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I am writing an addendum to explain the seven point increase in my LSAT score. To summarize, I feel that the approaches I used in studying explains the increase (I know this is obvious). The first time round I took an accelerated course shortly before the test, and primarily relied on their methods. The second time was complete independent self-study with my own methods. I feel that the second score is more indicative of my ability. I am not sure though how to phrase it though in addendum form.

I know there is talk about whether or not an addendum is needed, but some of the schools I am applying asked for an addendum to explain to them which test score they should place more weight on

Any thoughts?

I would say something along the lines that you took an accelerated course, implemented their strategies during the test, and did not do as well as you thought you would. Then, you regrouped, studied on your own - using your own methods and study habits - and increased your score significantly. You should point out that you made a mistake the first time and regret it. However, after recognizing your mistake, and knowing that you could increase your score, you put your nose to the grind-stone, impletmented your study habits and methods, and increased your score significantly. Subsequently, you feel that the second score is indicative of your abilities and you are confident that that same dedication to excel will help you succeed at XYZ school as you will not settle for anything less than your best.