I sense that's there's a little bit of confusion about how your earnings can be independent of the pool's hashing rate and perhaps I haven't explained it very well. Best thing is to give a few examples.
First a definition: by earnings I mean the rate of income per difficulty round. This could be expressed as the average number of bitcoins earned per day over the difficulty round.
Let's assume the network hash rate is 2000 TH/s (it's higher now, but was at that a couple of weeks ago) and the difficulty round has just begun. Let's also assume that the hash rate of the Slush pool is 200 TH/s (1/10 of the total network hash rate) and you're a miner in Slush with 200 GH/s (1/1000 of Slush's hash rate).
Let's look at three scenarios:
1. The network hash rate is stable (maybe there's a world shortage of solder and nobody's shipping miners...), Slush's daily earnings are 360 bitcoins (2016 * 25 / 14 * 0.1). Your daily earnings are 0.36 bitcoins (360 / 1000). This rate continues for 14 days at which point there's a new difficulty round with the same difficulty (earnings don't change).
2. The network hash rate is stable but 200 TH/s moves from BTCGuild to Slush (for some reason). Slush now has 400 TH/s and earns 720 bitcoins per day (Slush's block rate has doubled). Your earnings are still 0.36 per day - while there are twice as many blocks now for Slush, your share of each of them has halved. Again, this difficulty round lasts for 14 days and the next one has the same difficulty (earnings don't change).
3. EvilASIC(TM) company dumps an extra 2000 TH/s on the network right at the start of the difficulty round and mines into EvilASIC pool. Network hash rate is now 4000 TH/s and there's a block every 5 minutes instead of every 10 minutes with half of the blocks going to EvilASIC. Slush's daily earnings stay the same (360 bitcoins) and so do yours, but this difficulty round will only last for 7 days instead of 14. When the new difficulty round starts, Slush's and your earnings will be halved (180 and 0.18 respectively).
Thank you. Looks like it's necessary to make a post like this from time to time.
Once a month or so there appear one or more miners here who don't catch the principle. They post a nonsense of some kind here, and instead of doing some reading, they claim the explanation here.
Fortunately, somebody always appears here who is willing to make a new explainig post, again and again.. ;-)
Interestingly, it's often a junior member willing to give away his time, energy and knowledge, and to explain the mechanism to some older, but too a lazy member. :-))