable: Left Right Indicator
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
246
ﻭﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺸﻜل 16-6ﺍﻟﺴﺎﺒﻕ ﻨﺴﺘﻁﻴﻊ ﺃﻥ ﻨﻼﺤﻅ ﺃﻥ ﺍﻟﺠﺩﻭل ﺍﻷﻭل ﻴﺤﺘﻭﻱ ﻋﻠﻰ ﻤﺠﻤﻭﻉ ﺍﻟﺭﺘﺏ Ranksﻟﻜل ﻤﻥ ﺍﻟﻤﺸﺎﻫﺩﺍﺕ ﻋﻠﻰ ﻴﻤﻴﻥ ﻭﻋﻠﻰ ﻴﺴﺎﺭ ﺍﻟﺸﺎﺸﺔ ،ﻭﻴﺤﺘﻭﻱ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻋﻠﻰ ﻗﻴﻡ ﺩﻭﺍل ﺍﻹﺤﺼﺎﺀ ﻻﺨﺘﺒﺎﺭﺍﺕ ﻤﺨﺘﻠﻔﺔ
ﻤﻥ ﺒﻴﻨﻬﺎ ﺍﺨﺘﺒﺎﺭ ﻤﺎﻥ ﻭﻴﺘﻨﻲ Mann-Whitney U Testﻭﻗﻴﻡ p-valueﺍﻟﺘﻘﺭﻴﺒﻴﺔ
ﺍﻟﻤﺼﺎﺤﺒﺔ ﻟﻬﺎ )) (Asymp. Sig. (2(tailedﻭﺍﻟﺘﻲ ﺘﺒﺩﻭ ﻓﻲ ﺍﻟﻨﺘﺎﺌﺞ ﺃﻜﺒﺭ ﻤﻥ 0.05
ﻤﻤﺎ ﻴﺅﻜﺩ ﺍﻟﻨﺘﻴﺠﺔ ﺍﻟﺴﺎﺒﻘﺔ )ﻓﻲ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺴﺘﻘﻠﺔ( ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻏﻴﺭ ﻤﻌﻨﻭﻱ،
ﺃﻱ ﻻ ﻴﻭﺠﺩ ﻓﺭﻕ ﻤﻌﻨﻭﻱ ﺒﻴﻥ ﻭﻀﻊ ﺍﻟﻜﻠﻤﺎﺕ ﻋﻠﻰ ﺠﻬﺘﻲ ﺍﻟﺸﺎﺸﺔ ،ﻭﺒﺎﻟﺘﺎﻟﻲ ﻴﻤﻜﻥ ﺘﻠﺨﻴﺹ ﺍﻟﻨﺘﻴﺠﺔ ﻜﻤﺎ ﻴﻠﻲ: ﻏﻴﺭ ﻤﻌﻨﻭﻱ Z = -0.605 ; Asymp. Sig. (2(tailed) = 0.545; NS
ﻴﺠﺩﺭ ﺒﺎﻟﺫﻜﺭ ﻫﻨﺎ ﺇﻟﻰ ﺃﻥ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻹﺨﺘﺒﺎﺭ Wﺍﻟﻤﺫﻜﻭﺭﺓ ﻓﻲ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ
ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﺃﻤﺎ ﺍﺴﻡ ﻭﻴﻠﻜﻭﻜﺴﻥ Wilcoxon Wﻫﻲ ﻋﺒﺎﺭﺓ ﻋﻥ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﺨﺘﺒﺎﺭ ﻤﺎﻥ ﻭﻴﺘﻨﻲ ﺍﻟﻤﺼﺤﺤﺔ ﺍﻟﺘﻲ ﺍﻗﺘﺭﺤﻬﺎ ﻭﻴﻠﻜﻭﻜﺴﻥ ،ﻭﻫﻲ ﺘﺅﺩﻱ ﻏﺎﻟﺒﹰﺎ ﺇﻟﻰ ﻨﻔﺱ ﻨﺘﻴﺠﺔ
ﺍﺨﺘﺒﺎﺭ ﻤﺎﻥ ﻭﻴﺘﻨﻲ ،ﻭﻟﺫﺍ ﻴﺴﻤﻰ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﻓﻲ ﺒﻌﺽ ﺍﻟﻤﺭﺍﺠﻊ ﺍﺨﺘﺒﺎﺭ ﻭﻴﻠﻜﻭﻜﺴﻥ ﻤﺎﻥ ﻭﻴﺘﻨﻲ ، Wilcoxon-Mann-Whitney Testﻭﻫﻭ ﻴﺨﺘﻠﻑ ﻋﻥ ﺍﺨﺘﺒﺎﺭ
