]†Â<ë^£]<Ø’ËÖ l]Çj¹]<°e<íÎøÃÖ]<ìçÎ<Œ^éÎ Measuring Statistical Association
.1 .11ﻣﻘﺪﻣﺔ .2 .11ﺗﺤﻠﻴﻞ اﻻرﺗﺒﺎط ﺑﻴﻦ ﻇﻮاهﺮ آﻤﻴﺔ .3 .11ﻣﻘﺎﻳﻴﺲ اﻻرﺗﺒﺎط ﻟﻠﺒﻴﺎﻧﺎت اﻟﺘﺮﺗﻴﺒﻴﺔ .4 .11ﻣﻘﺎﻳﻴﺲ اﻟﺘﺮاﺑﻂ ﻓﻲ اﻟﺒﻴﺎﻧﺎت اﻟﻮﺻﻔﻴﺔ
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
372
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
373
]†Â<ë^£]<Ø’ËÖ l]Çj¹]<°e<íÎøÃÖ]<ìçÎ<Œ^éÎ Measuring Statistical Association .1 .11ﻣﻘﺪﻣﺔ: ﻓﻲ ﺍﻟﻔﺼﻭل ﺍﻟﺴﺎﺒﻘﺔ ﻜﺎﻥ ﻤﺤﻭﺭ ﺍﻫﺘﻤﺎﻤﻨﺎ ﻴﺩﻭﺭ ﺤﻭل ﺍﻟﻁﺭﻕ ﺍﻹﺤﺼﺎﺌﻴﺔ
ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺎﻟﻤﻘﺎﺭﻨﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻭﺴﻁﺎﺕ ﺒﻴﻥ ﻭﺩﺍﺨل ﻋﻴﻨﺎﺕ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﻲ ﻴﻤﻜﻥ ﺒل
ﻴﺘﻭﻗﻊ ﺃﻥ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺍﺨﺘﻼﻑ ﺒﻴﻨﻬﺎ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻭﻯ ﺍﻟﻌﺎﻡ ،ﻓﻌﻠﻰ ﺴﺒﻴل ﺍﻟﻤﺜﺎل ﻴﻤﻜﻥ
ﻤﻘﺎﺭﻨﺔ ﻨﺘﺎﺌﺞ ﺍﻟﺫﻜﻭﺭ ﻤﻊ ﻨﺘﺎﺌﺞ ﺍﻹﻨﺎﺙ ﺃﻭ ﺃﺩﺍﺀ ﺍﻟﻤﺘﺩﺭﺒﻴﻥ ﻤﻊ ﺃﺩﺍﺀ ﺍﻟﻐﻴﺭ ﻤﺘﺩﺭﺒﻴﻥ ﺃﻭ
ﺃﺩﺍﺀ ﺍﻷﺸﻭﻟﻴﻴﻥ ﻤﻊ ﺃﺩﺍﺀ ﺍﻟﻌﺎﺩﻴﻴﻥ ﻭﻫﻜﺫﺍ..
ﻭﺍﻵﻥ ﻟﻨﻔﺘﺭﺽ ﺃﻥ ﻟﺩﻴﻨﺎ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﻤﺭﺘﺒﻁﺔ ﻭﺍﻟﺘﻲ ﻴﻤﻜﻥ ﺃﻥ ﺘﻨﺘﺞ
ﻋﻠﻰ ﺴﺒﻴل ﺍﻟﻤﺜﺎل ﻋﻥ ﻁﺭﻴﻕ ﺃﺨﺫ ﻋﻴﻨﺔ ﻤﻥ ﺍﻷﺸﺨﺎﺹ ﺍﻟﺒﺎﻟﻐﻴﻥ ﻭﺇﻋﻁﺎﺌﻬﻡ ﺩﻭﺭﺓ ﻟﻴﺎﻗﺔ ﺒﺩﻨﻴﺔ ،ﻭﻗﺩ ﺃﺨﺫﺕ ﺃﻭﺯﺍﻨﻬﻡ ﻗﺒل ﻭﺒﻌﺩ ﻫﺫﻩ ﺍﻟﺩﻭﺭﺓ ،ﻓﻘﺩ ﻜﺎﻥ ﺍﻫﺘﻤﺎﻤﻨﺎ ﻓﻲ ﺍﻟﻔﺼﻭل ﺍﻟﺴﺎﺒﻘﺔ ﻓﻲ ﻤﺜل ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺤﻭل ﻤﻘﺎﺭﻨﺔ ﻤﺘﻭﺴﻁ ﺃﻭﺯﺍﻥ ﻫﺅﻻﺀ ﺍﻷﺸﺨﺎﺹ ﺒﻌﺩ
ﺍﻟﺩﻭﺭﺓ ﻤﻊ ﻤﺘﻭﺴﻁ ﺃﻭﺯﺍﻨﻬﻡ ﻗﺒل ﺍﻟﺩﻭﺭﺓ ﻭﺫﻟﻙ ﻟﻤﻌﺭﻓﺔ ﺃﺜﺭ ﻫﺫﻩ ﺍﻟﺩﻭﺭﺓ ﻋﻠﻰ ﺃﻭﺯﺍﻥ
ﻫﺅﻻﺀ ﺍﻷﺸﺨﺎﺹ ،ﻭﻟﻜﻥ ﻤﻥ ﺍﻟﻤﺘﻭﻗﻊ ﺃﻥ ﺘﻅﻬﺭ ﻤﺜل ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻤﻼﻤﺢ ﺃﺨﺭﻯ،
ﻓﺎﻟﺸﺨﺹ ﺍﻷﺜﻘل ﻭﺯﻨﹰﺎ ﻗﺒل ﺍﻟﺩﻭﺭﺓ ﻗﺩ ﻴﻅل ﺍﻷﺜﻘل ﻭﺯﻨﹰﺎ ﺒﻌﺩ ﺍﻟﺩﻭﺭﺓ ﻭﺍﻟﻌﻜﺱ ﻗﺩ ﻴﺒﻘﻰ
ﺍﻟﺸﺨﺹ ﺍﻷﻗل ﻭﺯﻨﹰﺎ ﻗﺒل ﺍﻟﺩﻭﺭﺓ ﺃﻗل ﻭﺯﻨﹰﺎ ﺒﻌﺩﻫﺎ ﺩﺍﺨل ﻫﺫﻩ ﺍﻟﻤﺠﻤﻭﻋﺔ ﻤﻥ
ﺍﻷﺸﺨﺎﺹ ،ﻭﺒﺎﻟﻤﺜل ﻓﺈﻥ ﺍﻷﺸﺨﺎﺹ ﻓﻲ ﻭﺴﻁ ﺍﻟﻤﺠﻤﻭﻋﺔ ﻗﺒل ﺍﻟﺩﻭﺭﺓ ﺴﻴﺒﻘﻭﻥ ﻓﻲ
ﻭﺴﻁ ﺍﻟﻤﺠﻤﻭﻋﺔ ﺒﻌﺩﻫﺎ ،ﻭﻫﺫﺍ ﺍﻻﺘﺠﺎﻩ ﻫﻭ ﻤﺎ ﻴﻁﻠﻕ ﻋﻠﻴﻪ ﻭﺠﻭﺩ ﺍﺭﺘﺒﺎﻁ correlation
ﺃﻭ ﺘﺭﺍﺒﻁ associationﺒﻴﻥ ﺃﻭﺯﺍﻥ ﺍﻷﺸﺨﺎﺹ ﻗﺒل ﻭﺒﻌﺩ ﺍﻟﺩﻭﺭﺓ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
374
ﺇﻥ ﻭﺠﻭﺩ ﺘﺭﺍﺒﻁ ﺇﺤﺼﺎﺌﻲ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﻴﻤﻜﻥ ﺃﻥ ﻴﻅﻬﺭ ﺒﻭﻀﻭﺡ ﻋﻨﺩ ﻭﺼﻑ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻋﻥ ﻁﺭﻴﻕ ﺘﻤﺜﻴﻠﻬﺎ ﺒﻴﺎﻨﻴﹰﺎ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ) Scatter plotﺃﻨﻅﺭ
ﺍﻟﻔﺼل ﺍﻟﺨﺎﻤﺱ( ﻓﺈﺫﺍ ﺘﺒﻴﻥ ﻤﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﺃﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﻫﺫﺍ ﺍﻟﺸﻜل ﻤﺘﺩﻓﻘﺔ ﻓﻲ ﻤﺠﺭﻯ ﺤﻭل ﺨﻁ ﻤﺴﺘﻘﻴﻡ ﻓﺈﻨﻪ ﻴﻘﺎل ﻋﻨﺩﺌﺫ ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﺨﻁﻴﺔ
Linear
relationshipﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ،ﻭﺇﺫﺍ ﻜﺎﻥ ﻤﻴل ﻫﺫﺍ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﻤﻭﺠﺏ ﻓﺈﻨﻪ ﻴﻘﺎل ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﻁﺭﺩﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ Positively correlatedﺃﻤﺎ ﺇﺫﺍ ﻜﺎﻥ ﺍﻟﻤﻴل ﺴﺎﻟﺏ
ﻓﺈﻨﻪ ﻴﻘﺎل ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﻋﻜﺴﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ، Negatively correlatedﻭﻜﻠﻤﺎ ﻜﺎﻨﺕ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻗﺭﻴﺒﺔ ﻤﻥ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ )ﻤﺘﺩﻓﻘﺔ ﻓﻲ ﺍﻟﺸﻜل ﻓﻲ ﻤﺠﺭﻯ ﻀﻴﻕ( ﻓﺈﻥ
ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ﺘﻜﻭﻥ ﺃﻗﻭﻯ ،ﻭﻜﻠﻤﺎ ﺍﺒﺘﻌﺩﺕ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻋﻥ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ )ﻤﺘﺩﻓﻘﺔ ﻓﻲ
ﺍﻟﺸﻜل ﻓﻲ ﻤﺠﺭﻯ ﻤﺘﺴﻊ( ﻜﻠﻤﺎ ﻀﻌﻔﺕ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ،ﻭﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﻤﻨﺘﺸﺭﺓ ﻓﻲ ﺸﻜل
ﺩﺍﺌﺭﻱ ﺘﺩل ﻋﻠﻰ ﻋﺩﻡ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ.
ﻓﻲ ﻫﺫﺍ ﺍﻟﻔﺼل ﺴﻨﻬﺘﻡ ﺒﻘﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻭﻟﻜﻥ ﻤﻥ ﺍﻟﻤﻤﻜﻥ ﺇﺫﺍ
ﻤﺎ ﻋﻠﻤﻨﺎ ﺒﻭﺠﻭﺩ ﻋﻼﻗﺔ ﻗﻭﻴﺔ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﺃﻭ ﺃﻜﺜﺭ ﻓﺈﻥ ﻴﻤﻜﻥ ﺘﻘﺩﻴﺭ ﻫﺫﻩ ﺍﻟﻌﻼﻗﺔ
ﺍﻟﺨﻁﻴﺔ ﻭﺇﻴﺠﺎﺩ ﻤﻌﺎﺩﻟﺔ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﺍﻟﺫﻱ ﻴﺸﻜل ﺃﻓﻀل ﺨﻁ ﻤﺴﺘﻘﻴﻡ ﻴﻤﺜل ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﻫﺫﺍ ﻤﺎ ﻴﺴﻤﻰ ﺒﺄﺴﻠﻭﺏ ﺍﻻﻨﺤﺩﺍﺭ Regressionﺍﻟﺫﻱ ﺴﻴﻜﻭﻥ ﻤﻭﻀﻭﻉ
ﺍﻫﺘﻤﺎﻤﻨﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ ﻋﺸﺭ ،ﻭﻴﺘﻭﻗﻊ ﻓﻲ ﺍﻟﻌﺎﺩﺓ ﺃﻥ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺍﻨﺤﺭﺍﻓﺎﺕ ﺒﺴﻴﻁﺔ
ﻟﻠﻘﻴﻡ ﻋﻥ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﺍﻟﺫﻱ ﺘﻡ ﺍﺸﺘﻘﺎﻗﻪ ،ﻫﺫﻩ ﺍﻻﻨﺤﺭﺍﻓﺎﺕ ﻴﻁﻠﻕ ﻋﻠﻴﻬﺎ ﺍﻟﺒﻭﺍﻗﻲ
، Residualsﻭﻴﺘﻭﻗﻊ ﻋﺎﺩﺓ ﺃﻥ ﺘﻜﻭﻥ ﻗﻴﻡ ﻫﺫﻩ ﺍﻟﺒﻭﺍﻗﻲ ﺼﻐﻴﺭﺓ ﻭﺃﺼﻐﺭ ﻤﻥ ﺍﻟﻘﻴﻡ ﺍﻷﺼﻠﻴﺔ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻁﺎﻟﻤﺎ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﺨﻁﻴﺔ ﻗﻭﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ.
ﻭﻴﻌﺘﺒﺭ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺃﺤﺩ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ ﻟﻘﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ
ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﻜﻤﻴﻴﻥ ﻗﻴﺎﺴﻴﻴﻥ ،ﻭﺃﻜﺜﺭ ﻤﻌﺎﻤﻼﺕ ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﻌﺭﻭﻓﺔ ﻫﻭ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ Pearson correlation coefficientﻭﻴﺭﻤﺯ ﻟﻪ ﺒﺎﻟﺭﻤﺯ ، rﻭﺃﻫﻤﻴﺘﻪ ﺃﻨﻪ
ﻤﻌﺭﻑ ﺠﻴﺩﹰﺍ ﺒﺤﻴﺙ ﻴﺄﺨﺫ ﻗﻴﻤﹰﺎ ﺘﺘﺭﺍﻭﺡ ﺒﻴﻥ -1ﻭ ، +1ﻭﻜﻠﻤﺎ ﻜﺎﻨﺕ ﻗﻴﻤﺔ ﺍﻟﻤﻌﺎﻤل
ﻗﺭﻴﺒﺔ ﻤﻥ ﺍﻟﻭﺍﺤﺩ ﻤﻭﺠﺒﹰﺎ ﻜﺎﻥ ﺃﻡ ﺴﺎﻟﺏ ﻜﻠﻤﺎ ﻜﺎﻨﺕ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ﺃﻗﻭﻯ ،ﻭﺘﻜﻭﻥ
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
375
ﺍﻟﻌﻼﻗﺔ ﺘﺎﻤﺔ ﺃﻱ ﺠﻤﻴﻊ ﺍﻟﻘﻴﻡ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺘﻘﻊ ﻋﻠﻰ ﺍﻟﺨﻁ ﺍﻟﻤﺴﺘﻘﻴﻡ ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﻤﺴﺎﻭﻴﺔ ﺘﻤﺎﻤﺎ ﻟﻠﻭﺍﺤﺩ ،ﻭﻋﻨﺩﻤﺎ ﻻ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻓﺴﻭﻑ ﺘﻜﻭﻥ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻗﺭﻴﺒﺔ ﻤﻥ ﺍﻟﺼﻔﺭ ﻭﺴﻭﻑ ﺘﻜﻭﻥ ﺍﻟﻘﻴﻡ ﻓﻲ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺃﺸﺒﻪ ﺒﺸﻜل ﺩﺍﺌﺭﻱ )ﺃﻨﻅﺭ ﺸﻜل .(1-11
ﺸﻜل : 1-11ﺃﺸﻜﺎل ﺍﻻﻨﺘﺸﺎﺭ Scatterplotsﻟﻤﺠﻤﻭﻋﺎﺕ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺘﻭﻀﺢ ﺍﻟﻤﺴﺘﻭﻴﺎﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻟﻼﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ. r=1
r=0 Y
Y
60
26 24
50
22
40
20 30 18 20 16 10
40
20
30
14
0
12
-10
10 40
10
X
20
30
10
X
r = -1
r = +0.8 Y
Y
30
26 24 22
20
20 18 16
10
14 12 0 40
30
X
20
10
10 40
30
20
10
X
ﻭﻴﻤﻜﻥ ﻤﻥ ﺨﻼل ﺍﻟﻨﻅﺭ ﻓﻲ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ scatterplotﺍﻟﺤﺼﻭل ﻋﻠﻰ
ﺍﻟﻔﺎﺌﺩﺘﻴﻥ ﺍﻟﺘﺎﻟﻴﺘﻴﻥ:
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
376
ﻼ ﺍﺭﺘﺒﺎﻁ ﺨﻁﻲ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ،ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻓﺈﻨﻪ .1ﻤﻌﺭﻓﺔ ﻤﺎ ﺇﺫﺍ ﻜﺎﻥ ﻫﻨﺎﻙ ﻓﻌ ﹰ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻡ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺒﺄﻤﺎﻥ ﻭﺤﺴﺎﺒﻪ ﺴﻴﻜﻭﻥ ﻟﻪ ﻤﻌﻨﻰ. .2ﺘﺨﻤﻴﻥ )ﺒﺩﺭﺠﺔ ﻋﺎﻟﻴﺔ ﻤﻥ ﺍﻟﺩﻗﺔ ﺃﺤﻴﺎﻨﹰﺎ( ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻓﻲ ﺤﺎﻟﺔ ﺤﺴﺎﺒﻬﺎ.
