What is the time complexity improvement of skip lists from linked lists in insertion and deletion?

What is the time complexity improvement of skip lists from linked lists in insertion and deletion? Correct Answer O(n) to O(logn) where n is number of elements

In Skip list we skip some of the elements by adding more layers. In this the skip list resembles balanced binary search trees. Thus we can change the time complexity from O (n) to O (logn)
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To which datastructure are skip lists similar to in terms of time complexities in worst and best cases?