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This is an alphabet filter:

example

It assumes the user knows what the first letter of the item is. It is also an inherited method from the time of thumb indexes for books like dictionaries and address books.

When sifting through a long list, there are much more modern ways to index lists such predictive search or categorization.

What are the cases where one would use this type of filter and how effective is it?

I just find it so archaic but would love to see cases when you'd use this type of filter. Is it a one-trick pony for your address book or are there other scenarios where this would fit instead of other types of filters?

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Your question:

What are the cases where one would use this type of filter and how effective is it?

Is something you answered previously:

[When you can] assume the user knows what the first letter of the item is.

Context-wise, I think your two examples are likely the most applicable uses: dictionaries and address books. iOS7's address book, for example, uses this. Granted, it also offers predictive searching/filtering so it's merely there as a 'nice-to-have' for those that prefer it.

Why it makes sense in this situation is that you may not know how to spell someone's last name, but you may very well know what letter it begins with. Predictive search could help, but only of it's a limited data set. If it's too large, it'd be a pain to have to try and guess the spelling to find a match.

To turn that all into an answer, I'd say:

An alphabet navigation/filter makes sense when a) it's a large data-set b) we know the user likely knows what letter the item begins with c) But there is liklihood that they may not know how to spell the entire word correctly.

This makes sense with an address book. But probably doesn't make sense for an online store, where a user would likely know how to spell the item and therefore predictive search/filter would make a whole lot more sense.

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One of the primary reasons these filters are used is because of their simplicity of implementation. Have a look at this discussion on the SitePoint forums. It goes through implementing one of these filters; one of the best suggestions there is to use a small SQL snippet. With some basic client-side processing, this can easily be turned into a filter.

Of course, filters like this do also have uses for the client: in some applications (both web, native, and desktop), these filters are used either on their own or often in conjunction with a search box, usually to list names. For example, many email clients use this feature for address (contact) books. My email client lists contacts alphabetically by default, then provides this filter at the top so I can easily look through all my contacts.

There are much more modern ways to index lists such as [...]

True. Since this type of sorting was developed (around the 30's, for use in - guess what - address books, if you're interested), there have been many new developments, including computers themselves. But modern is not synonymous to better. As systems become modernised and more complex, the chance of destroying a good UX with new features increases.

So one possible reason why these filters are still used is for 'historical' reasons - perhaps the website was originally developed with them 10 years ago and the developers haven't seen fit to change that because the users are used to it. Another reason is that it's simple and easy to understand. If you add this to a page:

Filter by: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All

it's pretty easy to understand.

So when should these filters be used?

  1. When it's likely the user knows the first letter.
    For example, names or places. I asked a few people a couple of minutes ago - all of them knew that the capital city of Spain started with an M but 50% of them didn't know the name.

  2. When it makes sense.
    Having an alphabetic filter is useless if you have a list of numbers. You only need to use a filter like this in cases where it actually makes sense to have it, such as:

  3. Long lists (of strings)
    Short lists don't need filters. Long lists of numbers don't either. What are we left with? Long lists of strings. Obviously there are a couple of other cases too, but this is the main case you'd want a filter like this.

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