ﺒﻤﻌﻨﻰ ﺁﺨﺭ ﻓﺈﻨﻪ ﻤﻥ ﻓﺤﺹ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻓﻘﻁ ﻴﻤﻜﻥ ﺍﺴﺘﻨﺒﺎﻁ ﻗﻭﺓ ﻭﻁﺒﻴﻌﺔ
ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻗﻴﺩ ﺍﻟﺩﺭﺍﺴﺔ ،ﻭﺒﺎﻟﺘﺎﻟﻲ ﺘﺄﺘﻲ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻜﻤﻴﺔ ﺘﺩﻋﻴﻤﹰﺎ ﻟﻠﻔﻜﺭﺓ ﺍﻟﺘﻲ ﺘﻡ ﺘﻜﻭﻴﻨﻬﺎ ﻤﻥ ﺨﻼل ﺍﻟﺭﺴﻡ ﻋﻥ ﻫﺫﻩ ﺍﻟﻌﻼﻗﺔ.
ﻭﻟﻜﻥ ﺍﻟﻌﻜﺱ ﻟﻴﺱ ﺼﺤﻴﺢ ،ﻓﺈﺫﺍ ﺤﺴﺒﺕ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻓﻘﻁ
)ﺒﺩﻭﻥ ﺭﺴﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ( ﻓﺈﻥ ﻫﻨﺎﻙ ﻤﺤﺎﺫﻴﺭ ﺠﻭﻫﺭﻴﺔ ﻋﻨﺩ ﻤﺤﺎﻭﻟﺔ ﺘﻔﺴﻴﺭ ﻗﻴﻤﺘﻪ،
ﻼ ﺃﻥ ﺘﻜﻭﻥ ﻓﺄﺤﻴﺎﻨﹰﺎ ﺘﻜﻭﻥ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻤﻀﻠﻠﺔ ﻟﻠﺤﻘﻴﻘﺔ ،ﻓﻴﻤﻜﻥ ﻤﺜ ﹰ
ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻗﺭﻴﺒﺔ ﻤﻥ ﺍﻟﺼﻔﺭ ﺭﻏﻡ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﻗﻭﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻭﻟﻜﻥ ﻫﺫﻩ ﺍﻟﻌﻼﻗﺔ ﻏﻴﺭ ﺨﻁﻴﺔ ﻭﻫﺫﻩ ﺍﻟﺤﻘﻴﻘﺔ ﻟﻥ ﺘﺘﻀﺢ ﺇﻻ ﻤﻥ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ، ﻭﺍﻟﻌﻜﺱ ،ﻴﻤﻜﻥ ﺃﻻ ﺘﻜﻭﻥ ﻫﻨﺎﻙ ﺃﻱ ﻋﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻭﻟﻜﻥ ﻭﺠﻭﺩ ﻗﻴﻤﺔ ﺸﺎﺫﺓ ﺃﻭ
ﻤﺘﻁﺭﻓﺔ ﻗﺩ ﻴﺅﺩﻱ ﺇﻟﻰ ﻗﻴﻤﺔ ﻜﺒﻴﺭﺓ ﻟﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻗﺩ ﺘﻔﺴﺭ ﻋﻠﻰ ﺃﻥ ﻫﻨﺎﻙ
ﻋﻼﻗﺔ ﻗﻭﻴﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺇﺫﺍ ﻟﻡ ﻨﻨﻅﺭ ﺇﻟﻰ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ .
ﻭﻟﺫﻟﻙ ﻴﺤﺴﻥ ﺩﺍﺌﻤﹰﺎ ﻜﻠﻤﺎ ﺭﻏﺒﻨﺎ ﻓﻲ ﺤﺴﺎﺏ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺃﻥ ﻨﺭﺴﻡ
ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻟﻨﻘﺭﺭ ﺒﻨﺎﺀ ﻋﻠﻴﻪ ﺃﻥ ﻨﻘﺒل ﺃﻭ ﻨﺭﻓﺽ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻨﺎﺘﺠﺔ ﻤﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻗﺒل ﺃﻥ ﻨﻔﺴﺭ ﺘﻠﻙ ﺍﻟﻘﻴﻤﺔ ،ﻭﺒﺎﺨﺘﺼﺎﺭ ﻨﺴﺘﻁﻴﻊ ﺍﻟﻘﻭل ﺃﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ
ﺒﻴﺭﺴﻭﻥ ﻫﻭ ﻤﻘﻴﺎﺱ ﻟﻘﻭﺓ ﻋﻼﻗﺔ ﺨﻁﻴﺔ ﻤﻔﺘﺭﻀﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ،ﻭﺍﻓﺘﺭﺍﺽ ﺍﻟﻌﻼﻗﺔ ﺍﻟﺨﻁﻴﺔ ﻴﺠﺏ ﺃﻥ ﻴﺘﺄﻜﺩ ﻤﻥ ﺨﻼل ﺭﺴﻡ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
377
.2 .11ﺗﺤﻠﻴﻞ اﻻرﺗﺒﺎط ﺑﻴﻦ ﻇﻮاهﺮ آﻤﻴﺔ : Correlational Analysis for Quantitative Data: ﻓﻲ ﺃﺤﺩ ﺍﻟﻤﻌﺎﻫﺩ ﺍﻟﺭﻴﺎﻀﻴﺔ ﺃﻋﺘﻘﺩ ﻤﺩﻴﺭ ﺍﻟﻤﻌﻬﺩ ﺃﻥ ﺇﺠﺎﺩﺓ ﺍﻟﻁﻠﺒﺔ ﻓﻲ ﻟﻌﺒﺔ ﺍﻟﺘﻨﺱ
ﺘﻌﺘﻤﺩ ﻋﻠﻰ ﻗﺩﺭﺘﻬﻡ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ،ﻭﻟﻠﺘﺤﻘﻕ ﻤﻥ ﺼﺤﺔ ﻫﺫﻩ ﺍﻟﻤﻼﺤﻅﺔ ﺃﺨﺫ ﻗﻴﺎﺴﺎﺕ
ﻋﻴﻨﺔ ﻤﻥ ﺍﻟﻁﻠﺒﺔ ﺍﻟﻤﺴﺘﺠﺩﻴﻥ ﻓﻲ ﺃﺤﺩ ﺩﻭﺭﺍﺕ ﺍﻟﺘﻨﺱ ﺘﺘﻌﻠﻕ ﺒﻘﺩﺭﺘﻬﻡ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial coordinationﻭ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ ﻜﺫﻟﻙ ﺃﺨﺫ ﻤﻘﻴﺎﺴﹰﺎ ﻟﻜﻔﺎﺀﺘﻬﻡ
ﻓﻲ ﺍﻟﻠﻌﺏ ، Final Proficiencyﻭﻴﻭﻀﺢ ﺍﻟﺸﻜل 2-11ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﻨﺎﺘﺠﺔ.
ﺸﻜل : 2-11ﺒﻴﺎﻨﺎﺕ ﻋﻴﻨﺔ ﻤﻥ ﺍﻟﻤﺘﺩﺭﺒﻴﻥ ﻓﻲ ﺃﺤﺩ ﺩﻭﺭﺍﺕ ﺍﻟﺘﻨﺱ ﺤﻭل ﻗﺩﺭﺘﻬﻡ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial Coordinationﻭﻜﻔﺎﺀﺘﻬﻡ ﻓﻲ ﻨﻬﺎﻴﺘﻬﺎ Final .Proficiency A set of paired data Final Proficiency
Initial Cordination
Pupil
4
1
1
5
4
2
6
5
3
2
2
4
6
10
5
2
4
6
5
7
7
6
8
8
9
9
9
3
5
10
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
378
ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻴﻤﻜﻥ ﺇﺩﺨﺎﻟﻬﺎ ﻟﻨﻅﺎﻡ SPSSﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﻁﺭﻕ ﺍﻟﺘﻲ ﺘﻡ ﻋﺭﻀﻬﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﻫﺫﺍ ﺍﻟﻜﺘﺎﺏ ﺒﺘﻌﺭﻴﻑ ﺜﻼﺙ ﻤﺘﻐﻴﺭﺍﺕ ﻭﺇﻋﻁﺎﺀ ﺩﻟﻴل ﻟﻜل ﻤﻬﻡ ﻭﺘﺸﻤل ﺭﻗﻡ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﺍﻟﻌﻴﻨﺔ Caseﻭﻗﺩﺭﺘﻪ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial
Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ . Final Proficiency
ﻭﻟﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial
Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ Final Proficiencyﻨﺒﺩﺃ ﺒﺭﺴﻡ
ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatter plotﻟﻠﻅﺎﻫﺭﺘﻴﻥ ﺒﺎﻟﻁﺭﻕ ﺍﻟﺴﺎﺒﻘﺔ ﻋﻥ ﻁﺭﻴﻕ ﺍﺘﺒﺎﻉ ﺍﻟﺨﻁﻭﺍﺕ ﺍﻟﺘﺎﻟﻴﺔ:
• ﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﻟﻨﻅﺎﻡ SPSSﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻟﺭﺴﻭﻤﺎﺕ ﺍﻟﺒﻴﺎﻨﻴﺔ Graphsﻭﻤﻨﻬﺎ ﺍﺨﺘﺭ ﺃﻤﺭ ﺭﺴﻡ ﺃﺸﻜﺎل ﺍﻻﻨﺘﺸﺎﺭ ، Scatterﺴﻭﻑ ﺘﻅﻬﺭ ﻨﺎﻓﺫﺓ ﺍﺨﺘﻴﺎﺭﺍﺕ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ) Scatterplotﻜﻤﺎ ﻓﻲ ﺸﻜل (3-11ﻓﺎﺨﺘﺭ ﺍﻟﺸﻜل ﺍﻟﺒﺴﻴﻁ Simpleﻭﻤﻥ ﺜﻡ
ﺃﻤﺭ ﺍﻟﺘﻌﺭﻴﻑ . Define
ﺸﻜل : 3-11ﻨﺎﻓﺫﺓ ﺍﺨﺘﻴﺎﺭﺍﺕ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatterplot
• ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ ﺍﻟﺠﺩﻴﺩﺓ ﺃﺩﺨل ﺍﺴﻡ ﻤﺘﻐﻴﺭ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ
Initial Coordinationﻓﻲ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ ﺒﺎﻟﻤﺤﻭﺭ ﺍﻷﻓﻘﻲ x-axisﻭﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﻜﻔﺎﺀﺓ ﺍﻟﻤﺘﺩﺭﺏ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ Final Proficiencyﻓﻲ ﺍﻟﻤﺭﺒﻊ ﺍﻟﺨﺎﺹ
ﺒﺎﻟﻤﺤﻭﺭ ﺍﻟﺭﺃﺴﻲ . y-axis
• ﺍﻀﻐﻁ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﻭﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺍﻟﺸﻜل ﺍﻟﻤﻁﻠﻭﺏ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
379
ﻭﺸﻜل 4-11ﻴﺒﻴﻥ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺍﻟﻨﺎﺘﺞ ﻤﻥ ﺘﻨﻔﻴﺫ ﻫﺫﺍ ﺍﻷﻤﺭ ﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ ، Final Proficiencyﻭﻴﺒﻴﻥ ﻫﺫﺍ ﺍﻟﺸﻜل ﺍﺘﺠﺎﻩ ﺨﻁﻲ ﻤﺘﻨﺎﺴﻕ ﺩﻭﻥ ﻭﺠﻭﺩ ﺃﻱ ﻗﻴﻡ ﺸﺎﺫﺓ ﺃﻭ ﻤﺘﻁﺭﻓﺔ.
ﺸﻜل : 4-11ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatterplotﻟﻤﺘﻐﻴﺭﻱ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺘﻬﺎ Final Proficiency
Scatter Plot of Final Tennis Proficiency Against Initial Co-ordination
8
6
Final Proficiency
10
4
2
0 12
10
8
6
4
2
0
Initial Cordination
ﻭﻤﻥ ﺍﻟﻤﻤﻜﻥ ﺘﺼﻨﻴﻑ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﺍﻟﺸﻜل ﺍﻟﺴﺎﺒﻕ ﺒﺈﺩﺨﺎل ﺍﺴﻡ ﻤﺘﻐﻴﺭ ﺍﻟﺘﺼﻨﻴﻑ ﻭﻟﻴﻜﻥ ﺍﻟﺠﻨﺱ sexﺒﺎﻟﻤﺴﺘﻭﻴﻴﻥ ﺫﻜﻭﺭ malesﻭﺇﻨﺎﺙ femalesﻓﻲ ﻨﺎﻓﺫﺓ ﺘﻌﺭﻴﻑ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﻭﺍﺨﺘﻴﺎﺭ ﻤﺭﺒﻊ ﺘﺼﻨﻴﻑ ﺍﻟﻨﻘﺎﻁ Set Markers Byﺤﻴﺙ ﺴﺘﻅﻬﺭ ﺍﻟﻨﻘﺎﻁ ﻟﻜل
ﻤﻥ ﺍﻟﺫﻜﻭﺭ ﻭﺍﻹﻨﺎﺙ ﺒﺄﻟﻭﺍﻥ ﻤﺨﺘﻠﻔﺔ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
380
ﻭﺍﻵﻥ ،ﻭﻟﺤﺴﺎﺏ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ
Final Proficiencyﻨﺘﺒﻊ ﺍﻟﺨﻁﻭﺍﺕ ﺍﻟﺘﺎﻟﻴﺔ :
• ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ) Analyzeﺃﻭ (Statisticsﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ. • ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ Correlateﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺴﺎﺒﻘﺔ )ﺸﻜل .(5-11 • ﺍﺨﺘﺭ ﺃﻤﺭ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ Bivariateﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺴﺎﺒﻘﺔ ﻟﺘﻅﻬﺭ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﺜﻨﺎﺌﻲ )ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ( ، Bivariateﻭﺘﻅﻬﺭ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ
ﺒﻌﺩ ﺇﺩﺨﺎل ﺠﻤﻴﻊ ﺨﻴﺎﺭﺍﺘﻬﺎ ﺘﻅﻬﺭ ﻓﻲ ﺸﻜل . 6-11 ﺸﻜل : 5-11ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﺃﻤﺭ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ .Bivariate Correlate
• ﺍﻨﻘل ﺃﺴﻤﺎﺀ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ
Initial
Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﻨﻬﺎﻴﺘﻬﺎ Final Proficiencyﺇﻟﻰ ﻤﺭﺒﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ Variablesﻓﻲ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ، Bivariate Correlations ﻭﻴﻤﻜﻥ ﻤﻥ ﻤﺭﺒﻊ ﺍﻟﺨﻴﺎﺭﺍﺕ Optionsﺍﺨﺘﻴﺎﺭ ﺤﺴﺎﺏ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻭﺼﻔﻴﺔ ﻤﺜل ﺍﻟﻭﺴﻁ ﺍﻟﺤﺴﺎﺒﻲ ﻭﺍﻻﻨﺤﺭﺍﻑ ﺍﻟﻤﻌﻴﺎﺭﻱ Means and Standard Deviationsﻟﻜل ﻤﺘﻐﻴﺭ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
381
ﺸﻜل : 6-11ﻨﺎﻓﺫﺓ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ .Bivariate Correlations
• ﺍﻀﻐﻁ ﻤﺭﺒﻊ ﺍﻻﺴﺘﻤﺭﺍﺭ Continueﺜﻡ ﻤﺭﺒﻊ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ
ﻭﺍﻟﺤﺼﻭل ﻋﻠﻰ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﻭﻜﺫﻟﻙ ﻋﻠﻰ ﺠﺩﻭل ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ
ﺍﻟﻤﻁﻠﻭﺒﺔ ﺍﺨﺘﻴﺎﺭﻴﺎﹰ ،ﻭﺸﻜل 7-11ﻴﻭﻀﺢ ﻫﺫﻩ ﺍﻟﻨﺘﺎﺌﺞ .
ﻭﺘﺒﻴﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺍﻟﺸﻜل 7-11ﺠﺩﻭﻟﻴﻥ ﻴﻌﻁﻲ ﺍﻟﺠﺩﻭل ﺍﻷﻭل ﻤﻨﻬﺎ
ﻗﻴﻤﺘﻲ ﺍﻟﻤﺘﻭﺴﻁﻴﻥ ﺍﻟﺤﺴﺎﺒﻴﻴﻥ ﻭﺍﻻﻨﺤﺭﺍﻓﻴﻥ ﺍﻟﻤﻌﻴﺎﺭﻴﻴﻥ ﻟﻠﻤﺘﻐﻴﺭﻴﻥ ﻜﻤﺎ ﻁﻠﺏ ﻓﻲ
ﺍﻟﺨﻴﺎﺭﺍﺕ ،optionsﻭﻴﻌﻁﻲ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ the correlation
coefficientﺒﺎﻹﻀﺎﻓﺔ ﺇﻟﻰ ﻗﻴﻤﺔ p-valueﻻﺨﺘﺒﺎﺭ ﻤﻌﻨﻭﻴﺔ ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ.
ﻭﺒﻘﻴﻤﺔ ﻟﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ rﻤﺴﺎﻭﻴﺔ 0.775ﻭﻤﻌﻨﻭﻴﺔ ﺍﺨﺘﺒﺎﺭ p-valueﺜﻨﺎﺌﻲ
ﺍﻟﻁﺭﻑ ﻤﺴﺎﻭﻴﺔ 0.008ﻴﻤﻜﻨﻨﺎ ﺍﺴﺘﻨﺘﺎﺝ ﺃﻥ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﻤﻌﻨﻭﻱ ﺒﻤﺴﺘﻭﻯ ﻤﻌﻨﻭﻴﺔ
ﺃﻗل ﻤﻥ ، 0.01ﺃﻱ ﺃﻥ ﻫﻨﺎﻙ ﺩﻟﻴل ﻜﺎﻑ ﻋﻠﻰ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ،ﻭﻴﻤﻜﻥ ﺼﻴﺎﻏﺔ ﻫﺫﻩ ﺍﻟﻨﺘﻴﺠﺔ ﻋﻠﻰ ﺍﻟﺼﻭﺭﺓ :
p < 0.01 ; Significant .
;
R = 0.77 ; n = 10
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
382
ﺸﻜل : 7-11ﻗﺎﺌﻤﺔ ﻨﺘﺎﺌﺞ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻱ ﻗﺩﺭﺓ ﺍﻟﻁﺎﻟﺏ ﻋﻠﻰ ﺍﻟﻘﻨﺹ ﻓﻲ ﺒﺩﺍﻴﺔ ﺍﻟﺩﻭﺭﺓ Initial Coordinationﻭﻜﻔﺎﺀﺘﻪ ﻓﻲ ﺍﻟﻠﻌﺏ ﻓﻲ ﻨﻬﺎﻴﺘﻬﺎ Final Proficiency Descriptive Statistics N
Std. Deviation
Mean
10
2.57
5.80
Initial Cordination
10
2.15
4.80
Final Proficiency
Correlations Final Proficiency
Initial Cordination Initial Cordination Pearson Correlation )Sig. (2-tailed N **.775
Pearson Correlation
.008
)Sig. (2-tailed
10
Final Proficiency
N
**. Correlation is significant at the 0.01 level (2-tailed).
ﻭﻴﻤﻜﻨﻨﺎ ﺃﻥ ﻨﻼﺤﻅ ﻤﻥ ﺍﻟﺠﺩﻭل ﺍﻟﺜﺎﻨﻲ ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﺴﺎﺒﻘﺔ ﺃﻥ ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺘﻅﻬﺭ ﻓﻲ ﺠﺩﻭل ﻴﺸﺒﻪ ﺍﻟﻤﺼﻔﻭﻓﺔ ﺍﻟﻤﺭﺒﻌﺔ ﺭﻏﻡ ﺃﻥ ﺍﻟﻤﻁﻠﻭﺏ ﻫﻭ
ﺤﺴﺎﺏ ﻗﻴﻤﺔ ﻭﺤﻴﺩﺓ ﻟﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ،ﻭﻫﺫﺍ ﻴﺭﺠﻊ ﺇﻟﻰ ﺤﻘﻴﻘﺔ ﺃﻨﻪ ﻴﻤﻜﻨﻨﺎ
ﻤﻥ ﺨﻼل ﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ ﻤﺭﺓ ﻭﺍﺤﺩﺓ ﺤﺴﺎﺏ ﻗﻴﻡ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻟﺠﻤﻴﻊ ﺃﺯﻭﺍﺝ
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻤﻤﻜﻨﺔ ﺒﻴﻥ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻴﺘﻡ ﺇﺩﺨﺎل ﺃﺴﻤﺎﺀﻫﺎ ﻓﻲ ﻤﺭﺒﻊ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ Variablesﻓﻲ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ
Bivariate
، Correlationsﻭﺴﺘﻅﻬﺭ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺃﻴﻀﹰﺎ ﺒﻨﻔﺱ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺴﺎﺒﻘﺔ ﻓﻲ ﺸﻜل ﻤﺼﻔﻭﻓﺔ ﻤﺭﺒﻌﺔ ﺘﻭﻀﺢ ﻗﻴﻡ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻟﺠﻤﻴﻊ ﺍﻷﺯﻭﺍﺝ ﺍﻟﻤﻤﻜﻨﺔ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﻭﻴﻁﻠﻕ ﻋﻠﻴﻬﺎ ﻤﺼﻔﻭﻓﺔ ﺍﻻﺭﺘﺒﺎﻁ . Correlation Matrix
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
383
ﻭﺭﻏﻡ ﺃﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻴﺴﺘﺨﺩﻡ ﻓﻘﻁ ﻟﻘﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﻜﻤﻴﻴﻥ ﻗﻴﺎﺴﻴﻴﻥ ﻴﻔﺘﺭﺽ ﺃﻥ ﻴﻜﻭﻥ ﺘﻭﺯﻴﻌﻬﻤﺎ ﺍﻻﺤﺘﻤﺎﻟﻲ ﻫﻭ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻟﻁﺒﻴﻌﻲ
ﺇﻻ ﺃﻨﻪ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻤﻪ ﺃﻴﻀﹰﺎ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﺃﺤﺩ ﻫﺫﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻫﻭ ﻤﺘﻐﻴﺭ ﺜﻨﺎﺌﻲ
ﺍﻟﻘﻴﻤﺔ ) dichotomyﻴﺄﺨﺫ ﻗﻴﻤﺘﻴﻥ ﻓﻘﻁ( ﻤﺜل ﻤﺘﻐﻴﺭ ﺍﻟﺠﻨﺱ )ﺫﻜﺭ ﺒﺎﻟﻘﻴﻤﺔ 1ﻭﺃﻨﺜﻰ
ﺒﺎﻟﻘﻴﻤﺔ (0ﺃﻭ ﻨﺘﻴﺠﺔ ﺍﻟﻁﺎﻟﺏ )ﻨﺎﺠﺢ ﺒﺎﻟﻘﻴﻤﺔ 1ﻭﺭﺍﺴﺏ ﺒﺎﻟﻘﻴﻤﺔ ،(0ﻭﻋﻨﺩﻤﺎ ﻴﺤﺴﺏ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻟﻤﺜل ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻓﺈﻨﻪ ﻴﻁﻠﻕ ﻋﻠﻴﻪ ﻤﻌﺎﻤل Point-biserialb
) ، correlation ( rpbﻭﺒﺫﻟﻙ ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺤﺴﺎﺏ ﻫﺫﺍ ﺍﻟﻤﻌﺎﻤل ﻓﻲ ﻤﺜﺎﻟﻨﺎ ﻟﻠﻤﺘﻐﻴﺭﻴﻥ
ﻜﻔﺎﺀﺓ ﺍﻟﻁﺎﻟﺏ ﻓﻲ ﻨﻬﺎﻴﺔ ﺍﻟﺩﻭﺭﺓ Final Proficiencyﺒﺎﺴﺘﺨﺩﺍﻡ ﻨﻔﺱ ﺍﻟﻁﺭﻴﻘﺔ ﺍﻟﺴﺎﺒﻘﺔ
ﻟﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ.
.3 .11ﻣﻘﺎﻳﻴﺲ اﻻرﺗﺒﺎط ﻟﻠﺒﻴﺎﻧﺎت اﻟﺘﺮﺗﻴﺒﻴﺔ : Measures of Association for Ordinal Data : ﻓﺤﻴﺙ ﻴﺴﺘﺨﺩﻡ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻟﻘﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﻜﻤﻴﻴﻥ
ﻗﻴﺎﺴﻴﻴﻥ ﺇﻻ ﺃﻨﻪ ﻻ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻤﻪ ﻟﻠﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﺭﺘﻴﺒﻴﺔ ) Ordinal dataﻭﺘﺸﻤل ﺭﺘﺏ ﺍﻟﻘﻴﻡ ﻭﻜﺫﻟﻙ ﺍﻟﻔﺌﺎﺕ ﺫﺍﺕ ﺍﻟﻘﻴﻡ ﺍﻟﺘﻲ ﻴﻤﻜﻥ ﺘﺭﺘﻴﺒﻬﺎ( ﻭﻻ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻤﻪ ﺃﻴﻀﹰﺎ ﻟﻠﺒﻴﺎﻨﺎﺕ
ﺍﻟﻭﺼﻔﻴﺔ ) Categorical dataﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺫﺍﺕ ﺍﻟﻔﺌﺎﺕ ﺍﻟﺘﻲ ﻻ ﻤﻌﻨﻰ ﻟﺘﺭﺘﻴﺒﻬﺎ( ،ﻭﻓﻲ ﻫﺫﺍ ﺍﻟﻘﺴﻡ ﺴﻨﻭﻀﺢ ﻤﻘﺎﻴﻴﺱ ﺍﻟﺘﺭﺍﺒﻁ ﻟﻠﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﺭﺘﻴﺒﻴﺔ ﻭﺴﻨﻭﻀﺢ ﻓﻲ ﺍﻟﻘﺴﻡ ﺍﻟﻼﺤﻕ ﻫﺫﻩ ﺍﻟﻤﻘﺎﻴﻴﺱ ﻟﻠﺒﻴﺎﻨﺎﺕ ﺍﻟﻭﺼﻔﻴﺔ.
ﻴﺴﺘﺨﺩﻡ ﺘﻌﺒﻴﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﺭﺘﻴﺒﻴﺔ Ordinal dataﻟﻠﺩﻻﻟﺔ ﻋﻠﻰ ﻗﻴﻡ ﺘﻠﻙ
ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻜﻤﻴﺔ ﺍﻟﺘﻲ ﻟﻴﺴﺕ ﻗﻴﺎﺴﺎﺕ ﻤﺴﺘﻘﻠﺔ ﺘﻘﺎﺱ ﺒﻭﺤﺩﺍﺕ ﻤﺤﺩﺩﺓ ﺒل ﻗﺩ ﺘﻜﻭﻥ
ﻋﺒﺎﺭﺓ ﻋﻥ ﺭﺘﺏ ranksﻟﻤﺜل ﻫﺫﻩ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺃﻭ ﻟﻤﺘﻐﻴﺭﺍﺕ ﻭﺼﻔﻴﺔ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻤﻌﻨﻰ
ﻤﺤﺩﺩ ﻤﻥ ﺘﺭﺘﻴﺒﻬﺎ ،ﻓﻌﻠﻰ ﺴﺒﻴل ﺍﻟﻤﺜﺎل ﻴﻤﻜﻥ ﺘﺭﺘﻴﺏ ﻗﻴﺎﺴﺎﺕ ﺃﻁﻭﺍل ﻋﻴﻨﺔ ﻤﻥ 10
ﻁﻼﺏ ﻋﻠﻰ ﺃﻥ ﻴﻌﻁﻰ ﺍﻟﻁﺎﻟﺏ ﺍﻷﻁﻭل ﺍﻟﺭﺘﺒﺔ 10ﻭﺍﻟﻁﺎﻟﺏ ﺍﻷﻗﺼﺭ ﺍﻟﺭﺘﺒﺔ 1
ﻭﻫﻜﺫﺍ ...ﻓﺈﻥ ﺍﻟﻘﻴﻡ ﺍﻟﻨﺎﺘﺠﺔ ﻫﻲ ﻋﺒﺎﺭﺓ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﺭﺘﻴﺒﻴﺔ ﻭﺫﻟﻙ ﻷﻥ ﺭﺘﺒﺔ
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
384
ﺍﻟﻁﺎﻟﺏ ﻻ ﺘﺘﻀﻤﻥ ﻁﻭﻟﻪ ﺒﺎﻟﺴﻨﺘﻴﻤﺘﺭ ﺃﻭ ﺍﻹﻨﺵ ﺃﻭ ﺃﻱ ﻭﺤﺩﺓ ﻗﻴﺎﺱ ﺃﺨﺭﻯ ﻟﻠﻁﻭل، ﻓﺎﻟﺭﺘﺒﺔ ﺘﻌﺒﺭ ﻓﻘﻁ ﻋﻥ ﻁﻭل ﺍﻟﻔﺭﺩ ﻤﻘﺎﺭﻨﺔ ﺒﺄﻁﻭﺍل ﺍﻷﻓﺭﺍﺩ ﺍﻵﺨﺭﻴﻥ ﻓﻲ ﺘﻠﻙ ﺍﻟﻌﻴﻨﺔ ﻼ( ﺒﺎﻟﺘﺤﺩﻴﺩ ،ﻭﺇﺫﺍ ﻁﻠﺏ ﻤﻥ ﺍﺜﻨﻴﻥ ﻤﻥ ﺍﻟﻤﺤﻜﻤﻴﻥ ﺃﻥ ﻴﻌﻁﻲ ﻜل ﻤﻨﻬﻡ ﺭﺘﺒﺎﹰ ﻟﻌﺸﺭﺓ )ﻤﺜ ﹰ
ﻤﻥ ﺍﻟﻠﻭﺤﺎﺕ ﺍﻟﻔﻨﻴﺔ ﺤﺴﺏ ﻤﺴﺘﻭﺍﻫﺎ ﺍﻟﻔﻨﻲ ﻋﻠﻰ ﺃﻥ ﺘﺄﺨﺫ ﺍﻟﻠﻭﺤﺔ ﺍﻷﻓﻀل ﺍﻟﺭﺘﺒﺔ 1
ﻭﺍﻷﺴﻭﺃ ﺍﻟﺭﺘﺒﺔ 10ﻭﻫﻜﺫﺍ ...ﻓﺈﻨﻪ ﺴﻭﻑ ﻴﻜﻭﻥ ﻟﺩﻴﻨﺎ ﻋﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ ﻤﻥ ﺍﻟﺭﺘﺏ.
