When comparing a front-end jquery slider widget against a list of links that filter by price range, within the context of faceted searches that reduce the number of items in a catalogue, which of the two aforementioned interface elements is best when considering the speed at which a user can restrict the catalogue products to the range that represents the amount they want to spend?
Slider has more cognitive load for a user. Also interaction implementation using slider could lead to some time losses.
Having the set of price ranges as hyperlinks, user interaction consists of just two steps:
Sliders give free choice of the price range.
Problems with Sliders
However, since they are usually one of multiple criteria, and the majority of the screen should present results rather than the filter, they are usually quite small.
Range needs to be limited by other query aspects as to not having to span $.01 .. $10k in a single linear slider, but that often gives awkward steps.
Selecting $100..$200 might give exactly two results and hide dozens of options at $99.99.
Affordance is two drag-and-aim operation, vs. a single click.
Why would I even want to filter by price?
I might have a hard budget limit, or a soft one, "$99.99, not a cent more" vs. "about $100 for a quality kettle is fine"
An upper limit can also be used to rule out unwanted product features: I don't want an talking kettle with an integrated recipe browser.
A lower limit is usually used to exclude incorrect matches, e.g. I've searched for kettles, and get two pages of kettle stickers for $.99, or for a perceived minimum quality - I want a heavy duty kettle, not the flimsy mostly-plastic ones.
Note that price is often a convenient proxy for another attribute that's hard(er) to filter for.
Two sliders or a range slider are usually the simplest implementation.
Price ranges need either manual configuration, or a decent algorithm. A good algorithm can look for price clusters and automatically suggest meaningful ranges that actually reflect the available results.
To vercome the fixed limits, a "custom range" popup can be used, employing large size sliders with "natural" steps and ideally immediate feedback how many results would be in that range.
Alternatively: Price is in almost all applications the primary sort condition. This could be exploited in the presentation of results.
When prices differe significantly, instead of showing all results, group by price range. E.g. instead of two pages of kettle stickers, show the top 5 and a link to "more for less than $1"
You could also provide navigation aids, e.g. when sorting by price, instead of page numbers, use a price indicator.
I would be okay with price sliders if the filtered results changes while the user is sliding, and user doesn't have to click another button to apply the filter.
Much like pricing slider on Heroku here https://www.heroku.com/pricing
As long as you can show apply filter while user is sliding the filter (assuming that all the data is already loaded), then slider will be helpful.
Otherwise, it will become even more tedious for the user to first move the slider by dragging his mouse, then you will download the filtered values and then show them.