What You May Be Experiencing
To be more specific, defiant behaviors aren't just yelling and screaming, they include passive defiance, nasty physical and verbal explosions, and lying and deceitfulness. By this age, children are capable of a small amount of scheming and plotting, and are aware that their behavior affects others; and they are perfectly capable of adhering to your rules.
The Passive Defiant
Procrastinating and pretending to be lost in thought (which can become so ingrained, the child actually becomes lost in thought) are two big acts of passive defiance. They're “sins of omission,” so to speak: you ask your child to brush her teeth, and twenty minutes later, she's still standing in front of the mirror with her toothbrush, though she's been capable of brushing her teeth for years. Often, she's even very sweet and apologetic about “forgetting,” or wants to tell you how she's caught up in a sophisticated fantasyland that amazes you for how creative it is. This is still defiance. If you have told your child to do something and it's not getting done although she is fully capable of doing it, she is defying you, and you must take action or it will get worse.
On the other hand, back talk, tantrums, and hitting are examples of “explosions,” and in that order escalate from least disruptive to most disruptive. Back talk is common and normal; tantrums are common and normal but should be decreasing to virtually nil during these years; hitting is unacceptable and is not normal if it happens regularly. Again, the normalcy of defiant behaviors doesn't mean that any of them should be excused or tolerated; it means that your concern as a parent should be immediate and direct rather than long-term. It means you should take swift action so that your child's behavior continues to develop normally.
Lying and Deceitfulness
By the time a child is four years old, she's capable of the abstract thought necessary to lie, hide, or sneak something in order to extend fun or delay boring or unpleasant activities. In order to be an effective parent now and in the future, you need to foster an environment of honesty and trust starting now, so you can't tolerate lying or deceitfulness, ever.
A positive first step toward an honest environment is to read with your child a kids' book about telling the truth. This will provide a framework for future discussions on honesty, and help cement the idea over time as you incorporate the book into your child's collection.
The best way to prevent lying or deceitfulness is by helping your child stay out of trouble. When you think your child is on the cusp of a lie, step in and say, “It looks like you're feeling embarrassed/ashamed. Did you break the window/flush the toy down the toilet?” Give your child the chance to tell the truth, and reward her with hugs and encouragement when she does. Say something such as, “I know it was hard for you to tell the truth because you didn't want to get in trouble. Thank you for doing that.” If a rule has been broken, you must follow through with consequences, but you can do it with an understanding smile, and can reward the child for telling the truth once the consequences have been completed. A public recognition of the child's courage, such as telling your spouse about how brave your child was to tell the truth, is helpful. Note: this love, attention, and reward becomes invalid if your child confesses after you've handed down a consequence.