ﻭﺒﻬﺫﺍ ﻓﺈﻥ ﺘﻌﺒﻴﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﺭﺘﻴﺒﻴﺔ Ordinal dataﻴﺸﺘﻤل ﻋﻠﻰ ﺭﺘﺏ ﻜل ﻤﻥ
ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻜﻤﻴﺔ ﻭﻜﺫﻟﻙ ﺭﺘﺏ ﻓﺌﺎﺕ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻭﺼﻔﻴﺔ ،ﻭﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻟﺩﻴﻨﺎ ﻋﻴﻨﺘﻴﻥ ﻤﺭﺘﺒﻁﺘﻴﻥ ﻤﻥ ﺍﻟﺭﺘﺏ )ﻜﻤﺎ ﻓﻲ ﺤﺎﻟﺔ ﺍﻟﻤﺤﻜﻤﻴﻥ( ﻓﺈﻨﻨﺎ ﺴﻨﻬﺘﻡ ﺍﻵﻥ ﺒﻘﻴﺎﺱ ﻗﻭﺓ
ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﺍﻟﻠﺘﻴﻥ ﻗﻴﺴﺘﺎ ﻋﻠﻰ ﻤﺴﺘﻭﻯ ﺭﺘﺒﻬﻤﺎ ﻭﻟﻴﺱ ﻋﻠﻰ ﻤﺴﺘﻭﻯ ﻓﺌﺎﺘﻬﻤﺎ.
.1 .3 .11ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ )ﻟﻠﺭﺘﺏ( : The Spearman rank correlation (rs or ρ) : ﺇﺫﺍ ﺍﻓﺘﺭﻀﻨﺎ ﺃﻥ ﻫﺫﻴﻥ ﺍﻟﻤﺤﻜﻤﻴﻥ ﻗﺎﻤﺎ ﺒﺈﻋﻁﺎﺀ ﺍﻟﺭﺘﺏ ﻟﻠﻌﺸﺭ ﻟﻭﺤﺎﺕ ﻓﻨﻴﺔ ﻓﻲ
ﺍﻟﻤﺜﺎل ﺍﻟﻤﺫﻜﻭﺭ ﺃﻋﻼﻩ ﻭﺤﺼﻠﻨﺎ ﻋﻠﻰ ﺘﻠﻙ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻭﻜﺎﻨﺕ ﻜﻤﺎ ﻓﻲ ﺍﻟﺠﺩﻭل ﻓﻲ ﺸﻜل
8-11ﺍﻟﺘﺎﻟﻲ ،ﻓﺄﺤﺩ ﺍﻟﻁﺭﻕ ﻟﻘﻴﺎﺱ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺘﻘﺩﻴﺭﺍﺕ ﺍﻟﻤﺤﻜﻤﻴﻥ ﻫﻲ ﻋﻥ ﻁﺭﻴﻕ
ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺒﻴﻥ ﻤﺠﻤﻭﻋﺘﻲ ﺍﻟﺭﺘﺏ ،ﺇﻻ ﺃﻨﻪ ﻴﻤﻜﻥ ﺇﺜﺒﺎﺕ ﺃﻥ ﻤﻌﺎﻤل
ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻴﻤﻜﻥ ﺍﺴﺘﻨﺒﺎﻁﻪ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺼﻴﻐﺔ ﺃﺒﺴﻁ ﻁﺎﻟﻤﺎ ﺍﺴﺘﺨﺩﻤﺕ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﺭﺘﺏ ،ﻭﻫﺫﻩ ﺍﻟﺼﻴﻐﺔ ﺘﻌﺭﻑ ﺒﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ
)ﻟﻠﺭﺘﺏ( The Spearman rank correlation coefficientﻭﻴﺭﻤﺯ ﻟﻪ ﺒﺎﻟﺭﻤﺯ ﺍﻹﻏﺭﻴﻘﻲ ) ρﺭﻭﻩ( ،ﻭﺘﻌﻁﻲ ﺼﻴﻐﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ﻓﻲ ﻤﺜل ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ
ﻗﻴﻤﺔ ﻤﺴﺎﻭﻴﺔ ﻟﻘﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻁﺎﻟﻤﺎ ﺍﺴﺘﺨﺩﻤﺕ ﺍﻟﺭﺘﺏ ﻓﻲ ﺤﺴﺎﺒﻬﻤﺎ،
)ﻟﻠﺘﻔﺎﺼﻴل ﺃﻨﻅﺭ ﻋﻜﺎﺸﺔ ، 2001 ،ﻜﺘﺎﺏ ﺍﻹﺤﺼﺎﺀ ﺍﻟﺘﻁﺒﻴﻘﻲ(.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
385
ﺸﻜل : 8-11ﺒﻴﺎﻨﺎﺕ ﻤﻥ ﻤﺠﻤﻭﻋﺘﻴﻥ ﻤﻥ ﺍﻟﺭﺘﺏ ﻟﺘﺭﺘﻴﺏ ﻋﻴﻨﺔ ﻤﻥ 10ﻟﻭﺤﺎﺕ ﻓﻨﻴﺔ ﺃﻋﻁﻴﺕ ﺒﻭﺍﺴﻁﺔ ﻤﺤﻜﻤﻴﻥ ﻤﺨﺘﻠﻔﻴﻥ ﺤﺴﺏ ﺃﻓﻀﻠﻴﺘﻬﺎ. Ranks assigned by two judges to each of ten paintings Second Judge
First Judge
1
1
Painting A
3
2
B
2
3
C
4
4
D
6
5
E
5
6
F
8
7
G
7
8
H
10
9
I
9
10
J
ﺇﻥ ﺍﺴﺘﺨﺩﺍﻡ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ﻟﻴﺱ ﻤﻘﺘﺼﺭﹰﺍ ﻋﻠﻰ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺘﺭﺘﻴﺒﻴﺔ
ﻓﻘﻁ ،ﺒل ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻤﻪ ﺃﻴﻀﹰﺎ ﻓﻲ ﺤﺎﻟﺔ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ ﺍﻟﻜﻤﻴﺔ ﺍﻟﻘﻴﺎﺴﻴﺔ ﺨﺎﺼﺔ ﻋﻨﺩﻤﺎ
ﻴﺒﻴﻥ ﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ ﺃﻥ ﻫﻨﺎﻙ ﻗﻴﻤﹰﺎ ﺸﺎﺫﺓ ﺃﻭ ﻤﺘﻁﺭﻓﺔ ،ﻭﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻓﺈﻥ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ﻜﺒﺩﻴل ﻋﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺴﻴﺨﻔﻑ ﺃﺜﺭ ﺘﻠﻙ ﺍﻟﻘﻴﻡ
ﻋﻠﻰ ﻗﻴﻤﺔ ﻤﻘﻴﺎﺱ ﺍﻻﺭﺘﺒﺎﻁ .
ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﺤﺠﻡ ﺍﻟﻌﻴﻨﺔ ﺼﻐﻴﺭ ﻓﺈﻨﻪ ﺴﻴﻜﻭﻥ ﻤﻥ ﺍﻟﺼﻌﺏ ﺤﺴﺎﺏ ﻗﻴﻤﺔ ﺩﻗﻴﻘﺔ
ﻟﻤﻌﻨﻭﻴﺔ p-valueﻟﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ،ﺨﺎﺼﺔ ﻋﻨﺩﻤﺎ ﺘﺘﺴﺎﻭﻯ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﻘﻴﻡ ﻭﺒﺎﻟﺘﺎﻟﻲ ﺭﺘﺏ ﻫﺫﻩ ﺍﻟﻘﻴﻡ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ،ﻭﻴﻤﻜﻥ ﺇﻴﺠﺎﺩ ﺠﺩﺍﻭل ﺨﺎﺼﺔ ﺒﺎﻟﻘﻴﻡ
ﺍﻟﺤﺭﺠﺔ ﻟﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ﻓﻲ ﻋﺩﺩ ﻜﺒﻴﺭ ﻤﻥ ﺍﻟﻜﺘﺏ )ﺃﻨﻅﺭ ﻋﻜﺎﺸﺔ1999 ، "ﺍﻟﻘﻭﺍﻨﻴﻥ ﻭﺍﻟﺠﺩﺍﻭل ﺍﻹﺤﺼﺎﺌﻴﺔ ﻭﺍﻟﺘﻭﺯﻴﻌﺎﺕ ﺍﻻﺤﺘﻤﺎﻟﻴﺔ( ،ﻭﻟﻜﻥ ﻴﺠﺏ ﺃﺨﺫ ﺍﻟﺤﻴﻁﺔ ﻭﺍﻟﺤﺫﺭ ﻋﻨﺩ ﺍﺴﺘﺨﺩﺍﻡ ﻫﺫﻩ ﺍﻟﺠﺩﺍﻭل ﻋﻨﺩﻤﺎ ﺘﺘﺴﺎﻭﻯ ﻤﺠﻤﻭﻋﺔ ﻜﺒﻴﺭﺓ ﻤﻥ ﺍﻟﻘﻴﻡ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
386
.2 .3 .11ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل ) τﺘﻭﻩ( ﻟﻼﺭﺘﺒﺎﻁ : The Kendall’s tau ( τ ) Statistic: ﻼ ﻋﻥ ﻴﻌﺘﺒﺭ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﻜﻤﻘﻴﺎﺱ ﻟﻼﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ ﺘﺭﺘﻴﺒﻴﻴﻥ ﺒﺩﻴ ﹰ
ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ،ﻭﻴﺄﺨﺫ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﻋﺩﺓ ﺼﻴﻎ ﻴﺸﺎﺭ ﺇﻟﻴﻬﺎ ﺒﺎﻟﺭﻤﻭﺯ a
ﻭ bﻭ ، cﻭﺍﻟﻔﺭﻕ ﺒﻴﻨﻬﻤﺎ ﻫﻭ ﻓﻲ ﺘﻌﺩﻴل ﻁﻔﻴﻑ ﻨﺘﻴﺠﺔ ﺍﻷﺨﺫ ﻓﻲ ﺍﻟﺤﺴﺒﺎﻥ ﻋﺩﺩ ﺍﻟﻘﻴﻡ
ﺍﻟﻤﺘﺴﺎﻭﻴﺔ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻭﺒﺎﻟﺘﺎﻟﻲ ﻋﺩﺩ ﺍﻟﺭﺘﺏ ﺍﻟﻤﺘﺴﺎﻭﻴﺔ ،ﻭﻋﻨﺩﻤﺎ ﻻ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺭﺘﺏ ﻤﺘﺴﺎﻭﻴﺔ ﻓﺈﻥ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﺍﻟﺼﻴﻐﺔ aﻭﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﺍﻟﺼﻴﻐﺔ bﺘﺘﺴﺎﻭﻴﺎﻥ،
ﻟﻜﻥ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﺍﻟﺼﻴﻐﺔ cﺼﻤﻡ ﻤﻥ ﺃﺠل ﺍﺴﺘﺨﺩﺍﻤﻪ ﻟﺤﺴﺎﺏ ﻤﻘﻴﺎﺱ ﻟﻼﺭﺘﺒﺎﻁ
ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻫﻨﺎﻙ ﻤﺠﻤﻭﻋﺘﻴﻥ ﻤﻥ ﺍﻟﺭﺘﺏ ﻏﻴﺭ ﻤﺘﺴﺎﻭﻴﺘﻲ ﺍﻟﻌﺩﺩ .
ﻭﻴﺘﻤﻴﺯ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﻋﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ﻓﻲ ﺃﻨﻪ ﻴﻤﻜﻥ ﺇﻴﺠﺎﺩ ﻗﻴﻤﹰﺎ ﺤﺭﺠﺔ p-valueﺩﻗﻴﻘﺔ ﺒﺴﻬﻭﻟﺔ ﻹﺤﺼﺎﺀ ﻜﻨﺩﺍل τﺨﺎﺼﺔ ﻋﻨﺩﻤﺎ ﻴﻜﻭﻥ ﻋﺩﺩ ﺍﻟﻘﻴﻡ
ﺼﻐﻴﺭ ﻭﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻗﻴﻡ ﻭﺒﺎﻟﺘﺎﻟﻲ ﺭﺘﺏ ﻤﺘﺴﺎﻭﻴﺔ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ.
ﻭﻟﺤﺴﺎﺏ ﻜل ﻤﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ ﻭﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل τﻴﻠﺯﻡ ﻓﻲ ﺍﻟﺒﺩﺍﻴﺔ
ﺃﻥ ﺘﺩﺨل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺇﻟﻰ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data Editorﻋﻠﻰ ﺸﻜل ﻋﻤﻭﺩﻴﻥ ﻴﻤﺜل ﻜل ﻤﻨﻬﻤﺎ ﻤﺘﻐﻴﺭ ﻴﺘﻡ ﺇﻋﻁﺎﺅﻩ ﺍﺴﻡ ﻤﻤﻴﺯ ﻭﻴﺩﺨل ﺒﻪ ﻤﺠﻤﻭﻋﺔ ﺍﻟﺭﺘﺏ )ﻜﻤﺎ ﻓﻲ ﺸﻜل 8-11
ﺃﻋﻼﻩ( ﺜﻡ ﻴﺘﻡ ﺍﺘﺒﺎﻉ ﺍﻟﺨﻁﻭﺍﺕ ﺍﻟﺘﺎﻟﻴﺔ :
• ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ) Analyzeﺃﻭ (Statisticsﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ. • ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ Correlateﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺴﺎﺒﻘﺔ )ﺸﻜل .(5-11 • ﺍﺨﺘﺭ ﺃﻤﺭ ﺤﺴﺎﺏ ﻤﻌﺎﻤل ﺍﻻﺭﺘﺒﺎﻁ ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ Bivariateﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺴﺎﺒﻘﺔ
ﻟﺘﻅﻬﺭ ﻨﺎﻓﺫﺓ ﺘﺤﻠﻴل ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﺜﻨﺎﺌﻲ )ﺒﻴﻥ ﻤﺘﻐﻴﺭﻴﻥ( Bivariateﻜﻤﺎ ﻓﻲ ﺸﻜل 6-11
ﺃﻋﻼﻩ .
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
387
• ﺴﺘﺠﺩ ﻓﻲ ﺘﻠﻙ ﺍﻟﻨﺎﻓﺫﺓ ﺃﻨﻪ ﻗﺩ ﺍﺨﺘﻴﺭ ﺍﻟﻤﻘﻴﺎﺱ ﺍﻟﺘﻠﻘﺎﺌﻲ ﻭﻫﻭ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ Pearsonﻓﺎﺨﺘﺭ ﺃﻴﻀﹰﺎ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل Kendall's tau-bﻭﻜﺫﻟﻙ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ . Spearman
• ﺍﻀﻐﻁ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﻠﺤﺼﻭل ﻋﻠﻰ ﻤﻘﺎﻴﻴﺱ ﺍﻻﺭﺘﺒﺎﻁ ﺍﻟﻤﻁﻠﻭﺒﺔ ﻜﻤﺎ ﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺍﻟﺸﻜل 9-11ﺃﺩﻨﺎﻩ .
