The two are usually correlated to some extent. As more money moves  into Bitcoin, no doubt, some of the BTC will flow into altcoins. The reverse is also true. However, when there is big news for altcoins and bad news for Bitcoins, you will see a drop in BTC price and a rise in altcoin price. At moments like these, the effect is stronger than the normal levels because the drop in BTC price may increase the buy pressure and increase the number of BTC in the hands of investors. When this happens, you find an overwhelming rising in some altcoin prices. This demonstrates the whole greater than the sum of its parts.