Some people (Jakob Nielsen calls them “search-dominant” users) will almost always look for a search box as soon as they enter a site. (These may be the same people who look for the nearest clerk as soon as they enter a store.) Other people (Nielsen’s “link-dominant” users) will almost always browse first, searching only when they’ve run out of likely links to click or when they have gotten sufficiently frustrated by the site. For everyone else, the decision whether to start by browsing or searching depends on their current frame of mind, how much of a hurry they’re in, and whether the site appears to have decent browsable navigation.
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