ﻻﺤﻅ ﺃﻨﻪ ﻴﻤﻜﻥ ﺤﺴﺎﺏ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل ﻟﻠﺒﻴﺎﻨﺎﺕ ﺍﻟﻭﺼﻔﻴﺔ ﺃﻴﻀﹰﺎ ﺒﻌﺩ ﺘﺼﻨﻔﻴﻬﺎ
ﺒﺎﺴﺘﺨﺩﺍﻡ ﺃﻤﺭ ﺍﻟﺘﺼﻨﻴﻑ ﺍﻟﻤﺯﺩﻭﺝ Crosstabsﻭﻟﻜﻥ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻴﻔﻀل ﺍﺴﺘﺨﺩﺍﻡ ﺍﻟﺼﻴﻐﺔ cﻤﻥ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل ) Kendall's tau-cﺃﻨﻅﺭ ﺍﻟﻘﺴﻡ ﺍﻟﺘﺎﻟﻲ(. ﺸﻜل : 9-11ﻨﺘﺎﺌﺞ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ Spearmanﻭﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل Kendall
tau-bﺒﻴﻥ ﺭﺘﺏ ﺍﻟﻤﺤﻜﻡ ﺍﻷﻭل First Judgeﻭﺭﺘﺏ ﺍﻟﻤﺤﻜﻡ ﺍﻟﺜﺎﻨﻲ Second Judge Nonparametric Correlations Correlations Second Judge
First Judge
**.822
1.000
.001
.
10
10
Correlation Coefficient )Sig. (2-tailed N
**.822
Correlation Coefficient
.
.001
)Sig. (2-tailed
10
10
1.000
**.952
1.000
.000
.
10
10
Second Judge
N Correlation Coefficient )Sig. (2-tailed
Spearman First 's rho Judge
N
**.952
Correlation Coefficient
.
.000
)Sig. (2-tailed
10
10
1.000
First Judge
Kendall's tau_b
Second Judge
N
**. Correlation is significant at the .01 level (2-tailed).
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
388
ﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﺸﻜل 9-11ﻴﺘﻀﺢ ﺃﻥ ﻗﻴﻤﺔ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل Kendall's
tau-bﻤﺴﺎﻭﻴﺔ 0.822ﻭﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺴﺒﻴﺭﻤﺎﻥ Spearman's rhoﻤﺴﺎﻭﻴﺔ ، 0.952ﻓﻌﻠﻰ ﺍﻟﺭﻏﻡ ﻤﻥ ﺍﺨﺘﻼﻑ ﺍﻟﻘﻴﻤﺘﻴﻥ ﺇﻻ ﺍﻨﻬﻤﺎ ﻴﻌﻁﻴﺎ ﻨﻔﺱ ﺍﻟﻤﺩﻟﻭل ،ﻭﻤﻥ
ﺍﻟﻁﺒﻴﻌﻲ ﺃﻥ ﺘﺨﺘﻠﻑ ﻗﻴﻤﺘﻲ ﺍﻹﺤﺼﺎﺀﻴﻥ ﻨﻅﺭﹰﺍ ﻷﻨﻬﻤﺎ ﺍﺴﺘﺨﺩﻤﺎ ﺃﺴﺎﺴﻴﻥ ﻨﻅﺭﻴﻴﻥ
ﻤﺨﺘﻠﻔﻴﻥ ﻓﻲ ﺍﺴﺘﻨﺒﺎﻁﻬﻤﺎ ،ﻭﺒﺎﻟﺼﺩﻓﺔ ﻓﻘﻁ ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﺃﻋﻁﻰ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ
ﺒﻴﺭﺴﻭﻥ Pearson correlation coefficientﻗﻴﻤﺔ ﻤﺴﺎﻭﻴﺔ ﻟﻘﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ
ﺴﺒﻴﺭﻤﺎﻥ ﻤﺴﺎﻭﻴﺔ 0.952ﻭﻟﻜﻥ ﻫﺫﻩ ﻟﻴﺴﺕ ﻗﺎﻋﺩﺓ) ،ﻗﻴﻤﺔ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﻟﻡ ﺘﻅﻬﺭ ﻓﻲ ﺸﻜل 9-11ﻷﻨﻬﺎ ﺘﻅﻬﺭ ﻓﻲ ﺠﺩﻭل ﻗﺎﺌﻡ ﺒﺫﺍﺘﻪ ﻀﻤﻥ ﺍﻟﻨﺘﺎﺌﺞ( ،ﻭﻫﺫﻩ ﺍﻟﻨﺘﺎﺌﺞ
ﻴﻤﻜﻥ ﺼﻴﺎﻏﺘﻬﺎ ﻋﻠﻰ ﺍﻟﺼﻭﺭﺓ : ; Significant Significant .
; p < 0.01 ; p < 0.01
; n = 10 ; n = 10
; τ = 0.822 ; ρ = 0.952
.4 .11ﻣﻘﺎﻳﻴﺲ اﻟﺘﺮاﺑﻂ ﻓﻲ اﻟﺒﻴﺎﻧﺎت اﻟﻮﺻﻔﻴﺔ : Measures of Association for Categorical Data : ﺇﺫﺍ ﻜﺎﻥ ﻟﺩﻴﻨﺎ ﺒﻴﺎﻨﺎﺕ ﻋﻥ ﺘﻭﺯﻴﻊ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻷﺸﺨﺎﺹ ﺤﺴﺏ ﻓﺌﺎﺕ
ﻼ ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﺘﺼﻨﻴﻑ ﻅﺎﻫﺭﺘﻴﻥ ﻤﺜل ﺍﻟﻨﻭﻉ Genderﻭﻓﺼﻴﻠﺔ ﺍﻟﺩﻡ Blood groupﻤﺜ ﹰ
ﺒﻴﺎﻨﺎﺕ ﻫﺎﺘﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﻤﻌﹰﺎ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺃﻤﺭ ﺍﻟﺘﺼﻨﻴﻑ ﺍﻟﻤﺯﺩﻭﺝ crosstabsﻟﻨﺤﺼل ﻋﻠﻰ ﺠﺩﻭل ﻴﻁﻠﻕ ﻋﻠﻴﻪ ﺍﺴﻡ ﺍﻟﺠﺩﻭل ﺍﻟﺘﻜﺭﺍﺭﻱ ﺍﻟﻤﺯﺩﻭﺝ Crosstabulationﺃﻭ
ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ ﺃﻭ ﺍﻟﺘﻭﺍﻓﻕ ) Contingency Tableﺃﻨﻅﺭ ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ ﻟﻠﺤﺼﻭل
ﻋﻠﻰ ﻁﺭﻕ ﺍﻟﺘﺼﻨﻴﻑ ﻓﻲ ﺍﻟﻨﻅﺎﻡ( ،ﻓﻲ ﺘﺤﻠﻴل ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ ﺘﻌﺘﺒﺭ ﻫﺫﻩ ﺍﻟﺠﺩﺍﻭل
ﺫﺍﺘﻬﺎ ﻤﻌﺎﺩﻟﺔ ﻟﺸﻜل ﺍﻻﻨﺘﺸﺎﺭ Scatterplotﻤﻥ ﻨﺎﺤﻴﺔ ﻭﺼﻔﻬﺎ ﻟﻠﺒﻴﺎﻨﺎﺕ ﻭﺇﺒﺭﺍﺯ ﺍﻟﻌﻼﻗﺔ ﻼ ﻤﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﻓﻲ ﺍﻟﺠﺩﻭل ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ،ﻻﺤﻅ ﺃﻥ ﻴﺠﺏ ﺃﻥ ﺘﻜﻭﻥ ﻓﺌﺎﺕ ﻜ ﹰ ﻤﺘﻨﺎﻓﻴﺔ ﻭﺸﺎﻤﻠﺔ ﺒﻤﻌﻨﻰ ﺃﻨﻪ ﻤﻔﺭﺩﺓ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻴﺠﺏ ﺃﻥ ﺘﻨﺘﻤﻲ ﺇﻟﻰ ﺨﻠﻴﺔ ﻭﺍﺤﺩﺓ )ﻭﺨﻠﻴﺔ
ﻭﺍﺤﺩﺓ ﻓﻘﻁ(.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
389
ﻓﻲ ﻨﻅﺎﻡ SPSSﻴﻤﻜﻥ ﺇﺠﺭﺍﺀ ﺍﻟﺘﺼﻨﻴﻑ ﺍﻟﻤﺯﺩﻭﺝ ﻟﻠﺒﻴﺎﻨﺎﺕ Crosstabulation
ﻓﻘﻁ ﻤﻥ ﺨﻼل ﺃﻤﺭ ﺍﻟﺘﺼﻨﻴﻑ ﺍﻟﻤﺯﺩﻭﺝ Crosstabsﺍﻟﺫﻱ ﻴﻤﻜﻥ ﺍﻟﻭﺼﻭل ﺇﻟﻴﻪ ﻤﻥ
ﺨﻼل ﻗﺎﺌﻤﺔ ﺘﻠﺨﻴﺹ ﺍﻟﺒﻴﺎﻨﺎﺕ Summarizeﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ Analyze
)ﺃﻭ (Statisticsﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ،ﻭﺒﺩﺍﺨل ﻨﺎﻓﺫﺓ ﺍﻟﺘﺼﻨﻴﻑ ﺍﻟﻤﺯﺩﻭﺝ Crosstabs
ﻴﻭﺠﺩ ﺨﻴﺎﺭ ﺍﻹﺤﺼﺎﺀﺍﺕ Statisticsﻀﻤﻥ ﺨﻴﺎﺭﺍﺕ ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ )ﺃﻨﻅﺭ ﺸﻜل 15-11
ﺃﺩﻨﺎﻩ( ،ﻭﺍﺨﺘﻴﺎﺭ ﻫﺫﺍ ﺍﻟﻤﺭﺒﻊ ﺴﻴﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺍﻹﺤﺼﺎﺀﺍﺕ ) Statisticsﺸﻜل (16-11
ﺍﻟﺘﻲ ﺘﺤﺘﻭﻱ ﻋﻠﻰ ﻤﺠﻤﻭﻋﺔ ﻤﻥ ﺍﻟﺨﻴﺎﺭﺍﺕ ﻟﻠﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ ﻟﻠﻌﻼﻗﺔ ﺒﻴﻥ ﻅﺎﻫﺭﺘﻴﻥ ، Measures of Associationﻤﻌﻅﻡ ﻫﺫﻩ ﺍﻹﺤﺼﺎﺀﺍﺕ ﻤﺒﻨﻴﺔ ﻋﻠﻰ ﺃﺴﺎﺱ ﺍﻹﺤﺼﺎﺀ ﺍﻟﻤﻌﺭﻭﻑ ) χ 2ﻜﺎﻱ ﺴﻜﻭﻴﺭ( ﻭﺍﻟﺫﻱ ﻴﺴﺘﺨﺩﻡ ﻻﺨﺘﺒﺎﺭ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﺒﻴﻥ ﻅﺎﻫﺭﺘﻴﻥ
ﻭﺼﻔﻴﺘﻴﻥ ،ﻭﺭﻓﺽ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﺒﻨﺎﺀ ﻋﻠﻰ ﺍﺨﺘﺒﺎﺭ ) χ 2ﺃﻱ ﺃﻥ ﺍﻻﺨﺘﺒﺎﺭ
ﻤﻌﻨﻭﻱ( ﺴﻭﻑ ﻴﻌﻨﻲ ﻓﻘﻁ ﻭﺠﻭﺩ ﻋﻼﻗﺔ ﺒﻴﻥ ﻫﺎﺘﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ،ﻭﻟﻜﻥ ﻟﻥ ﻴﻌﻁﻴﻨﺎ ﻤﻘﻴﺎﺴﹰﺎ ﻟﻘﻭﺓ ﻫﺫﻩ ﺍﻟﻌﻼﻗﺔ ،ﻓﻲ ﺍﻟﻭﺍﻗﻊ ﺇﻥ ﺍﺨﺘﺒﺎﺭ χ 2ﻴﺒﻘﻰ ﺍﺨﺘﺒﺎﺭ ﻭﻟﻜﻨﻪ ﻟﻴﺱ ﻤﻘﻴﺎﺱ
ﻟﻘﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﻅﺎﻫﺭﺘﻴﻥ ﻷﻨﻪ ﻴﺘﺄﺜﺭ ﺒﻤﺠﻤﻭﻉ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ.
