If you're looking for anime similar to The Disappearance of Nagato Yuki-chan: Toaru Ichinichi (Light Novel), you might like these titles.
Q-Tarou is a mischief maker who likes to fly around scaring people and stealing food, though he is deathly afraid of dogs.
The story is set at the elite Omega High School, where test results decide everything. The high-scorers in the student council, in particular the student council president, have a lot of authority. Yuria Aikawa comes to this school, and though she seems like an ordinary girl who loves fun things and her boyfriend Shuri, she's actually a super-genius who gets the top score on every test. She becomes student council president and tries to make school life more fun in various ways.
Yamazaki comes to Earth from another planet, hoping to conquer our planet. But he soon realizes that in order to conquer the world, he has to conquer his own classroom first. That's why he comes up with lots of different ideas to get everybody to follow him. Also, he spends most of his time making Tatsuya (the class rep.) miserable. Having his loyal and strange dog Watanabe always by his side, and the help from his grandparents, Yamazaki is always doing crazy things with his class, completely forgetting his primary goal, and only thinking in becoming "The King of the Class".
One hot summer day, Class 5-2 heads to the school pool for gym class. As everyone prepares to leave, they go to wash their eyes, but when Ryota tries to get away without doing so, Chika soon berates him by saying that he’ll regret it later when they start to hurt. With Ryota refusing to give in, and the next class rapidly approaching, Chika and the others take it upon themselves to ensure that the stubborn boy washes his eyes, whether he likes it or not!
Shinnosuke and friends are experiencing a one-week stay as part of the "defense force" of Tenkatouitsu Kasukabe Private Academy (nicknamed "Tenkasu"), an elite boarding school that is administrated by a state-of-the-art AI. But when Kazama is attacked, with his intelligence reduced, and strange bite marks left on his butt, the mood begins to change. The Kasukabe defense force joins forces with the school's dropout student council president Chishio Atsuki to form a group of detectives and shed some light on the mystery.