ﻭﻴﻠﻜﻭﻜﺴﻥ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
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.4 .6ﺗﻄﺒﻴﻘﺎت Applications :
.1 .4 .6ﺣﺎﻟﺔ اﻻﺧﺘﺒﺎرات اﻟﻤﺘﻌﻠﻘﺔ ﺑﻌﻴﻨﺔ واﺣﺪة : The case of One-Sample Tests : ﻓﻲ ﻫﺫﺍ ﺍﻟﻔﺼل ﺘﻡ ﺘﻭﻀﻴﺢ ﺠﻤﻴﻊ ﺠﻭﺍﻨﺏ ﺍﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻔﺭﻀﻴﺎﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ
ﺒﺎﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ ،ﻭﻟﻜﻥ ﻫﻨﺎﻙ ﺤﺎﻻﺕ ﺘﺘﻌﻠﻕ ﺒﺎﺨﺘﺒﺎﺭ ﻓﺭﻀﻴﺎﺕ ﺤﻭل ﻤﺘﻭﺴﻁ ﻤﺠﺘﻤﻊ ﻭﺍﺤﺩ ،ﻓﻴﻜﻭﻥ ﻟﺩﻴﻨﺎ ﻋﻴﻨﺔ ﻭﺍﺤﺩﺓ ﻤﻥ ﺍﻟﻤﺸﺎﻫﺩﺍﺕ ﻭﻴﻜﻭﻥ ﺍﻟﻬﺩﻑ ﻫﻭ
ﺍﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﺍﻟﺘﻲ ﺘﻨﺹ ﻋﻠﻰ ﺃﻥ ﺍﻟﻌﻴﻨﺔ ﺴﺤﺒﺕ ﻤﻥ ﻤﺠﺘﻤﻊ ﺒﻭﺴﻁ ﺫﻭ
ﻗﻴﻤﺔ ﻤﺤﺩﺩﺓ ﻭﻗﺩ ﻻ ﺘﻜﻭﻥ ﺼﻔﺭﹰﺍ.
ﻓﺈﺫﺍ ﺍﻓﺘﺭﻀﻨﺎ ﺃﻨﻪ ﻟﺘﺤﺴﻴﻥ ﻤﺴﺘﻭﻯ ﺘﻼﻤﻴﺫ ﻓﺼل ﻤﻌﻴﻥ ﻓﻲ ﻤﺎﺩﺓ ﺍﻟﺭﻴﺎﻀﺎﺕ
ﺘﻘﺭﺭ ﺇﺠﺭﺍﺀ ﺘﺠﺭﺒﺔ ﻋﻠﻰ ﺸﻜل ﺩﻭﺭﺓ ﻗﺼﻴﺭﺓ ﻋﻠﻰ ﻋﻴﻨﺔ ﻋﺸﻭﺍﺌﻴﺔ ﻤﻥ ﺍﻟﺘﻼﻤﻴﺫ ،ﻓﺈﺫﺍ
ﻋﻠﻡ ﺃﻥ ﻤﺘﻭﺴﻁ ﺩﺭﺠﺎﺕ ﻤﺠﺘﻤﻊ ﺍﻟﺘﻼﻤﻴﺫ ﻓﻲ ﻫﺫﺍ ﺍﻟﻔﺼل ﻓﻲ ﺃﺤﺩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻓﻲ
ﺍﻟﺭﻴﺎﻀﻴﺎﺕ ﻗﺒل ﺍﻟﺩﻭﺭﺓ ﻤﺒﺎﺸﺭﺓ ﻫﻭ ،51ﻭﺘﻡ ﺇﻋﻁﺎﺀ ﺍﻟﺘﻼﻤﻴﺫ ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﺍﺨﺘﺒﺎﺭ ﺒﻨﻔﺱ
ﻤﺴﺘﻭﻯ ﺍﻻﺨﺘﺒﺎﺭ ﺍﻟﺴﺎﺒﻕ ﺒﻌﺩ ﺍﻟﺩﻭﺭﺓ ﻤﺒﺎﺸﺭﺓ ،ﻭﻜﺎﻥ ﻴﺅﻤل ﺃﻥ ﺘﺅﺩﻱ ﺍﻟﺩﻭﺭﺓ ﺇﻟﻰ
ﺘﺤﺴﻥ ﻤﻠﺤﻭﻅ ﻓﻲ ﻤﺘﻭﺴﻁ ﺩﺭﺠﺎﺕ ﺠﻤﻴﻊ ﺍﻟﺘﻼﻤﻴﺫ ﺍﻟﺫﻴﻥ ﻴﺤﻀﺭﻭﻨﻬﺎ ،ﻭﻟﻜﻥ ﺍﻟﻨﺘﺎﺌﺞ ﺃﺸﺎﺭﺕ ﺇﻟﻰ ﺃﻥ ﻤﺘﻭﺴﻁ ﺩﺭﺠﺎﺕ ﺍﻟﺘﻼﻤﻴﺫ ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﺒﻌﺩ ﺍﻟﺩﻭﺭﺓ ﻗﺩ ﺒﻠﻐﺕ ،60ﻭﻟﻬﺫﺍ