ﻭﻫﻨﺎﻙ ﺘﺤﺫﻴﺭ ﻫﺎﻡ ﻤﻥ ﺴﻭﺀ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ ، χ 2ﺇﻨﻪ ﻤﻥ ﺍﻟﻤﻬﻡ ﺃﻥ ﻨﺩﺭﻙ ﺃﻥ
ﻗﻴﻤﺔ χ 2ﺍﻟﻤﺤﺴﻭﺒﺔ ﻤﻥ ﺒﻴﺎﻨﺎﺕ ﺍﻟﻌﻴﻨﺔ ﻓﻲ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﺘﺘﺒﻊ ﺘﻘﺭﻴﺒﺎﹰ ﺍﻟﺘﻭﺯﻴﻊ ﺍﻻﺤﺘﻤﺎﻟﻲ χ 2ﺍﻟﻨﻅﺭﻱ ،ﻭﻜﻠﻤﺎ ﺯﺍﺩﺕ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻜﻠﻤﺎ ﻜﺎﻥ ﻫﺫﺍ ﺍﻟﺘﻘﺭﻴﺏ
ﺃﻗﻭﻯ ،ﻜﻤﺎ ﺃﻨﻪ ﻤﻥ ﺍﻟﻤﻬﻡ ﺃﻥ ﻨﺩﺭﻙ ﺃﻥ ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ χ 2ﻴﺘﻁﻠﺏ ﺃﻥ ﺘﻜﻭﻥ ﻜل ﻤﻔﺭﺩﺓ ﻓﻲ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺘﻨﺘﻤﻲ ﺇﻟﻰ ﺨﻠﻴﺔ ﻭﺍﺤﺩﺓ ﻓﻘﻁ ﻤﻥ ﺨﻼﻴﺎ ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ ،ﻭﻫﻨﺎﻙ
ﺃﻴﻀﹰﺎ ﺍﻟﻜﺜﻴﺭ ﻤﻥ ﺍﻟﻤﺤﺎﺫﻴﺭ ﺤﻭل ﺍﺴﺘﺨﺩﺍﻡ ﺍﺨﺘﺒﺎﺭ χ 2ﻓﻲ ﻫﺫﺍ ﺍﻟﺼﺩﺩ ،ﻭﻴﻤﻜﻥ ﺍﻟﻌﻭﺩﺓ ﺇﻟﻰ ﺘﻔﺎﺼﻴل ﺍﻟﻔﺭﻀﻴﺎﺕ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺒﺎﺨﺘﺒﺎﺭ χ 2ﻭﺍﻟﺘﻲ ﻻﺒﺩ ﻤﻥ ﻤﺭﺍﻋﺎﺘﻬﺎ ﻗﺒل ﺘﻁﺒﻴﻘﻪ
ﻓﻲ ﻤﺭﺍﺠﻊ ﺃﺴﺎﺴﻴﺔ ﻤﺜل ) Howell (1997ﻭﻜﺫﻟﻙ ). Agresti (1996
ﻫﻨﺎﻙ ﺍﻟﻌﺩﻴﺩ ﻤﻥ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ ﺍﻟﺘﻲ ﺘﻬﺩﻑ ﺇﻟﻰ ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ
ﻤﺘﻐﻴﺭﻴﻥ ﻭﺼﻔﻴﻴﻥ )ﺃﻨﻅﺭ ) Reynolds (1984ﻭﻜﺫﻟﻙ ) ،(Agresti (1996ﻭﺍﻟﻤﻘﻴﺎﺱ
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
390
ﺍﻟﻤﺜﺎﻟﻲ ﻫﻭ ﺍﻟﺫﻱ ﺘﻜﻭﻥ ﻗﻴﻤﺘﻪ ﻤﺴﺎﻭﻴﺔ 1ﻓﻘﻁ ﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﺘﺎﻤﺔ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﻭﺘﻜﻭﻥ ﻗﻴﻤﺘﻪ 0ﻋﻨﺩﻤﺎ ﻻ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﺒﻴﻨﻬﻤﺎ ،ﻭﺍﺨﺘﻴﺎﺭ ﺍﻟﻤﻘﻴﺎﺱ
ﺍﻷﻓﻀل ﻴﻌﺘﻤﺩ ﻋﻠﻰ ﻤﺎ ﺇﺫﺍ ﻜﺎﻥ ﺃﻱ ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺘﺭﺘﻴﺒﻲ ﺃﻭ ﻭﺼﻔﻲ ﻭﻜﺫﻟﻙ ﻋﻠﻰ ﻤﺎ
ﺇﺫﺍ ﻜﺎﻥ ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ ) 2×2ﻜل ﻅﺎﻫﺭﺓ ﻟﻬﺎ ﻓﺌﺘﻴﻥ ﻓﻘﻁ( ﺃﻭ ﺃﻜﺒﺭ ﻤﻥ ﺫﻟﻙ ،ﻓﻬﻨﺎﻙ ﻤﻌﺎﻤل Φﻭﺍﻟﺫﻱ ﻴﻨﺘﺞ ﻤﻥ ﻗﺴﻤﺔ ﻗﻴﻤﺔ χ 2ﺍﻟﻨﺎﺘﺠﺔ ﻋﻠﻰ ﻤﺠﻤﻭﻉ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺜﻡ ﺃﺨﺫ
ﺍﻟﺠﺭ ﺍﻟﺘﺭﺒﻴﻌﻲ ﻟﻠﻨﺎﺘﺞ ،ﻭﻟﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ ﺍﻟﺘﻲ ﺘﺤﺘﻭﻱ ﻋﻠﻰ ﻅﺎﻫﺭﺘﻴﻥ ﺃﻱ ﻤﻨﻬﻤﺎ
ﻴﺸﺘﻤل ﻋﻠﻰ ﺃﻜﺜﺭ ﻤﻥ ﻓﺌﺘﻴﻥ ﻴﻤﻜﻥ ﺍﺴﺘﺨﺩﺍﻡ ﺇﺤﺼﺎﺀ ﺁﺨﺭ ﻫﻭ ﺇﺤﺼﺎﺀ ﻜﺭﺍﻤﺭ V
،Cramer'sﻭﻫﻭ ﻤﻔﻀل ﻓﻲ ﺍﻟﺠﺩﺍﻭل ﺍﻷﻜﺜﺭ ﺘﻌﻘﻴﺩﹰﺍ ،ﻭﻫﻨﺎﻙ ﺃﻴﻀﹰﺎ ﻤﻘﻴﺎﺱ ﺁﺨﺭ ﻟﻘﻭﺓ
ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﻭﻫﻭ ﺇﺤﺼﺎﺀ ﺠﻭﺩﻤﺎﻥ ﻭﻜﺭﺴﻜﺎل Goodman & Kruskal's
) λﻻﻤﺒﺩﺍ ، (Lambdaﻭﺇﺫﺍ ﻜﺎﻥ ﻜل ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺘﺭﺘﻴﺒﻴﻴﻥ ﻓﺈﻨﻪ ﻻﺒﺩ ﻤﻥ ﺍﻟﻌﻭﺩﺓ
ﺇﻟﻰ ﺍﻟﻘﺴﻡ ﺍﻟﺴﺎﺒﻕ ﻭﻤﻥ ﺜﻡ ﺍﺴﺘﺨﺩﺍﻡ ﺇﺤﺼﺎﺀ ﻜﻨﺩﺍل Kendall's Statisticﺒﺄﻱ ﻤﻥ ﺼﻴﻐﺘﻴﻪ tau-bﺃﻭ . tau-c
ﻭﺍﻵﻥ ﻟﺘﻭﻀﻴﺢ ﻜﻴﻔﻴﺔ ﺘﺤﻠﻴل ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ 2×2
2x2 contingency
tablesﺴﻨﻔﺘﺭﺽ ﺃﻥ ﻫﻨﺎﻙ 50ﻤﻥ ﺍﻷﻭﻻﺩ ﻭ 50ﻤﻥ ﺍﻟﺒﻨﺎﺕ ﻭﺴﺌل ﻜل ﻤﻨﻬﻡ ﺃﻥ ﻴﺄﺨﺫ ﻟﻌﺒﺔ ﻤﻥ ﺃﺤﺩ ﺍﻟﺩﻭﺍﻟﻴﺏ ،ﺤﻴﺙ ﻜﺎﻥ ﻫﻨﺎﻙ ﻤﺠﻤﻭﻋﺔ ﻜﺒﻴﺭﺓ ﻤﻥ ﺍﻟﻠﻌﺏ ﺘﻡ ﺘﺼﻨﻴﻔﻬﻡ
ﺇﻟﻰ ﻓﺌﺘﻴﻥ )ﺃﻟﻌﺎﺏ ﻤﻴﻜﺎﻨﻴﻜﻴﺔ ﻭﺃﻟﻌﺎﺏ ﻏﻴﺭ ﻤﻴﻜﺎﻨﻴﻜﻴﺔ( ،ﻭﻴﺭﺍﺩ ﺍﺨﺘﺒﺎﺭ ﺍﻟﻔﺭﻀﻴﺔ ﺃﻥ
ﺍﻷﻭﻻﺩ ﻴﻔﻀﻠﻭﻥ ﺍﻷﻟﻌﺎﺏ ﺍﻟﻤﻴﻜﺎﻨﻴﻜﻴﺔ ﺒﻴﻨﻤﺎ ﺘﻔﻀل ﺍﻟﺒﻨﺎﺕ ﺍﻷﻟﻌﺎﺏ ﺍﻟﻐﻴﺭ ﻤﻴﻜﺎﻨﻴﻜﻴﺔ،
ﻭﺒﺫﻟﻙ ﻓﺈﻥ ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭﻴﻥ ﻭﺼﻔﻴﻴﻥ ﻫﻨﺎ ﻫﻤﺎ ﺍﻟﻨﻭﻉ ) Genderﺃﻭﻻﺩ Boysﻭﺒﻨﺎﺕ
(Girlsﻭﺍﺨﺘﻴﺎﺭﺍﺕ ﺍﻷﻁﻔﺎل ) Children's Choiceﻤﻴﻜﺎﻨﻴﻜﻴﺔ Mechanicalﻭﻏﻴﺭ ﻤﻴﻜﺎﻨﻴﻜﻴﺔ ،(Non-Mechanicalﻭﺴﺘﻜﻭﻥ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ H0ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﻫﻲ:
ﻻ ﻴﻭﺠﺩ ﻋﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ،ﻭﻴﺒﻴﻥ ﺸﻜل 10-11ﺍﺨﺘﻴﺎﺭﺍﺕ ﻫﺅﻻﺀ ﺍﻷﻁﻔﺎل.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
391
ﺸﻜل : 10-11ﺠﺩﻭل ﺍﻗﺘﺭﺍﻥ 2×2ﻴﺒﻴﻥ ﺃﻨﻭﺍﻉ ﺍﻷﻟﻌﺎﺏ ﺍﻟﺘﻲ ﻴﻔﻀﻠﻬﺎ ﺍﻷﻭﻻﺩ ﻭﺍﻟﺒﻨﺎﺕ
ﺍﻟﻨﻭﻉ
ﺍﺨﺘﻴﺎﺭﺍﺕ ﺍﻷﻁﻔﺎل ﻤﻴﻜﺎﻨﻴﻜﻴﺔ
ﻏﻴﺭ ﻤﻴﻜﺎﻨﻴﻜﻴﺔ
ﺍﻟﻤﺠﻤﻭﻉ
ﺃﻭﻻﺩ
30
20
50
ﺒﻨﺎﺕ
15
35
50
ﺍﻟﻤﺠﻤﻭﻉ
45
55
100
ﺒﺘﻔﺤﺹ ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ ﺍﻟﺴﺎﺒﻕ ﻗﺩ ﻴﺒﺩﻭ ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﺒﻴﻥ ﻨﻭﻉ ﺍﻟﻁﻔل
ﻭﺘﻔﻀﻴﻠﻪ ﻟﻨﻭﻉ ﻤﻌﻴﻥ ﻤﻥ ﺍﻷﻟﻌﺎﺏ ،ﻓﻤﻌﻅﻡ ﺍﻷﻭﻻﺩ ﻓﻲ ﺍﻟﻭﺍﻗﻊ ﺍﺨﺘﺎﺭﻭﺍ ﺍﻷﻟﻌﺎﺏ
ﺍﻟﻤﻴﻜﺎﻨﻴﻜﻴﺔ )ﺍﻟﻤﺘﺤﺭﻜﺔ( ﻭﻤﻌﻅﻡ ﺍﻟﺒﻨﺎﺕ ﺍﺨﺘﺭﻥ ﺍﻷﻟﻌﺎﺏ ﺍﻟﻐﻴﺭ ﻤﻴﻜﺎﻨﻴﻜﻴﺔ )ﺍﻟﺴﺎﻜﻨﺔ(.
ﻭﻹﺩﺨﺎل ﻤﺜل ﻫﺫﻩ ﺍﻟﺒﻴﺎﻨﺎﺕ ﺇﻟﻰ ﻨﻅﺎﻡ SPSSﻭﺘﻜﻭﻴﻥ ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ ﻭﺤﺴﺎﺏ
ﻤﻘﺎﻴﻴﺱ ﺍﻟﺘﺭﺍﺒﻁ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﺍﻟﻨﻭﻋﻴﺘﻴﻥ ﻴﺠﺏ ﺃﻥ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﻤﺘﻐﻴﺭﻱ ﺘﺼﻨﻴﻑ
ﻟﺘﻌﺭﻑ ﺨﻼﻴﺎ ﺍﻟﺠﺩﻭل ﺍﻟﻤﺨﺘﻠﻔﺔ ،ﺃﺤﺩﻫﻤﺎ ﻴﻤﺜل ﺒﺎﻟﺼﻔﻭﻑ )ﻭﻫﻨﺎ ﻤﺘﻐﻴﺭ ﺍﻟﻨﻭﻉ (Genderﻭﺍﻵﺨﺭ ﻴﻤﺜل ﺒﺎﻷﻋﻤﺩﺓ )ﺍﺨﺘﻴﺎﺭﺍﺕ ﺍﻷﻁﻔﺎل . (Children's choice
ﻭﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﻁﺭﻕ ﻭﺍﻷﺴﺎﻟﻴﺏ ﺍﻟﺘﻲ ﺘﻤﺕ ﻤﻌﺎﻟﺠﺘﻬﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﻫﺫﺍ
ﺍﻟﻜﺘﺎﺏ ﻴﻤﻜﻥ ﺇﺩﺨﺎل ﺒﻴﺎﻨﺎﺕ ﺍﻟﺠﺩﻭل ﻓﻲ ﺍﻟﺸﻜل ﺍﻟﺴﺎﺒﻕ ﺇﻟﻰ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ Data
Editorﻓﻲ ﻨﻅﺎﻡ SPSSﺒﺴﻬﻭﻟﺔ ﺒﺤﻴﺙ ﻴﺘﻡ ﺘﻌﺭﻴﻑ ﺜﻼﺙ ﻤﺘﻐﻴﺭﺍﺕ ﻫﻡ ﺍﻟﻨﻭﻉ
genderﻭﺍﺨﺘﻴﺎﺭﺍﺕ ﺍﻷﻁﻔﺎل choiceﻭﺍﻟﻌﺩﺩ ،countﻭﻴﻤﻜﻥ ﺃﻥ ﻴﻌﻁﻰ ﺩﻟﻴل ﻟﻘﻴﻡ ﻜل
ﻤﻥ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺍﻟﻨﻭﻉ ) 1ﻟﻠﻭﻟﺩ ﻭ 0ﻟﻠﺒﻨﺕ( ﻭﺍﺨﺘﻴﺎﺭﺍﺕ ﺍﻷﻁﻔﺎل ) 1ﻟﻠﻤﻴﻜﺎﻨﻴﻜﻴﺔ ﻭ 0
ﻟﻐﻴﺭ ﺍﻟﻤﻴﻜﺎﻨﻴﻜﻴﺔ( ،ﺜﻡ ﻴﺘﻡ ﺇﺩﺨﺎل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺒﺎﻟﻁﺭﻴﻘﺔ ﺍﻟﻤﻌﺘﺎﺩﺓ ﻜﻤﺎ ﻓﻲ ﺸﻜل .11-11
ﻭﺍﻟﺨﻁﻭﺓ ﺍﻟﺘﺎﻟﻴﺔ ﻀﺭﻭﺭﻴﺔ ﻷﻥ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﻤﺘﻐﻴﺭ ﺍﻟﻌﺩﺩ countﻋﺒﺎﺭﺓ ﻋﻥ
ﺘﻜﺭﺍﺭ ﻜل ﻗﻴﻤﺔ ﻤﻥ ﻗﻴﻡ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﻤﻌﹰﺎ )ﻭﻟﻴﺴﺕ ﻗﻴﻤﹰﺎ ﻟﻅﺎﻫﺭﺓ ﺤﻘﻴﻘﻴﺔ( ،ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﻬﻭ ﺒﻤﺜﺎﺒﺔ ﺃﻭﺯﺍﻥ ﻟﻘﻴﻡ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ،ﻭﻟﻬﺫﺍ ﻴﺘﻡ ﺘﻌﺭﻴﻔﻪ ﻟﻨﻅﺎﻡ SPSSﻜﺄﻭﺯﺍﻥ ﻜﻤﺎ ﻴﻠﻲ:
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
392
ﺸﻜل : 11-11ﺠﺎﻨﺏ ﻤﻥ ﻤﺤﺭﺭ ﺍﻟﺒﻴﺎﻨﺎﺕ ﻓﻲ ﻨﻅﺎﻡ SPSSﻴﻭﻀﺢ ﻜﻴﻔﻴﺔ ﺇﺩﺨﺎل ﺠﺩﻭل ﺍﻗﺘﺭﺍﻥ 2×2ﻴﻤﺜل ﺃﻨﻭﺍﻉ ﺍﻷﻟﻌﺎﺏ ﺍﻟﺘﻲ ﻴﻔﻀﻠﻬﺎ ﺍﻷﻭﻻﺩ ﻭﺍﻟﺒﻨﺎﺕ
• ﻴﻤﻜﻥ ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﺃﻤﺭ ﺇﻋﻁﺎﺀ ﺃﻭﺯﺍﻥ ﻟﻠﺒﻴﺎﻨﺎﺕ Weight Casesﻜﻤﺎ ﺘﻡ ﻤﻨﺎﻗﺸﺘﻪ
ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ ﻤﻥ ﻫﺫﺍ ﺍﻟﻜﺘﺎﺏ ﻤﻥ ﺨﻼل ﻗﺎﺌﻤﺔ ﺍﻟﺒﻴﺎﻨﺎﺕ Dataﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ
ﺍﻟﺭﺌﻴﺴﻴﺔ ﻟﻨﻅﺎﻡ SPSSﻜﻤﺎ ﻫﻭ ﻤﺒﻴﻥ ﻓﻲ ﺸﻜل 12-11ﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺃﻭﺯﺍﻥ ﺍﻟﻘﻴﻡ
. Weight Cases
ﺸﻜل : 12-11ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﺃﻤﺭ ﺇﻋﻁﺎﺀ ﺃﻭﺯﺍﻥ ﻟﻠﺒﻴﺎﻨﺎﺕ .Weight Cases
• ﻓﻲ ﻨﺎﻓﺫﺓ ﺃﻭﺯﺍﻥ ﺍﻟﻘﻴﻡ Weight Casesﺍﻟﺘﻲ ﻅﻬﺭﺕ ﻴﺘﻡ ﺍﺨﺘﻴﺎﺭ ﺇﻋﻁﺎﺀ ﺃﻭﺯﺍﻥ ﻟﻠﺒﻴﺎﻨﺎﺕ Weight Cases byﺜﻡ ﻴﺘﻡ ﺇﺩﺨﺎل ﺍﺴﻡ ﺍﻟﻤﺘﻐﻴﺭ ﺍﻟﺫﻱ ﻴﻤﺜل ﺍﻷﻭﺯﺍﻥ ﻭﻫﻭ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺍﻟﻌﺩﺩ countﻓﻲ ﻤﺭﺒﻊ ﻤﺘﻐﻴﺭ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ،Frequency Variable ﻭﺘﻅﻬﺭ ﻓﻲ ﺸﻜل 13-11ﻫﺫﻩ ﺍﻟﻨﺎﻓﺫﺓ ﻭﻗﺩ ﺩﺨﻠﺕ ﺒﻬﺎ ﺠﻤﻴﻊ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﺍﻟﻤﻁﻠﻭﺒﺔ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
393
ﺸﻜل : 13-11ﻨﺎﻓﺫﺓ ﺃﻭﺯﺍﻥ ﺍﻟﻘﻴﻡ Weight Casesﻓﻲ ﻗﺎﺌﻤﺔ ﺍﻟﺒﻴﺎﻨﺎﺕ . Data
• ﺍﻀﻐﻁ ﺃﻤﺭ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﺘﻨﻔﻴﺫ ﺃﻤﺭ ﺇﻋﻁﺎﺀ ﺃﻭﺯﺍﻥ ﻟﻠﺒﻴﺎﻨﺎﺕ )ﻻﺤﻅ ﺃﻨﻪ ﻴﺘﻡ ﺇﻟﻐﺎﺀ ﻫﺫﺍ ﺍﻷﻤﺭ ﺒﺈﻋﺎﺩﺓ ﻨﻔﺱ ﺍﻟﺨﻁﻭﺍﺕ ﺍﻟﺴﺎﺒﻘﺔ ﻭﻟﻜﻥ ﺒﺘﺤﺩﻴﺩ ﺍﻟﺨﻴﺎﺭ ﺍﻟﺘﻠﻘﺎﺌﻲ ﻭﻫﻭ ﻋﺩﻡ ﺇﻋﻁﺎﺀ ﺃﻭﺯﺍﻥ ﻟﻠﺒﻴﺎﻨﺎﺕ Do not weight casesﻜﻤﺎ ﻴﻅﻬﺭ ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ ﻓﻲ ﺍﻟﺸﻜل
ﺍﻟﺴﺎﺒﻕ.
