Here are five lines of anthropological evidence that group Ancient Egyptians and Nubians with North Africans, West/South Asians and Europeans (Caucasoids), and separate them from Sub-Saharan Africans (Negroids). Note that Horn Africans (Somalis) cluster with Caucasoids in some cases and Negroids in others, which indicates they're a racially mixed population that's not representative of either Sub-Saharan Africans or Egyptians and Nubians.
1. Craniometric
Combined samples of Pre-Dynastic (Naqada) and Late Dynastic (Giza) Egyptians, and Bronze Age, Early Christian and Medieval Nubians, cluster with combined samples of Ancient and Modern North Africans, East Indians and Europeans.
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Brace et al. "Clines and clusters versus 'Race:' a test in ancient Egypt and the case of a death on the Nile". Am J Phys Anthro, 1993.
2. Cranial Non-metric
Pre-Dynastic Egyptians from Naqada (#59), 26th-30th Dynasty Egyptians from Gizeh (#60), 12th-13th Dynasty Nubians from Kerma (#61), and Early Christian or Christian Nubians (#62) cluster with South Asians (#44) and several European groups: Greeks (#48), Scandinavians (#51 and #52) and Germans (#53). [NOTE that Somalis are up with Sub-Saharan Africans (#63)]
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Hanihara et al. "Characterization of biological diversity through analysis of discrete cranial traits". Am J Phys Anthro, 2003.
3. Dental Metric
Pre-Dynastic and 12th-29th Dynasty Egyptians cluster with Afghans and North Indians on the edge of a larger cluster of Europeans and West Asians. [NOTE that here again, Somalis show Sub-Saharan affinities and don't cluster with Ancient Egyptians.]
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Hanihara and Ishida. "Metric dental variation of major human populations". Am J Phys Anthro, 2005.
4. Dental Non-metric
12th Dynasty (Lisht), Roman/Byzantine (El Hesa), and Byzantine (Kharga) Egyptians, and Pharonic, Meroitic, X-group and Christian Nubians, cluster with other North Africans and Europeans (Poundbury, England).
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Joel D. Irish. "Diachronic and synchronic dental trait affinities of late and post-pleistocene peoples from North Africa". Homo, 1998b.
5. Prognathism
Ancient Egyptians from Badari, Pre-Dynastic Egyptians from Naqada, and 26th-30th Dynasty Egyptians from Gizeh, as well as 12th-13th Dynasty Nubians from Kerma and Early Christian or Christian Nubians, all cluster with Europeans and West/South Asians on the negative end of the prognathism scale.
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Tsunehiko Hanihara. "Frontal and Facial Flatness of Major Human Populations". Am J Phys Anthro, 2000.