ﻨﻭﺩ ﺍﺨﺘﺒﺎﺭ ﻤﺎ ﺇﺫﺍ ﻜﺎﻥ ﻫﺫﺍ ﺍﻟﺘﺤﺴﻥ ﻤﻌﻨﻭﻱ )ﺫﻭ ﺩﻻﻟﺔ( ﻭﻴﻌﺯﻯ ﺇﻟﻰ ﺘﻠﻙ ﺍﻟﺩﻭﺭﺓ ﻭﻟﻴﺱ ﺇﻟﻰ ﺍﻟﻌﺸﻭﺍﺌﻴﺔ ،ﻭﻟﻬﺫﺍ ﺍﻟﻐﺭﺽ ﻓﺈﻥ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺴﺘﻨﺹ ﻋﻠﻰ ﺃﻥ ﻤﺘﻭﺴﻁ ﺩﺭﺠﺎﺕ ﺠﻤﻴﻊ ﺍﻟﺘﻼﻤﻴﺫ ﺍﻟﺫﻴﻥ ﻴﺤﻀﺭﻭﻥ ﺍﻟﺩﻭﺭﺓ ﻻ ﻴﺨﺘﻠﻑ ﻋﻥ .51 ﻓﺈﺫﺍ ﻜﺎﻨﺕ ﻟﺩﻴﻨﺎ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻋﻥ ﺩﺭﺠﺎﺕ ﺍﻟﺘﻼﻤﻴﺫ ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﻭﺘﻡ ﺘﺨﺯﻴﻨﻬﺎ ﻓﻲ ﻤﻠﻑ
ﻓﺈﻨﻪ ﻴﻤﻜﻨﻨﺎ ﺇﺠﺭﺍﺀ ﺍﻻﺨﺘﺒﺎﺭ ﺒﺴﻬﻭﻟﺔ ﺒﺎﺴﺘﺨﺩﺍﻡ ﻨﻅﺎﻡ SPSSﻜﻤﺎ ﻴﻠﻲ:
ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ Analyzeﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﺔ ﻟﻨﻅﺎﻡ SPSS
ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﺎﺕ Compare Meansﻭﻤﻨﻬﺎ ﺇﻟﻰ ﺍﻷﻤﺭ ﺍﺨﺘﺒﺎﺭ t
ﻟﻠﻌﻴﻨﺔ ﺍﻟﻭﺍﺤﺩﺓ ،One-Sample T Testﻭﻫﺫﺍ ﺍﻷﻤﺭ ﺴﻴﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺔ
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
248
ﺍﻟﻭﺍﺤﺩﺓ One-Sample T Testﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل 17-6ﺃﺩﻨﺎﻩ ،ﻭﺒﻬﺎ ﻴﺘﻡ ﺇﺩﺨﺎل ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﻭﻫﻭ ﺍﻟﺩﺭﺠﺔ Mark
ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﺎﺒﻌﺔ )Test Variable(s
ﻭﺇﺩﺨﺎل ﻗﻴﻤﺔ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﻟﻠﻤﺘﻭﺴﻁ ،Test Valueﻭﻫﻲ ﻓﻲ ﺤﺎﻟﺘﻨﺎ 51ﻜﻤﺎ
ﺒﺎﻟﺸﻜل ، 17-6ﺜﻡ ﺍﻟﻀﻐﻁ ﻋﻠﻰ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﻭﺍﻟﻭﺼﻭل ﺇﻟﻰ ﺍﻟﻨﺘﺎﺌﺞ ﻜﻤﺎ ﻓﻲ ﺸﻜل 18-6ﺃﺩﻨﺎﻩ.
