"Analysis of this substance did not give results."
Translation:Анализ этого вещества не дал результатов.
If you are giving smth to smbd you should use the accusative:
- Я дал тебе (кого/что?) ту монету. I gave you (what?) that coin.
If you are getting smth from smbd you should use the accusative:
- Ты дал мне (кого/что?) ту монету. You gave me (what?) that coin.
But you will use the genitive if you have the particle не (-n't) and verbs like иметь (to have), получать (to get), доставать (to take/get), etc:
- Я не имею (кого/чего?) той монеты. У меня нет той монеты. I don't have (what?) that coin.
- Я не достал той монеты. I didn't get that coin.
- Я не получил от тебя той монеты. I didn't get that coin from you.
- Анализ не дал (мне) результатов. The analysis didn't give the results. Has the same meaning as "I didn't get results from the analysis"
It's only one case of interchangeability between the accusative and genitive in Russian grammar, there are many more of them.
[Source: http://www.evartist.narod.ru/text1/66.htm §201 (Розенталь)]
When negated, transitive verbs can have objects in either Accusative or Genitive. The choice of the Genitive case over Accusative usually intensifies the negation, but in certain situations only one option is correct. Here it's much better to use the Genitive form. I'm not entirely sure why, but I think it's because the object can be considered abstract.