ﻭﺍﻵﻥ ﻴﻤﻜﻥ ﺘﺤﻠﻴل ﺍﻟﺒﻴﺎﻨﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ ﻟﺘﻜﻭﻴﻥ ﺠﺩﻭل ﺍﻟﺘﻭﺍﻓﻕ ﻭﺤﺴﺎﺏ ﺍﻟﻤﻘﺎﻴﻴﺱ
ﺍﻟﻤﻁﻠﻭﺒﺔ ﻋﻥ ﻁﺭﻴﻕ ﺍﺴﺘﺨﺩﺍﻡ ﺃﻤﺭ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﻤﺯﺩﻭﺠﺔ Crosstabsﻜﻤﺎ ﺘﻤﺕ ﻤﻌﺎﻟﺠﺘﻪ ﺒﺎﻟﺘﻔﺼﻴل ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺭﺍﺒﻊ ﻜﻤﺎ ﻴﻠﻲ :
• ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ) Analyzeﺃﻭ (Statisticsﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ. • ﺍﺨﺘﺭ ﻗﺎﺌﻤﺔ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻟﻭﺼﻔﻴﺔ ) Descriptive Statisticsﺃﻭ ﺘﻠﺨﻴﺹ ﺍﻟﺒﻴﺎﻨﺎﺕ
(Summarizeﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺴﺎﺒﻘﺔ )ﺸﻜل .(14-11
• ﺍﺨﺘﺭ ﺃﻤﺭ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﺘﻜﺭﺍﺭﻴﺔ ﺍﻟﻤﺯﺩﻭﺠﺔ Crosstabsﻤﻥ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺴﺎﺒﻘﺔ ﻟﺘﻅﻬﺭ ﻨﺎﻓﺫﺓ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﺘﻜﺭﺍﺭﻴﺔ ﺍﻟﻤﺯﺩﻭﺠﺔ ) Crosstabsﺸﻜل .(15-11
• ﺃﺩﺨل ﺃﺴﻤﺎﺀ ﺍﻟﻤﺘﻐﻴﺭﻴﻥ ﺍﻟﻨﻭﻉ genderﻭﺍﺨﺘﻴﺎﺭﺍﺕ ﺍﻷﻁﻔﺎل choiceﻓﻲ ﻤﺭﺒﻌﻲ ﺍﻟﺼﻔﻭﻑ ) Row(sﻭﺍﻷﻋﻤﺩﺓ ) Column(sﻋﻠﻰ ﺍﻟﺘﺭﺘﻴﺏ ﻓﻲ ﺍﻟﻨﺎﻓﺫﺓ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
394
ﺸﻜل : 14-11ﺍﻟﻭﺼﻭل ﺇﻟﻰ ﺃﻤﺭ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﺘﻜﺭﺍﺭﻴﺔ ﺍﻟﻤﺯﺩﻭﺠﺔ Crosstabsﻤﻥ ﻗﺎﺌﻤﺔ ﺍﻟﺘﺤﻠﻴل ﺍﻹﺤﺼﺎﺌﻲ ﻓﻲ ﺍﻟﻘﺎﺌﻤﺔ ﺍﻟﺭﺌﻴﺴﻴﺔ ﻟﻨﻅﺎﻡ .SPSS
ﺸﻜل : 15-11ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﺘﻜﺭﺍﺭﻴﺔ ﺍﻟﻤﺯﺩﻭﺠﺔ . Crosstabs
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
395
• ﺍﻀﻐﻁ ﻋﻠﻰ ﻤﺭﺒﻊ ﺨﻴﺎﺭﺍﺕ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ Statisticsﻓﻲ ﺃﺴﻔل ﺍﻟﻨﺎﻓﺫﺓ ﻟﺘﺤﺩﻴﺩ ﺍﻻﺤﺼﺎﺀﺍﺕ ﺍﻟﻤﻁﻠﻭﺒﺔ ﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ Statistics
ﻜﻤﺎ ﻓﻲ ﺸﻜل 16-11ﺃﺩﻨﺎﻩ.
ﺸﻜل : 16-11ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ Statisticsﻤﻥ ﻨﺎﻓﺫﺓ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﺘﻜﺭﺍﺭﻴﺔ ﺍﻟﻤﺯﺩﻭﺠﺔ . Crosstabs
• ﻓﻲ ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﺍﻟﻤﻘﺎﻴﻴﺱ ﺍﻹﺤﺼﺎﺌﻴﺔ Statisticsﻗﻡ ﺒﺎﺨﺘﻴﺎﺭ ﺍﻹﺤﺼﺎﺀﺍﺕ
ﺍﻟﻤﻁﻠﻭﺒﺔ ﻭﻫﻲ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ :ﻜﺎﻱ ﺴﻜﻭﻴﺭ Chi-squareﻭﻓﺎﻱ ﻭﻜﺭﺍﻤﺭ Phi and
Cramer's Vﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل .16-11
• ﺍﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻻﺴﺘﻤﺭﺍﺭ Continueﻟﻠﻌﻭﺩﺓ ﺇﻟﻰ ﻨﺎﻓﺫﺓ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﺘﻜﺭﺍﺭﻴﺔ ﺍﻟﻤﺯﺩﻭﺠﺔ Crosstabsﺜﻡ ﻤﻔﺘﺎﺡ ﺍﻟﺘﻨﻔﻴﺫ OKﻟﺘﻨﻔﻴﺫ ﺍﻷﻤﺭ .
ﻫﻨﺎﻙ ﺨﻴﺎﺭ ﺁﺨﺭ ﻨﻨﺼﺢ ﺒﺎﺴﺘﺨﺩﺍﻤﻪ ﻭﻴﺘﻌﻠﻕ ﺒﺤﺴﺎﺏ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ
ﻟﻠﺨﻼﻴﺎ ،ﻤﻥ ﺨﻼل ﻫﺫﺍ ﺍﻟﺨﻴﺎﺭ ﻴﻤﻜﻥ ﻟﻠﻤﺴﺘﺨﺩﻡ ﺍﻟﺘﺤﻘﻕ ﻤﻥ ﺘﻭﻓﺭ ﺍﻟﺤﺩ ﺍﻷﺩﻨﻰ ﻤﻥ
ﺍﻟﺸﺭﻭﻁ ﺍﻟﻭﺍﺠﺏ ﺘﻭﺍﻓﺭﻫﺎ ﻟﻼﺴﺘﺨﺩﺍﻡ ﺍﻟﺴﻠﻴﻡ ﻻﺨﺘﺒﺎﺭ ، χ 2ﻭﻋﻠﻰ ﺍﻟﺭﻏﻡ ﻤﻥ ﺍﻟﺨﻼﻓﺎﺕ
ﻓﻲ ﺍﻟﻭﺴﻁ ﺍﻷﻜﺎﺩﻴﻤﻲ ﺤﻭل ﺘﻠﻙ ﺍﻟﺸﺭﻭﻁ ﺇﻻ ﺃﻥ ﻫﻨﺎﻙ ﺤﺩ ﺃﺩﻨﻰ ﻤﻨﻬﺎ ﻤﺘﻔﻕ ﻋﻠﻴﻪ، ﻭﻫﺫﻩ ﺍﻟﺸﺭﻭﻁ ﺘﺘﻀﻤﻥ :
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
396
) (1ﻓﻲ ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ 2×2ﻴﺠﺏ ﺃﻻ ﺘﻘل ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻓﻲ ﺃﻱ ﺨﻠﻴﺔ ﻤﻥ ﺨﻼﻴﺎ ﺍﻟﺠﺩﻭل ﺍﻷﺭﺒﻊ ﻋﻥ .5 ) (2ﻓﻲ ﺍﻟﺠﺩﺍﻭل ﺍﻷﻜﺒﺭ ﻤﻥ 2×2ﻴﺠﺏ ﺃﻻ ﻴﻜﻭﻥ ﺍﻟﺘﻜﺭﺍﺭ ﺍﻟﻤﺘﻭﻗﻊ ﻤﺴﺎﻭﻴﹰﺎ
ﻗﻴﻤﺔ ﺃﻗل ﻤﻥ ﺍﻟﻭﺍﺤﺩ ﺍﻟﺼﺤﻴﺢ ﻓﻲ ﺃﻱ ﺨﻠﻴﺔ ﻤﻥ ﺍﻟﺨﻼﻴﺎ ،ﻭﻻ ﻴﻜﻭﻥ ﻫﻨﺎﻙ ﺃﻜﺜﺭ ﻤﻥ 20%ﻤﻥ ﺨﻼﻴﺎ ﺍﻟﺠﺩﻭل ﺘﻘل ﻓﻴﻬﺎ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻋﻥ . 5
ﻭﻴﻤﻜﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻟﻠﺨﻼﻴﺎ ﻓﻲ ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ
ﺍﻟﻨﺎﺘﺠﺔ ﻋﻥ ﻁﺭﻴﻕ ﺍﻟﻀﻐﻁ ﻋﻠﻰ ﺨﻴﺎﺭ ﺍﻟﺨﻼﻴﺎ Cellsﻓﻲ ﺍﺴﻔل ﻨﺎﻓﺫﺓ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﻤﺯﺩﻭﺠﺔ ) Crosstabsﺸﻜل (15-11ﻟﺘﺒﺭﺯ ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﻅﻬﻭﺭ ﺍﻟﺨﻼﻴﺎ
) Crosstabs: Cell Displayﺸﻜل .(17-11ﻭﺒﻬﺎ ﻴﻤﻜﻥ ﺘﺤﺩﻴﺩ ﺨﻴﺎﺭﺍﺕ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺸﺎﻫﺩﺓ Observedﻭﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ Expectedﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل ﺃﺩﻨﺎﻩ ،ﻭﻓﻲ
ﺍﻟﻨﻬﺎﻴﺔ ﺍﻟﻀﻐﻁ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻻﺴﺘﻤﺭﺍﺭ Continueﺜﻡ ﻋﻠﻰ ﻤﻔﺘﺎﺡ ﺍﻟﺘﻨﻔﻴﺫ OKﻓﻲ ﻨﺎﻓﺫﺓ ﺘﻜﻭﻴﻥ ﺍﻟﺠﺩﺍﻭل ﺍﻟﻤﺯﺩﻭﺠﺔ . Crosstabs
ﺸﻜل : 17-11ﻨﺎﻓﺫﺓ ﺨﻴﺎﺭﺍﺕ ﻅﻬﻭﺭ ﺍﻟﺨﻼﻴﺎ Crosstabs: Cell Display
ﻭﻨﺘﺎﺌﺞ ﻫﺫﻩ ﺃﻤﺭ ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ Crosstabsﺘﺒﺩﺃ ﺒﻤﻠﺨﺹ ﻋﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
ﻭﺃﻋﺩﺍﺩ ﺍﻟﻤﺸﺎﻫﺩﺍﺕ ) Case Processing Summaryﻟﻡ ﻴﻌﺭﺽ ﻫﻨﺎ( ﻴﻠﻴﻪ ﺍﻟﺠﺩﻭل
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
397
ﺍﻟﺘﻜﺭﺍﺭﻱ ﺍﻟﻤﺯﺩﻭﺝ )ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ( ﺍﻟﺫﻱ ﻴﺘﻡ ﺘﻜﻭﻴﻨﻪ ﻜﻤﺎ ﻴﻅﻬﺭ ﻓﻲ ﺸﻜل 18-11 ﻭﺘﺒﺩﻭ ﺒﻪ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺸﺎﻫﺩﺓ Countﻭﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ Expected Countﻟﻜل
ﺨﻠﻴﺔ ﻭﺫﻟﻙ ﻜﻤﺎ ﺘﻡ ﻁﻠﺒﻪ ﻤﻥ ﺨﻴﺎﺭ ﻅﻬﻭﺭ ﺍﻟﺨﻼﻴﺎ ، Crosstabs: Cell Display ﻻﺤﻅ ﺃﻨﻪ ﻻ ﻴﻭﺠﺩ ﻓﻲ ﺍﻟﺠﺩﻭل ﺨﻼﻴﺎ ﺘﺤﺘﻭﻱ ﻋﻠﻰ ﺘﻜﺭﺍﺭﺍﺕ ﻤﺘﻭﻗﻌﺔ ﺃﻗل ﻤﻥ . 5
ﺸﻜل : 18-11ﺍﻟﺠﺯﺀ ﺍﻷﻭل ﻤﻥ ﻨﺘﺎﺌﺞ ﺍﻟﺠﺩﺍﻭل ﺍﻟﻤﺯﺩﻭﺠﺔ )ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ( Crosstabs Gender * Choice Crosstabulation Choice Total
Mechanical Non-Mechanical
50
20
30
50.0
27.5
22.5
50
35
15
50.0
27.5
22.5
100
55
45
100.0
55.0
45.0
Count
Boys
Gender
Expected Count Count
Girls
Expected Count Count
Total
Expected Count
ﻭﻴﺒﻴﻥ ﺸﻜل 19-11ﻨﺘﺎﺌﺞ ﺤﺴﺎﺏ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ χ 2ﺍﻟﻤﻁﻠﻭﺒﺔ ﻭﺒﻌﺽ ﺩﻭﺍل
ﺍﻻﺨﺘﺒﺎﺭ ﺍﻷﺨﺭﻯ ﺍﻟﻤﺸﺎﺒﻬﺔ ﻓﻲ ﺍﻟﻐﺭﺽ ﻻﺨﺘﺒﺎﺭ χ 2ﺍﻷﺴﺎﺴﻲ ﺍﻟﻤﺴﻤﻰ ﻫﻨﺎ Pearson
chi-squareﻨﺴﺒﺔ ﻷﻭل ﻤﻥ ﻭﻀﻊ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ، Pearsonﻭﻴﻤﻜﻥ ﻤﻌﺭﻓﺔ ﺍﻟﺘﻔﺴﻴﺭ ﻷﻱ ﻤﻥ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻤﻥ ﺨﻼل ﺍﻟﻤﺴﺎﻋﺩﺓ ﻓﻲ ﺩﺍﺨل ﻤﺤﺭﺭ ﺍﻟﻨﺘﺎﺌﺞ ﻓﻲ ﻨﻅﺎﻡ
ﻻ ﺜﻡ SPSSﻋﻥ ﻁﺭﻴﻕ ﺍﻟﻨﻘﺭ ﺒﺎﻟﻔﺄﺭﺓ ﻋﻠﻰ ﺍﺴﻡ ﻫﺫﺍ ﺍﻻﺨﺘﺒﺎﺭ ﻟﺘﺤﺩﻴﺩ ﻫﺫﺍ ﺍﻻﺴﻡ ﺃﻭ ﹰ ﺍﻟﻨﻘﺭ ﻋﻠﻰ ﻁﺭﻑ ﺍﻟﻔﺄﺭﺓ ﺍﻷﻴﻤﻥ ﻟﺘﻔﺘﺢ ﻨﺎﻓﺫﺓ ﺒﻌﻨﻭﺍﻥ ﻤﺎ ﻫﺫﺍ؟ ? What is thisﻭﺘﺤﺭﻴﻙ
ﺍﻟﻤﺅﺸﺭ ﺇﻟﻰ ﺍﻻﺴﻡ ﺍﻟﺫﻱ ﺘﺭﻴﺩ ﻤﻌﻠﻭﻤﺎﺕ ﻋﻨﻪ ﺜﻡ ﺍﻟﻨﻘﺭ ﻋﻠﻰ ﺍﻟﻁﺭﻑ ﺍﻷﻴﺴﺭ ﻟﻠﻔﺄﺭﺓ ﻟﻔﺘﺢ
ﻨﺎﻓﺫﺓ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﻋﻥ ﺫﻟﻙ ﺍﻻﺨﺘﺒﺎﺭ ﻋﻠﻰ ﺍﻟﺸﺎﺸﺔ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
398
ﺸﻜل : 19-11ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻨﻲ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ Crosstabs Chi-Square Tests
Exact Sig. )(1-sided
Exact Sig. )(2-sided
.002
.005
Asymp. Sig. )(2-sided
df
.003
1
Value b
Pearson Chi-Square
9.091 a
.005
1
7.919
Continuity Correction
.002
1
9.240
Likelihood Ratio Fisher's Exact Test
.003
1
9.000
Linear-by-Linear Association
100
N of Valid Cases
a. Computed only for a 2x2 table b. 0 cells (.0%) have expected count less than 5. The minimum expected count is 22.50.