ﺸﻜل : 17-6ﻨﺎﻓﺫﺓ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺔ ﺍﻟﻭﺍﺤﺩﺓ .One-Sample T Test
ﻭﻴﺒﻴﻥ ﺍﻟﺠﺩﻭل ﺍﻷﻭل ﻓﻲ ﺍﻟﻨﺘﺎﺌﺞ ﺘﻘﺩﻴﺭﺍﺕ ﻟﻠﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ ﻤﻥ ﺍﻟﻌﻴﻨﺔ ﻭﻫﻲ ﻋﺩﺩ ﺍﻟﻘﻴﻡ 20ﻭﺍﻟﻤﺘﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ 60ﻭﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ 15.82ﻭﺍﻟﺨﻁﺄ
ﺍﻟﻤﻌﻴﺎﺭﻱ ﻟﻠﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ ، 3.54ﻭﻴﺒﻴﻥ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﺨﺘﺒﺎﺭ tﻭﻫﻲ 2.545ﻭﺩﺭﺠﺎﺕ ﺤﺭﻴﺘﻬﺎ 19ﻭﻗﻴﻤﺔ p-valueﺍﻟﻤﺼﺎﺤﺒﺔ ﻟﻬﺎ 0.020ﺍﻷﻤﺭ ﺍﻟﺫﻱ
ﻴﺩل ﻋﻠﻰ ﺃﻥ ﻫﻨﺎﻙ ﺍﺨﺘﻼﻑ ﻤﻌﻨﻭﻱ ﺒﻤﺴﺘﻭﻯ ﻤﻌﻨﻭﻴﺔ ﺃﻗل ﻤﻥ ، 0.05ﺃﻱ ﺃﻥ ﺍﻟﺩﻭﺭﺓ
ﻟﻬﺎ ﺘﺄﺜﻴﺭ ﻤﻌﻨﻭﻱ ﻓﻲ ﺘﺤﺴﻴﻥ ﻤﺴﺘﻭﻯ ﺍﻟﺘﻼﻤﻴﺫ ،ﻫﺫﻩ ﺍﻟﻨﺘﻴﺠﺔ ﺘﺅﻜﺩﻫﺎ ﺍﻟﻨﺘﺎﺌﺞ ﺍﻹﻀﺎﻓﻴﺔ ﺍﻟﺘﻲ ﺘﺘﻌﻠﻕ ﺒﻔﺘﺭﺓ 95%ﺜﻘﺔ ﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁ ﺍﻟﺩﺭﺠﺎﺕ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ ﻭﻗﻴﻤﺔ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ ﻟﻠﻤﺘﻭﺴﻁ Test Valueﻭﻫﻲ ) 1.6ﻭ ،(16.4ﻭﻫﺫﻩ ﺍﻟﻔﺘﺭﺓ ﻻ
ﺘﺤﺘﻭﻱ ﺍﻟﺼﻔﺭ ﺒﺩﺍﺨﻠﻬﺎ ﻤﻤﺎ ﻴﺩل ﻋﻠﻰ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
249
ﺸﻜل : 18-6ﻜﺸﻑ ﻨﺘﺎﺌﺞ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺔ ﺍﻟﻭﺍﺤﺩﺓ Listings of the results of One-Samples T Test T-Test One-Sample Statistics Std. Error Mean
