Originally Posted by cny-bikeman

Pics are not likely to help, as the wear is often not discernible to the naked eye. This is a VERY common problem, and it does not take much riding on the small cog (even with the small chainring) to cause enough wear to skip on a new chain. If you are a scientist then you understand that diagnosing a problem requires logic first. The only thing you changed was the chain, which as it is new is unlikely to cause the problem. The problem occurs only when high force is applied, and the part that is experiencing the highest force is the rear cog, due to having the fewest teeth. Therefore one would logically conclude that the cog is the problem.

BTW, another basic tenet of science is the necessity to gather and convey all the relevant information before making an analysis. I am unable to fully answer because you have not indicated in what gear combos the problem occurs.

Originally Posted by FastJake

Jumps in the smaller or favorite cogs only - cassette/freewheel is worn and needs to be replaced.

Jumps in all the cogs including the largest cog - probably a RD adjustment issue. You can verify this by pedaling it slowing by hand in a bike stand.

Originally Posted by Homebrew01

In some cases, if the skipping is mild, you can "live with it" until the chain wears a bit and the skipping might go away.
Replacing the cassette or freewheel is likely the better option.

Originally Posted by FBinNY

new chain on old sprocket is prone to skipping under load. If it's a RARE occurrence on only a single sprocket, and you can live with it a little while, it will cure itself over time. But if it nearly always skips under load, you won't have the patience to wait for it to resolve and need to replace the sprocket (usually the entire cassette)