Here are some examples of original research.
A previous version of the article Let's trim our hair in accordance with the socialist lifestyle contained the assertion shown in bold. The assertion is original research because it is not supported by a source.
"Let's trim our hair in accordance with the socialist lifestyle"[1] was part of a North Korean government propaganda campaign promulgating grooming and dress standards. It was broadcast on the state-run Korean Central Television in the capital of Pyongyang. The television program claimed that hair length can affect human intelligence, in part because of the deprivation to the rest of the body of nutrients required for hair to grow. This is at odds with the mainstream medical understanding that hair growth is unaffected by the amount of previously grown hair that remains attached to the body.
The two following examples show violations of WP:SYNTHESIS in bold.
Intelligence officers of the attacking forces claimed to have telephoned the residents of buildings where military assets were suspected of being stored, to warn them to leave before it was bombed.[Sourced to an article about the bombing] During the war, 90% of the telephone system was down.[Sourced to an article that does not mention the bombing] (Implied: Thus the attacking forces could not have warned 90% of the residents whose buildings were bombed.)
Organisation X called for a pre-Christmas product boycott. They subsequently claimed on their website that it had a dramatic effect. [This was properly sourced.] In the run-up to Christmas that year, Retailer Z suffered disappointing sales, [source mentions sales drop for retailer Z, but does not mention Organisation X, nor the boycott] and its share price dropped. [The share price source for Retailer Z does not mention Organisation X or the boycott either.] (Implied: Organisation X's boycott may have had something to do with the drop in sales and subsequent drop in share price of retailer Z.)
A previous version of the article Taiwan (island) contained the following sentence:
[In Taiwan], since the 2008 election of President Ma, unemployment rate has risen to over 5.9% and Economic Growth fallen to -2.9%.
This is original research because no source makes the correlation between the rise in unemployment and the election of President Ma. Later, in this edit, the sentence was changed to the following:
Since the global financial crisis starting with United States in 2007, unemployment rate has risen to over 5.9% and Economic Growth fallen to -2.9%.
A previous version of the article on the sinking of the ROKS ship Cheonan, a section titled "Controversies" contained the following statements:
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Although each statement can be verified and no conclusion is drawn, the section as a whole represents a synthesis. This is because the editors have gathered unrelated details in the same place, possibly to imply that the sinking was the result of a conspiracy.
This is a simple adding-up to promote a medical treatment:
"Severe vomiting in pregnant women is normally managed by a class of drugs called antiemetics. THC, the active compounds in marijuana, is an antiemetic; therefore, pregnant women are usually prescribed marijuana to stop vomiting."