Std. Deviation
3.54
15.82
N
Mean 60.00
Marks
20
One-Sample Test Test Value = 51 95% Confidence nterval of the Difference Upper 16.40
Lower 1.60
Sig. Mean (2-tailed) Difference 9.00
.020
df 19
t 2.545
Marks
.2 .4 .6اﺧﺘﺒﺎر اﻟﻔﺮﺿﻴﺎت اﻟﻤﺘﻌﻠﻘﺔ ﺑﻨﺴﺐ اﻟﺤﺪوث : Tests Concerning Proportions: ﻓﻲ ﺍﻷﻗﺴﺎﻡ ﺍﻟﺴﺎﺒﻘﺔ ﻤﻥ ﻫﺫﺍ ﺍﻟﻔﺼل ﺘﻡ ﺍﻟﺘﻌﺎﻤل ﺒﻁﺭﻴﻘﺔ ﻤﻔﺼﻠﺔ ﻤﻊ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ
ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﻤﺘﻭﺴﻁﺎﺕ ﺍﻟﻤﺠﺘﻤﻌﺎﺕ ﻭﻓﻲ ﺍﻟﻨﻬﺎﻴﺔ ﺘﻡ ﺍﻟﺘﻌﺭﺽ ﺇﻟﻰ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺘﻲ ﻴﺘﻡ
ﺍﻟﺘﻌﺎﻤل ﺒﻬﺎ ﻓﻲ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﻤﺘﻭﺴﻁ ﻤﺠﺘﻤﻊ ﻭﺍﺤﺩ ،ﻭﻫﻨﺎ ﻻﺒﺩ ﺃﻥ ﻨﺘﻌﺭﺽ
ﺇﻟﻰ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﺘﻲ ﺘﺘﻌﻠﻕ ﺒﻨﺴﺏ ﺍﻟﺤﺩﻭﺙ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ.
ﻓﺈﺫﺍ ﻜﺎﻥ ﻟﺩﻴﻨﺎ ﻋﻴﻨﺔ ﻤﻥ ﺍﻷﺸﺨﺎﺹ ﺘﻡ ﺍﻻﺴﺘﻔﺴﺎﺭ ﻤﻨﻬﻡ ﺤﻭل ﺭﺃﻴﻬﻡ ﻓﻲ
ﻤﺸﺭﻭﻉ ﻗﺎﻨﻭﻥ ﻤﻌﻴﻥ ﻋﻠﻰ ﺃﻥ ﺘﻜﻭﻥ ﺍﻹﺠﺎﺒﺔ ﻫﻲ ﺃﺤﺩ ﺍﻹﺠﺎﺒﺎﺕ "ﻤﻭﺍﻓﻕ" ﻭ "ﻏﻴﺭ
ﻤﻭﺍﻓﻕ" ﺃﻭ "ﻨﻌﻡ" ﻭ "ﻻ" ﻓﺈﻨﻪ ﻟﻠﺘﻌﺎﻤل ﻤﻊ ﻨﺴﺒﺔ ﺍﻟﻤﻭﺍﻓﻘﻴﻥ ﺃﻭ ﺍﻟﺫﻴﻥ ﺃﺠﺎﺒﻭﺍ ﺒﻨﻌﻡ ﻻ ﺒﺩ
ﻤﻥ ﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺇﻟﻰ ﺍﻟﺤﺎﺴﻭﺏ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﺘﺎﻟﻴﺔ:
