פירוש על ברכות 37:9

[THEY REQUIRED HER] TO DRINK [BECAUSE SHE WAS] LIKE THEM. Akavyo argued with the Rabanan who said that the waters of the sotoh, called the bitter water, which are supposed to test the suspected adulteress are given to a convert and a freed slave woman. When the Rabanan presented the case of Karkamis, a freed slave woman who was given the bitter water, Akavyo responded with the words דוגמא השקוה. The word דוגמא literally means similar or an example. How exactly does this word relate to the confrontation between Akavyo and the Rabanan?
Rashi explained that since she was a convert as they, Sh’mayoh and Avtalyon, were converts. Since they themselves were converts they tended to deal with her as a full-fledged Jewess and had her drink the bitter water, but they were not correct for doing so. And so too, it appears in Yerushalmee of Moaid Koton (perek 3): The Yerushalmee asks what is דוגמא? That she was like them. She was a convert as they were converts.
Tosfos suggests another explanation of the word דוגמא as it is used in this Mishna. The Oruch explains that השקוה דוגמא does not refer to the Rabanan who said that she must drink the bitter water, but to the water that she drank water which was dyed so that it appeared as if it was bitter water, but they were not actually the bitter waters and they did not erase the Torah onto the water as is prescribed in Parsha Noso. Obviously that water did not have the power to verify whether she had committed adultery or not, but they gave her the water to drink in order to cause her to fear the consequences of her action.

Num. v. 11 ff.

They merely pretended to give her the bitter waters. This is the interpretation of many commentators. Rashi renders; "They administered them to one who was like themselves," i.e. despising Shemayah and Abtalion on the ground that they were not of pure Jewish stock. According to Gittin 57b they were descendants of Sennacherib, king of Assyria.