Should I use a question mark at the end of a question fragment? [duplicate]

At the risk of being obvious, a question mark goes at the end of a question, whether or not it forms a complete sentence. Usually, 'How to measure' is (for example) the title of an instruction set; the formally grammatical equivalent would be "The correct way to measure is..." But these are specifically formed as questions (which is why they appear in the "Questions" list), and the equivalent would be "How do I measure?"

I believe this common formula was once a sentence fragment. That shouldn't come as a great surprise, since many types of titles are fragments:

• [Treatise/essay/etc.] On the Origin of Species
• The Way We Live Now
• Ulysses

Titles may be full sentences, but they are often nominal constituents (things that act as nouns) or other single constituents (parts of speech); and only sentences require punctuation marks at all.

In normal speech, I believe the how to construction appears only in subordinate position to a verb or noun:

• *Peter, how to open this door? — sounds like a non-native speaker to me.
• Peter, I don't know how to open this door. — that's more like it.

Because we're dealing with a fragment here, we have considerable freedom in whether and how we wish to complete the hypothetical sentence:

• Please tell me how to open this door. — This makes it into an imperative, which requires a full stop.
• Could you show me how to open this door? — This makes it into a full question.
• How to open this door — this leaves it as a fragment the completion of which would be useless, like the book titles above.

However, since the punctuation mark at the end should normally be used only if you wish to present it as a sentence, I think no punctuation mark at all makes the most sense. By a "sentence" I mean here a unit that you would mark by a capital at the beginning and .?! at the end in a normal paragraph. If circumstances extrinsic to the title itself dictate a full stop, then use that (when all titles in a list are punctuated, for example, I'd use a full stop).

The British linguist David Crystal describes strings of words that lack a finite verb as minor sentences, and such are these. None of them needs a question mark.

After reading Tim’s answer I now see that these examples could indeed be questions, depending on the context. Taking the first one as an example, it might be a heading with a following paragraph or two of instructions. In that case, no question mark is required. However, it could equally well be followed by something like ‘Is that a question you’ve ever asked yourself? We bet it is, and we think we’ve got the answers.’ In that case, a question mark would be required.