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
250
ﻴﻌﻁﻰ ﺍﻟﺫﻴﻥ ﺃﺠﺎﺒﻭﺍ "ﻨﻌﻡ" ﺍﻟﻘﻴﻤﺔ ،1ﻭﻴﻌﻁﻰ ﺍﻟﺫﻴﻥ ﺃﺠﺎﺒﻭﺍ "ﻻ" ﺍﻟﻘﻴﻤﺔ ، 0ﻭﺫﻟﻙ ﻓﻲ ﻤﺘﻐﻴﺭ ﻜﻤﻲ ﺠﺩﻴﺩ ﻴﻤﻜﻥ ﺃﻥ ﻴﻌﺭﻑ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺃﻤﺭ ﺍﻟﺘﺼﻨﻴﻑ Recodeﺃﻭ ﻤﻨﺫ ﺍﻟﺒﺩﺍﻴﺔ ﺒﺈﺩﺨﺎل ﺘﻠﻙ ﺍﻟﻘﻴﻡ ﻜﻘﻴﻡ ﻟﻬﺫﺍ ﺍﻟﻤﺘﻐﻴﺭ ﻤﻊ ﺇﻋﻁﺎﺀ ﺍﻟﺩﻟﻴل "ﻨﻌﻡ" ﻟﻠﻘﻴﻤﺔ 1ﻭﺍﻟﺩﻟﻴل
"ﻻ" ﻟﻠﻘﻴﻤﺔ ، 0ﻭﺒﻬﺫﻩ ﺍﻟﻁﺭﻴﻘﺔ ﺴﻭﻑ ﻴﻜﻭﻥ ﻋﺩﺩ ﻤﻥ ﺃﺠﺎﺒﻭﺍ "ﻨﻌﻡ" ﻴﺴﺎﻭﻱ ﻤﺠﻤﻭﻉ ﻗﻴﻡ
ﻫﺫﺍ ﺍﻟﻤﺘﻐﻴﺭ ﻭﺒﺎﻟﺘﺎﻟﻲ ﺍﻟﻨﺴﺒﺔ ﻓﻲ ﺍﻟﻌﻴﻨﺔ ﻤﻘﺩﺭﺓ ﺒﺎﻟﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ ﻟﻬﺫﻩ ﺍﻟﻌﻴﻨﺔ ،ﻭﺴﻭﻑ
ﺘﺘﺤﻭل ﺒﺎﻟﺘﺎﻟﻲ ﻤﺴﺄﻟﺔ ﺍﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻀﻴﺎﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺎﻟﻨﺴﺒﺔ ﻭﺒﺎﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻨﺴﺒﺘﻲ
ﺤﺩﻭﺙ ﺇﻟﻰ ﻤﺴﺄﻟﺔ ﺍﺨﺘﺒﺎﺭ ﻓﺭﻀﻴﺎﺕ ﺘﺘﻌﻠﻕ ﺒﺎﻟﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ ﻭﺍﻟﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ ﺤﺴﺎﺒﻴﻴﻥ ﻓﻲ ﺍﻟﻤﺠﺘﻤﻊ ،ﻭﻫﺫﻩ ﺍﻟﻁﺭﻴﻘﺔ ﺘﺠﻌل ﺍﺴﺘﺨﺩﺍﻡ ﺠﻤﻴﻊ ﺍﻟﻁﺭﻕ ﺍﻟﺴﺎﺒﻘﺔ ﺍﻟﻤﺘﻌﻠﻘﺔ
ﺒﺎﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻭﺴﻁﻴﻥ ﻤﻤﻜﻨﺔ ﻟﻠﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﺘﻲ ﺘﺤﺘﻭﻱ ﻋﻠﻰ ﺍﻟﻘﻴﻡ 0ﻭ 1ﻓﻘﻁ .
