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Focusing specifically on physics periodicals, I show that the journal Impact Factor is not correlated with Hirsch's $h$-index. This implies that the Impact Factor is not a good measure of research quality or influence because the $h$-index is a reflection of peer review, and thus a strong indicator of research quality. The impact gap between multidisciplinary journals and physics-only journals is significantly reduced when $h$ is used instead of the Impact Factor. Additionally, the impact of journals specializing in review articles is inherently deflated using $h$ because of the limited number of annual publications in such periodicals. Finally, a reordering of the top ranking journals occurs with $h$ when only the physics articles of multidisciplinary journals are considered, falling more in line with the average physicist's interpretation of a journal's prestige.
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