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I read about this study, and it surprised me to read that kids who stayed at home had better social skills, because it's the opposite of my experience. I stayed at home until kindergarten, and I had great difficulty with "social skills" when I started school. I was an only child, at a time before "play dates" and "quality time". But I never developed many social skills, since I didn't spend much time around other children - I was home alone with Mom. When I started kindergarten, I was shy and withdrawn, and my lack of "social skills" made it difficult for me to do well in school. But I'm just one example, and I wondered if my experience was atypical.
But after reading more about the study, I began to wonder how "social skills" were measured. The article mentions "aggression" and "non-compliance" and "demanding". It doesn't mention "shy" or "withdrawn" or "plays alone". Both of those things can result from a lack of social skills, and both can lead to problems in school later on. But a quiet and shy child might not be seen as "lacking social skills", and instead just be seen as a good child, "compliant" and "undemanding" - the opposite of the aggressive and non-compliant child who attracts attention.
If the study is only counting the aggressive and non-compliant kids as "lacking social skills", then it's probably not counting accurately - and may be missing part of the picture.