Method 1 and method 2 are identical with the only difference is that method 1 needs to parse the scope passed and translate it to a call to $parent.find(".child").show();.

Method 4 and Method 5 both need to parse the selector and then just call: $('#parent').children().filter('.child') and $('#parent').filter('.child') respectively.

So method 3 will always be the fastest because it needs to do the least amount of work and uses the most direct method to get first-level children.

Based on Anurag's revised speed tests here: http://jsfiddle.net/QLV9y/1/

Speed test: (More is Better)

On Chrome , Method 3 is the best then method 1/2 and then 4/5

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On Firefox , Method 3 is still best then method 1/2 and then 4/5

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On Opera , Method 3 is still best then method 4/5 and then 1/2

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On IE 8 , while slower overall than other browsers, it still follows the Method 3, 1,2,4,5 ordering.

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Overall, method 3 is the overal best method to use as it is called directly and it doesn't need to traverse more than one level of child elements unlike method 1/2 and it doesn't need to be parsed like method 4/5

Though, keep in mind that in some of these we are comparing apples to oranges as Method 5 looks at all children instead of first-level ones.