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I have research on this topic that is accepted for publication but not yet in print so I cannot direct you to the resource quite yet. My work in this area is preliminary - I am replicating it across multiple science courses to ensure it was not just an effective strategy for chemistry students; the early data shows the trends holds. 

My conclusions were:

• Students who can benefit from multiple attempts tend to complete a second attempt
• Students who use a second attempt tend to do better (average 10pt gain on 100pt scale)
• Students who use a second attempt tend to spend twice as long on the activity (self-evident but worth noting the time investment)
• The difference in average final assessment grades between students who used 1 attempt vs. 2 attempts was not statistically different (this demonstrates that it closes the achievement gap)

The key was not just to allow multiple attempts but to provide high-quality feedback in between attempts. 

Managing multiple attempts and feedback can be made easier by leveraging your learning management system. 

This research is now in print! 

Faulconer, E., Griffith, J., Frank, H. (2019) If at first you do not succeed: the student benefits of multiple trials on summative assessments. Teaching in Higher Education. doi: 10.1080/13562517.2019.1664454

I have struggled with this same question as a new teacher- but my current school has sort of shaped my opinions on it. The goal of any class is for students to master the given objective. If that is our goal, then students should be able to re-take tests becuase we want them to show mastery of that material. With that being said, I don't think that students should use this as a pass to not try at first and then bank on a second chance. If you put the proper requirements into place, I think you will find that students who really need the second chance will do what it takes and deserve a re-test. We have requirements that are set by each class for what a student has to do before a re-take can be done. For example, in physical science they have to complete test corrections, come to a tutoring session, and complete a remediation packet. This provides those students with the opportunity to go back and truly understand the standards. It does require work on their part, so you don't see studnets who do not need this opportunity taking it up. Students generally do better their second time and truly do show a better understanding and mastery of the content which is what we want them to be able to do. 

Like mentioned above I have not seen a huge improvement in grades when the test is given a second time. I made a test correction sheet for one class and was able to offer back 1/2 credit for the questions but only if they exhibited that they understood what they got wrong and why the correct answer was right. You could tell the students that put in a lot of work and those that did not and credit was given back based on that. 

For students that are required to retake giving them a review helps if the students are willing to put in the effort on thier side. I have seen students jump from an F to a B but only because they were very devoted to getting the better grade. 

One thing I think I would like to do in my future classroom is allow students to retake an assessment but that they will have to prove that they are trying to improve their understanding. Meaning that they must have all classwork turned in and can recognize their mistakes from their previous assessment in a discussion with me. Then I would allow them to take another assessment that was different from the first but is still addressing the same concept or skill. 

It's interesting to see different school's retake policies for test and summative work.  In my high school, each department has similar but slightly different reassessment policies.  For my department (math), each student is allowed to retake each assessment one time to earn full credit back.  The new assessment has similar standards but different problems.  When students reassess, they only need to demonstrate their new learning on the standards that they did not show mastery the first time and thus do not have to retake even the whole assessment.  Prior to any reassessment though, students need to make the necessary corrections to the original assessment, have completed any formative work associate with that unit, and have a conference with the teacher.  The science department allows one free reassessment per semester.  If students need any additional reassessment, then they have to work out a plan with the teacher for additional help, practices, behavior plans, etc depending on the situation.

I do believe that reassessment is a good practice in that we ultimately want students to learn and apply our content whether that is the first chance on a test or two weeks later on a retake.