ﻤﻥ ﺴﻁﺭ ﺒﻴﺭﺴﻭﻥ ﻜﺎﻱ ﺴﻜﻭﻴﺭ Pearson chi-squareﻓﻲ ﺍﻟﺸﻜل ﺍﻟﺴﺎﺒﻕ
ﻨﺠﺩ ﻗﻴﻤﺔ ﺩﺍﻟﺔ ﺍﻻﺨﺘﺒﺎﺭ Valueﻭﺩﺭﺠﺎﺕ ﺤﺭﻴﺘﻪ dfﻭﻤﻌﻨﻭﻴﺘﻪ ﺍﻟﺘﻘﺭﻴﺒﻴﺔ ﻻﺨﺘﺒﺎﺭ
ﺜﻨﺎﺌﻲ ﺍﻟﻁﺭﻑ )) Asymp. Sig. (2-sidedﻭﺫﻟﻙ ﻓﻲ ﻅل ﺼﺤﺔ ﺍﻟﻔﺭﻀﻴﺔ ﺍﻟﻌﺩﻤﻴﺔ
،(H0ﻭﻴﻤﻜﻥ ﻤﻥ ﺘﻠﻙ ﺍﻟﻘﻴﻡ ﻓﻲ ﺍﻟﺸﻜل ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﺍﺴﺘﻨﺘﺎﺝ ﺃﻨﻪ ﻴﻭﺠﺩ ﻋﻼﻗﺔ ﻤﻌﻨﻭﻴﺔ ﻤﺎ ﺒﻴﻥ ﻤﺘﻐﻴﺭ ﺍﻟﻨﻭﻉ groupﻭﺍﺨﺘﻴﺎﺭﻩ ﻟﻠﻌﺒﺔ ، choiceﻭﺫﻟﻙ ﻨﻅﺭﹰﺍ ﻟﻘﻴﻤﺔ ﺍﻟﻤﻌﻨﻭﻴﺔ p-
valueﺍﻟﻤﻨﺨﻔﻀﺔ )ﺃﻗل ﻤﻥ (0.01ﻟﺩﺍﻟﺔ ﻜﺎﻱ ﺴﻜﻭﻴﺭ ،ﻭﺒﺎﻟﺘﺎﻟﻲ ﻴﻤﻜﻥ ﺘﻠﺨﻴﺹ ﻫﺫﻩ ﺍﻟﻨﺘﻴﺠﺔ ﻋﻠﻰ ﺍﻟﺼﻭﺭﺓ: Significant.
; p < 0.01
; df = 1
; χ 2 = 9.09
ﻭﺍﻟﻤﻼﺤﻅﺔ ﺍﻟﻤﺸﺎﺭ ﺇﻟﻴﻬﺎ ﺒﺎﻟﺭﻤﺯ bﻓﻲ ﺍﻟﺸﻜل ﺘﻨﺒﻪ ﺍﻟﻤﺴﺘﺨﺩﻡ ﺒﻌﺩﺩ ﺍﻟﺨﻼﻴﺎ ﻓﻲ
ﺍﻟﺠﺩﻭل ﺍﻟﺘﻲ ﺘﻘل ﺒﻬﺎ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻋﻥ ، 5ﻭﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻻ ﻴﻭﺠﺩ ﺃﻱ ﻤﻨﻬﺎ ،ﻭﻫﺫﻩ ﻤﻌﻠﻭﻤﺔ ﻗﺩ ﺘﻜﻭﻥ ﻤﻔﻴﺩﺓ ﻜﺘﻨﺒﻴﻪ ﻟﻠﻤﺴﺘﺨﺩﻡ.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
399
ﻭﻋﻨﺩﻤﺎ ﺘﻜﻭﻥ ﺠﻤﻴﻊ ﺍﻟﺘﻜﺭﺍﺭﺍﺕ ﺍﻟﻤﺘﻭﻗﻌﺔ ﻓﻲ ﺨﻼﻴﺎ ﺠﺩﻭل ﺍﻻﻗﺘﺭﺍﻥ 2×2 ﺼﻐﻴﺭﺓ ﻓﺈﻨﻪ ﻴﻤﻜﻥ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ ﺍﺴﺘﺨﺩﺍﻡ ﺩﺍﻟﺔ ﺍﺨﺘﺒﺎﺭ ﻓﻴﺸﺭ ﺍﻟﺩﻗﻴﻘﺔ Fisher's
ﻻ ﻤﻥ ﺩﺍﻟﺔ ﺍﺨﺘﺒﺎﺭ ﻜﺎﻱ ﺴﻜﻭﻴﺭ ﺍﻟﺘﻘﻠﻴﺩﻴﺔ ﻟﺒﻴﺭﺴﻭﻥ Pearson chi- Exact Testﺒﺩ ﹰ
، squareﻭﻴﻤﻜﻥ ﺍﻟﺤﺼﻭل ﻋﻠﻰ ﺘﻔﺼﻴل ﻋﻥ ﺠﻤﻴﻊ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﻓﻲ Reynolds
) (1984ﻭﻜﺫﻟﻙ ). Agresti (1996
ﻭﻴﺒﻴﻥ ﺸﻜل 20-11ﺍﻟﺠﺯﺀ ﺍﻟﻨﻬﺎﺌﻲ ﻤﻥ ﻗﺎﺌﻤﺔ ﻨﺘﺎﺌﺞ ﺃﻤﺭ ﺘﺤﻠﻴل ﺍﻟﺠﺩﺍﻭل
ﺍﻟﻤﺯﺩﻭﺠﺔ Crosstabsﻗﻴﻤﺔ ﻤﻌﺎﻤل ﻓﺎﻱ Phi-Coefficientﻭﻜﺫﻟﻙ ﻤﻌﺎﻤل ﻜﺭﺍﻤﺭ Cramer's Vﻜﻤﻘﻴﺎﺴﻴﻥ ﻟﻘﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻅﺎﻫﺭﺘﻴﻥ ﻭﻜﺫﻟﻙ ﻟﻤﻌﻨﻭﻴﺔ ﻫﺫﻩ ﺍﻟﻌﻼﻗﺔ ﻭﻴﺸﺒﻬﺎﻥ ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺍﻟﺨﻁﻲ ﺍﻟﻤﺴﺘﺨﺩﻡ ﻟﻠﺒﻴﺎﻨﺎﺕ ﺍﻟﻜﻤﻴﺔ ﺍﻟﻘﻴﺎﺴﻴﺔ.
ﻭﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل ﻴﻤﻜﻥ ﻭﻀﻊ ﻨﺘﻴﺠﺔ ﻫﺫﻴﻥ ﺍﻟﻤﻘﻴﺎﺴﻴﻥ ﻋﻠﻰ ﺍﻟﺼﻭﺭﺓ ﺍﻟﺘﺎﻟﻴﺔ: Significant . Significant .
; p < 0.01
; p < 0.01
; Φ = -0.302
; Cramer’s V = 0.302
ﺸﻜل : 20-11ﺍﻟﺠﺯﺀ ﺍﻟﺜﺎﻟﺙ ﻤﻥ ﻨﺘﺎﺌﺞ ﺘﺤﻠﻴل ﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ Crosstabs Symmetric Measures Approx. Sig.
Asymp. Approx. Std. Errora Tb
Value
.003
-.302
Phi
.003
.302
Cramer's V
100
Nominal by Nominal N of Valid Cases
a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis.
) (11ﻗﻴﺎﺱ ﻗﻭﺓ ﺍﻟﻌﻼﻗﺔ ﺒﻴﻥ ﺍﻟﻤﺘﻐﻴﺭﺍﺕ
400
ﻻﺤﻅ ﺃﻥ ﻤﻌﺎﻤل ﻓﺎﻱ Phi-Coefficientﻴﻤﻜﻥ ﺃﻥ ﻴﺄﺨﺫ ﻗﻴﻤﹰﺎ ﺘﻨﺤﺼﺭ ﺒﻴﻥ -1 ﻭ +1ﻤﺜل ﻤﻌﺎﻤل ﺍﺭﺘﺒﺎﻁ ﺒﻴﺭﺴﻭﻥ ﺘﻤﺎﻤﺎﹰ ،ﻭﻟﻜﻨﻪ ﻤﺒﻨﻲ ﻋﻠﻰ ﺃﺴﺎﺱ ﺩﺍﻟﺔ ﻜﺎﻱ ﺴﻜﻭﻴﺭ χ 2ﻭﻴﺴﺘﺨﺩﻡ ﻟﺠﺩﺍﻭل ﺍﻻﻗﺘﺭﺍﻥ 2×2ﻓﻘﻁ ،ﻭﻓﻲ ﺤﺎﻟﺔ ﺠﺩﺍﻭل ﺍﻹﻗﺘﺭﺍﻥ ﺍﻟﻜﺒﻴﺭﺓ ﻻ
ﻴﻨﺼﺢ ﺒﺎﺴﺘﺨﺩﺍﻤﻪ ﺇﺫ ﺃﻥ ﻗﻴﻤﺘﻪ ﻗﺩ ﺘﺘﻌﺩﻯ ﺍﻟﻘﻴﻤﺔ ، +1ﺃﻤﺎ ﻤﻌﺎﻤل ﻜﺭﺍﻤﺭ Cramer's
Vﻫﻭ ﻤﻘﻴﺎﺱ ﻟﻠﺘﺭﺍﺒﻁ Measure of Associationﻭﻴﺄﺨﺫ ﻗﻴﻤﹰﺎ ﺘﺘﺭﺍﻭﺡ ﺒﻴﻥ ﺍﻟﺼﻔﺭ
ﻭ +1ﺃﻱ ﻻ ﻴﺄﺨﺫ ﻗﻴﻤﹰﺎ ﺴﺎﻟﺒﺔ ،ﻭﻟﺫﻟﻙ ﻭﻋﻠﻰ ﺍﻟﺭﻏﻡ ﻤﻥ ﺘﺴﺎﻭﻱ ﺍﻟﻘﻴﻤﺘﻴﻥ ﺍﻟﻤﻁﻠﻘﺘﻴﻥ
ﻟﻠﻌﺎﻤﻠﻴﻥ ﻓﻲ ﻫﺫﺍ ﺍﻟﻤﺜﺎل )ﻭﻟﻴﺱ ﺒﺎﻟﻀﺭﻭﺭﺓ ﺩﺍﺌﻤﹰﺎ( ﺇﻻ ﺃﻥ ﺇﺸﺎﺭﺘﻴﻬﻤﺎ ﺍﺨﺘﻠﻔﺘﺎ ،ﻭﻫﺫﺍ
ﺸﻲﺀ ﻁﺒﻴﻌﻲ ﻨﺘﻴﺠﺔﹰ ﻟﻠﻤﻼﺤﻅﺎﺕ ﺍﻟﺴﺎﺒﻘﺔ ،ﻭﻟﻤﺯﻴﺩ ﻤﻥ ﺍﻟﻤﻌﻠﻭﻤﺎﺕ ﺍﻟﻤﻔﺼﻠﺔ ﻓﻲ ﻫﺫﺍ ﺍﻟﺴﻴﺎﻕ ﻋﻥ ﻫﺫﻩ ﺍﻻﺨﺘﺒﺎﺭﺍﺕ ﺃﻨﻅﺭ ). Agresti (1996