ﻭﺭﻏﻡ ﺫﻟﻙ ﻓﻬﻨﺎﻙ ﺘﻁﻭﺭﺍﺕ ﻭﻁﺭﻕ ﺇﺤﺼﺎﺌﻴﺔ ﻤﺘﻁﻭﺭﺓ ﻭﺘﻬﺘﻡ ﻓﻘﻁ ﺒﺎﻟﻁﺭﻕ
ﺍﻟﺘﻲ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻤﻬﺎ ﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻭﺼﻔﻴﺔ ﺍﻟﺘﻲ ﺘﺄﺨﺫ ﻗﻴﻤﺘﻴﻥ ﻓﻘﻁ ) 0ﻭ (1
dichotomous qualitative variablesﻭﺘﻌﺒﺭﺍﻥ ﻋﻥ ﻗﻴﻤﺘﻴﻥ ﻓﻘﻁ ﻴﻤﻜﻥ ﺃﻥ ﻴﺄﺨﺫﻫﻤﺎ ﺍﻟﻤﺘﻐﻴﺭ ﻤﺜل ﻤﻭﺍﻓﻕ ﻭﻏﻴﺭ ﻤﻭﺍﻓﻕ ﺃﻭ ﻨﻌﻡ ﻭﻻ ﺃﻭ ﺸﻔﻲ ﻤﻥ ﺍﻟﻤﺭﺽ ﻭﻟﻡ ﻴﺸﻔﻰ ﺃﻭ ﻁﻌﻡ ﻭﻟﻡ ﻴﻁﻌﻡ ﻭﻫﻜﺫﺍ ...ﻭﻫﺫﻩ ﺍﻟﻁﺭﻕ ﺍﻹﺤﺼﺎﺌﻴﺔ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﻓﻲ ﺍﻟﻐﺎﻟﺏ ﺘﻨﻔﺭﺩ ﺒﺘﺤﻠﻴل ﻤﺜل
ﻫﺫﻩ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻭﻤﻥ ﺒﻴﻨﻬﺎ ﺍﺨﺘﺒﺎﺭ ﻤﻜﻨﻤﺎﺭ McNemarﻭﻫﻭ ﺃﺤﺩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ
ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﺍﻟﻤﻨﺎﻅﺭﺓ ﻻﺨﺘﺒﺎﺭ tﻟﻠﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired
Samples T Testﻭﺍﻟﺫﻱ ﺘﻡ ﺍﻟﺘﻌﺭﺽ ﺇﻟﻰ ﻜﻴﻔﻴﻔﺔ ﺘﻨﻔﻴﺫﻩ ﻋﻨﺩ ﺍﻟﺤﺩﻴﺙ ﻋﻥ
ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺎﻟﻔﺭﻕ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻴﻥ ﻟﻠﻌﻴﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ Paired ، Samplesﻭﻫﻨﺎﻙ ﺃﻴﻀ ﹰﺎ ﺍﺨﺘﺒﺎﺭ ﺁﺨﺭ ﻭﻫﻭ ﺍﺨﺘﺒﺎﺭ ﺘﻭﺯﻴﻊ ﺫﺍﺕ ﺍﻟﺤﺩﻴﻥ Binomial
Testﻓﻲ ﺤﺎﻟﺔ ﺍﻟﻤﺠﺘﻤﻊ ﺍﻟﻭﺍﺤﺩ ،ﻭﻫﻭ ﺃﻴﻀﹰﺎ ﺍﺨﺘﺒﺎﺭ ﻻﻤﻌﻠﻤﻲ ﻴﺘﻌﻠﻕ ﺒﻨﺴﺒﺔ ﻭﺍﺤﺩﺓ، ﻭﻴﻤﻜﻥ ﺘﻨﻔﻴﺫﻩ ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺍﻟﻼﻤﻌﻠﻤﻴﺔ Nonparametric Testsﻓﻲ ﻗﺎﺌﻤﺔ
ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ Analyzeﻭﺍﺨﺘﻴﺎﺭ ﺍﻷﻤﺭ Binomialﻟﻨﺼل ﺇﻟﻰ ﻨﺎﻓﺫﺓ ﺼﻐﻴﺭﺓ
ﻴﺘﻡ ﺒﻬﺎ ﺘﻌﺭﻴﻑ ﺍﻟﻤﺘﻐﻴﺭ ﻭﻗﻴﻤﺔ ﺍﻟﻨﺴﺒﺔ ﻓﻲ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ.
