GTA Graduate Teaching Assistant applicants have rated the interview process at LSE with 2 out of 5 (where 5 is the highest level of difficulty) and assessed their interview experience as 100% positive. To compare, the company-average is 70.2% positive. This is according to Glassdoor user ratings.
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It's quite straightforward process. Submit application and then get the outcome in one month. It casy by case, my department (psychology) doesn't go through any interviews. But I have heard that other departments such as IR, they do.