Positive Reinforcement is a common buzz word in the training and parrot communities but do you really understand what it means? Positive reinforcement should not be confused with "treat" or "reward." Positive reinforcement is sooner the concept than the thing the bird receives.
You see, positive reinforcement is determined specifically by results and value is measured in the quality or frequency of the outcome. A treat is a broad term for foods that are considered to be desired by the bird but not necessarily in a measurable way or reinforcement. The value of a reward is usually measured by the giver rather than the receiver. Let me provide some examples.
An example of a treat that is not positive reinforcement is hanging a strand of millet in a Cockatiel's cage. The bird will enjoy the seeds as a treat but it has not taught the bird any sort of behavior or cooperation with the human (outside of walking over to the millet inside the cage). A reward could be a super expensive toy or manufactured treat. The buyer of the expensive reward may feel that it should be of higher value than something cheaper. This does not mean that the bird will like it more and thus does not directly link it to positive reinforcement.
On the flipside, it is possible that a treat reward is also positive reinforcement. That is the goal in training: to make a treat-reward lead to encouraging the behavior in the future.
I think a lot of people have trouble with the concept of positive reinforcement because there is no instant feedback. It is literally measured by whether or not the learned behavior is more readily exhibited in the future. This future could be next training session or on the next cue, but the value will not be determined until then. If you are teaching a parrot to walk to you, taking a step further or coming sooner on the subsequent requests would be a demonstration that the treat/reward you are using is in fact positive reinforcement.
Why does this matter? I don't like to waste your time by being too technical. But the difference between simply a treat vs something that is actually positive reinforcement is essential to successful parrot training. In order to have success and maximize efficiency in training, you have to do what the bird finds to be most rewarding. It doesn't matter that the treat stick was more expensive than a mere seed. It doesn't matter if you think that head scratches are nice. It doesn't matter if you think pasta tastes better than sunflower seeds. Heck, it doesn't matter if my bird likes almonds more than sunflower seeds. All that matters is what your bird actually prefers. If you find what works best for your bird (or if you have several, than for each bird individually), then you will have better training progress. The bird will be more motivated and work harder because it is getting what it actually wants from you.
Keep in mind that the concept of a reward from the bird's perspective will shift. Sometimes it is in the mood for Sunflower seeds, sometimes pellets, and other times it is full and would rather just get a head scratch. Heck, at other times when it is in a bad mood, being left alone could be a greater reward than being force fed “treats.” Evaluate in real time the effectiveness of each treat. You can measure effectiveness through positive reinforcement and repeat results, but you can also watch for eagerness with which the food is consumed (or in the case of scratches, the eagerness with which it is received). If the parrot eats one food more carefully than another, pins its eyes on every bite, and turns to you looking for more, you can learn that this was a strong positive reinforcer.
Don't necessarily waste your best positive reinforcement treats. They are usually less healthy but even if not, if you over use them, they may lose value. An extreme example is feeding an all sunflower seed diet. To that bird, getting a sunflower seed for stepping up or doing a trick is worthless and it might as well not comply. Likewise, keep your strongest treats for super successful behavior, for socialization with other people, and for when you really need compliance from your bird. Don't give all the best treats during training and then discover that your bird has such a good time out that now it refuses to go back into the cage. Always save some super treats for ensuring that even “sucky things” can be reinforced.
With all this said, here is an article to the process of discovering effective treats (that most likely will correlate to positive reinforcement) for your parrot. Since each parrot has its own personality and preferences, you need to discover each bird's treat preferences and not rely on hearsay what someone else's parrot likes. Use effective positive reinforcement for success in training and your relationship with your parrot. Plenty more practical advice, training tips, and problem solving in my book, The Parrot Wizard's Guide to Well-Behaved Parrots.
Here is a video of my brother getting Rachel the Blue and Gold Macaw to learn to step up for him:
And here is a new video of how Rachel learned to step up for me some months back while visiting Coney Island outdoors. The fact that she kept trying and coming closer or onto my arm more readily is proof that letting her have the treats in my hand was positive reinforcement.