) (6ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ
251
ﻭﺍﻟﺸﻜﻠﻴﻥ 19-6ﻭ 20-6ﺍﻟﺘﺎﻟﻴﻴﻥ ﻴﻭﻀﺤﺎﻥ ﻨﺘﻴﺠﺘﻲ ﺍﺨﺘﺒﺎﺭ ﺘﺴﺎﻭﻱ ﻨﺴﺒﺔ ﺘﻤﺜﻴل ﺍﻷﻗﻠﻴﺎﺕ ﺒﻨﺴﺒﺔ 0.15ﺒﺎﺴﺘﺨﺩﺍﻡ ﻜل ﻤﻥ ﺍﺨﺘﺒﺎﺭ tﻭﺍﺨﺘﺒﺎﺭ ﺘﻭﺯﻴﻊ ﺫﺍﺕ ﺍﻟﺤﺩﻴﻥ
Binomial Testﻋﻠﻰ ﺒﻴﺎﻨﺎﺕ ﻤﺘﻐﻴﺭ ﺍﻷﻗﻠﻴﺎﺕ minorityﻓﻲ ﻤﻠﻑ employee
، dataﻭﺒﺎﻟﻨﻅﺭ ﺇﻟﻰ ﺘﻠﻙ ﺍﻟﻨﺘﺎﺌﺞ ﻨﺠﺩ ﺃﻨﻨﺎ ﺴﻨﺼل ﺇﻟﻰ ﻨﻔﺱ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻜل ﻤﻥ
ﺍﻻﺨﺘﺒﺎﺭﻴﻥ ،ﻓﻘﺩ ﺤﺼﻠﻨﺎ ﻋﻠﻰ ﺃﻥ ﻨﺴﺒﺔ ﺍﻟﻌﻴﻨﺔ ﻤﺴﺎﻭﻴﺔ 0.22ﻭﻫﻲ ﺘﺨﺘﻠﻑ ﺍﺨﺘﻼﻓﹰﺎ
ﻤﻌﻨﻭﻴﹰﺎ ﻋﻥ ،0.15ﺇﺫ ﺘﺒﻴﻥ ﺍﻟﻨﺘﺎﺌﺞ ﺃﻥ ﻗﻴﻤﺔ p-valueﻓﻲ ﺍﻟﺤﺎﻟﺘﻴﻥ ﺘﻘﺘﺭﺏ ﻤﻥ ﺍﻟﺼﻔﺭ
ﺍﻷﻤﺭ ﺍﻟﺫﻱ ﻴﺩل ﻋﻠﻰ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻱ ﻓﻲ ﺍﻟﺤﺎﻟﺘﻴﻥ.
ﺸﻜل : 19-6ﻜﺸﻑ ﻨﺘﺎﺌﺞ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ tﻟﻠﻌﻴﻨﺔ ﺍﻟﻭﺍﺤﺩﺓ Listings of the Results of One-Samples T Testﻋﻠﻰ ﻤﺘﻐﻴﺭ ﺍﻷﻗﻠﻴﺎﺕ.
T-Test
One-Sample Statistics Std. Error Mean
Std. Deviation
Mean
1.90E-02
.41
.22
N Minority Classification
474
One-Sample Test Test Value = 0.15 95% Confidence Interval of the Difference Upper .11
Lower 3.2E-02
Mean Difference
Sig. )(2-tailed
6.94E-02
.000
df 473
t 3.648
Minority Classification
( ﺍﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﻤﺘﻭﺴﻁﻲ ﻤﺠﺘﻤﻌﻴﻥ6)
252
Listings ﻜﺸﻑ ﻨﺘﺎﺌﺞ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ ﺘﻭﺯﻴﻊ ﺫﺍﺕ ﺍﻟﺤﺩﻴﻥ ﻟﻠﻌﻴﻨﺔ ﺍﻟﻭﺍﺤﺩﺓ: 20-6 ﺸﻜل . ﻋﻠﻰ ﻤﺘﻐﻴﺭ ﺍﻷﻗﻠﻴﺎﺕof the Results of Binomial Test NPar Tests
Descriptive Statistics
N Minority Classification
Mean
474
Std. Deviation Minimum Maximum
.22
.41
0
1
Binomial Test
Category Minority Group 1 No Classification Group 2 Yes Total a. Based on Z Approximation.
N
Asymp. Sig. Observed Test Prop. Prop. (1-tailed)
370
.78
104
.22
474
1.00
.15
a
.000