Skinner's Quadrants is widely accepted as a standard for understanding how animals learn and it is proven time and time again with dog training. The quadrants consist of positive and negative versions of reinforcement and punishment. Positive is adding something to interaction Negative is taking something away, like adding treat, praise or pain or taking away attention, discomfort or food. Reinforcement encourages a behavior to happen more often while punishment will discourage a behavior.
While all of the quadrants are methods that animals learn from there is a clear winner among them. R+ or positive reinforcement has been proven to inhibit much less stress and anxiety then the other quadrants and promote learning. Positive trainers and science based trainers stick to the R+ quadrant as much as possible for this reason. This best sets up a dog for success and progress. It's effects tend to be positive in nature, creating good associations, promoting learning and curiosity, as well as increasing confidence.
While R+ is best it is also extremely hard to stay in just one quadrant when training. The second least adverse quadrant is P- and is often seen used along with R+ though as little as possible since it does to some degree cause stress in dogs. P- by itself is tough on the dog but can be used to discourage a behavior and encourage the right one at the same time with R+.
An example of this would be you want your dog to greet you with all 4 paws on the ground so you practice greeting your dog by giving him attention when all 4 are on the ground and stopping if it jumps up. In this case you are giving attention as a reward for all 4 on the ground (R+) but then withholding it if an unwanted behavior happens (P-). Although it is easy to see how you are using two quadrants here it is also easy to see how for things like this it can be a bit more difficult to reward the right behavior but also not provide negative punishment when the desired behavior is changed to a unwanted behavior.
Although not the most adverse typically R- does cause significant stress and anxiety in dogs and is therefore not ideal for learning. The rush of unwanted stimuli to encourage behavior can have lasting effects causing constant anxiety and negative associations.
The most adverse and what has the most unwanted side effects is P+ or Positive Punishment. P+ is also often called corrections or redirection though using these terms to describe it is incorrect. It is also a key component of "Alpha/Traditional" dog training and "Balanced" dog training. P+ refers to things like squirting a dog for barking or shocking a dog for not sitting on command. This can lead to dogs making negative associations and extreme unwanted behavior, on top of this the added stress and anxiety making learning harder for the animal.
If a dog is shocked for licking a child it may associate the child with the sensation of being shocked. This can lead to the dog not approaching children anymore and being weary of them. Even worse if it is shocked for barking at a person the dog may learn that the barking behavior is not accepted but that takes out a warning before a bite as well as not improving the association with people, possibly even making it worse as well. This can lead to a dog that no longer barks before biting and is even more scared of people.
After taking a look at all the quadrants and their benefits and draw backs it is clear that science and ethics favors Positive Reinforcement. It is possible to get results with any quadrant but the methods do change the outcome of the training and the overall behavior and confidence of the dogs. Because of this we strongly hold R+ force free dog training as the number one choice. As a responsible pet owner it is important to understand that although there are many ways to learning it should also be a priority to make it enjoyable and productive.