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A Stanford University study has concluded that a controversial tenth-grade MCAS essay question that many students and teachers derided as racist hurt the performance of a small number of black students, state officials announced Friday, prompting them to take the unusual step of waiving the passing score for a limited number of students.

The essay question from this spring’s MCAS was based on a passage from Colson Whitehead’s book, “The Underground Railroad,’’ and asked students to write a journal entry from the perspective of a white woman who used derogatory language against a young runaway slave and was reluctant to hide her in her home. Students encountered the question on the second day of testing, although it did not appear on all the tests.

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Tenth-graders must pass the MCAS in order to receive their high school diplomas.

“The study, led by Stanford researchers, showed that while black students experienced a small difference in performance as compared to white students on the second day of the English Language Arts MCAS test, that small difference was within the normal variation of such differences on past MCAS tests,” Jeffrey Riley, the state’s education commissioner, wrote in a letter to school superintendents late Friday afternoon.

However, Riley added that the overarching finding was not applicable to all black students who encountered the question, noting a small number of them were probably adversely impacted. Consequently, “out of an abundance of caution,” he said, the department has decided to loosen some MCAS rules.

For instance, the department will waive the passing score for students who were on track to pass the English MCAS, but then saw their performance falter after confronting “The Underground Railroad’’ question.

The study comes three months after an uproar emerged over the question, prompting Riley to drop the question from the test and not count the responses from the students who answered it. Riley then tapped the Stanford researchers after some educators raised concerns that students may have been so upset by the question that it could have negatively affected their performance on the remainder of the test.

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The prospect of having to write from the perspective of a white racist woman offended some students who experienced discrimination, while others grappled with whether using racist language would be considered historically accurate or inappropriate.

Boston teachers and administrators, acting on concerns expressed by their students, were among those leading the charge. On Friday, Boston Superintendent Brenda Cassellius commended students who brought the issue forward and expressed appreciation that the state took them seriously.

“Commissioner Riley listened to the valid concerns of our students and is taking appropriate corrective action by not penalizing test-takers and giving them opportunities to qualify for a state scholarship,” Cassellius said in a statement. “This unfortunate situation reflects the serious consequences of high-stakes standardized tests, which can impact a student’s ability to graduate or obtain crucial financial assistance for college.”

Cassellius, who started as Boston’s superintendent in July, has long been a critic of testing. As Minnesota’s commissioner she ended that state’s testing requirement for graduation.

In conducting their analysis, the Stanford researchers examined how students who encountered the question performed on the latter part of the test in comparison to how students in previous years performed on the latter part of their tests.

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Although the researchers found small differences between the performance of black and white students who encountered the “Underground Railroad’’ passage, they concluded it was “similar to effects, both positive and negative, observed in other MCAS settings,” Riley said.

“Indeed, preliminary MCAS results show that the same percentage of students met the testing requirement for graduation this year as did last year,” Riley said. “That is true both for students overall and for black students.”

MCAS results are expected to be released publicly next month.

Other steps Riley is taking so that no students — regardless of their race or ethnicity — are unnecessarily penalized by the discarded MCAS question, include allowing students to retake the exam if they did not score high enough to earn a John and Abigail Adams Scholarship, which provides free tuition at state colleges and universities for up to eight semesters.

Also, students who failed the English portion of the MCAS will be able to seek an appeal from the testing requirement if they are unable to pass it twice instead of three times. A successful appeal, as established by the 1993 Education Reform Act, which created the testing requirement, enables students to demonstrate through their coursework that they have the knowledge and skills to satisfy the passing standard.

“We are taking the actions outlined here because we believe they are in the best interest of students,” Riley said.


James Vaznis can be reached at james.vaznis@globe.com.