A table containing both columns for an employee’s age and birth date is spelling trouble, there lurks an opportunity for a data inconsistency!
How are these addressed? By the third normal form.
3NF – Third Normal Form Definition
A table is in third normal form if:
- A table is in 2nd normal form.
- It contains only columns that are non-transitively dependent on the primary key
Wow! That’s a mouthful. What does non-transitively dependent mean? Let’s break it down.
When something is transitive, then a meaning or relationship is the same in the middle as it is across the whole. If it helps think of the prefix trans as meaning “across.” When something is transitive, then if something applies from the beginning to the end, it also applies from the middle to the end.
Since ten is greater than five, and five is greater than three, you can infer that ten is greater than three.
In this case, the greater than comparison is transitive. In general, if A is greater than B, and B is greater than C, then it follows that A is greater than C.
If you’re having a hard time wrapping your head around “transitive” I think for our purpose it is safe to think “through” as we’ll be reviewing to see how one column in a table may be related to others, through a second column.
An object has a dependence on another object when it relies upon it. In the case of databases, when we say that a column has a dependence on another column, we mean that the value can be derived from the other. For example, my age is dependent on my birthday. Dependence also plays an important role in the definition of the second normal form.
Now let’s put the two words together to formulate a meaning for transitive dependence that we can understand and use for database columns.
I think it is simplest to think of transitive dependence to mean a column’s value relies upon another column through a second intermediate column.
Consider three columns: AuthorNationality, Author, and Book. Column values for AuthorNationality and Author rely on the Book; once the book is known, you can find out the Author or AuthorNationality. But also notice that the AuthorNationality relies upon Author. That is, once you know the Author, you can determine their nationality. In this sense then, the AuthorNationality relies upon Book, via Author. This is a transitive dependence.
This can be generalized as being three columns: A, B and PK. If the value of A relies on PK, and B relies on PK, and A also relies on B, then you can say that A relies on PK though B. That is A is transitively dependent on PK.
Let’s look at some examples to understand further.
|Primary Key (PK)||Column A||Column B||Transitive Dependence?|
|PersonID||FirstName||LastName||No, In Western cultures a person’s last name is based on their father’s LastName, whereas their FirstName is given to them.|
|PersonID||BodyMassIndex||IsOverweight||Yes, BMI over 25 is considered overweight.It wouldn’t make sense to have the value IsOverweight be true when the BodyMassIndex was < 25.|
|PersonID||Weight||Sex||No:There is no direct link between the weight of a person and their sex.|
|VehicleID||Model||Manufacturer||Yes:Manufacturers make specific models. For instance, Ford creates the Fiesta; whereas, Toyota manufacturers the Camry.|
To be non-transitively dependent, then, means that all the columns are dependent on the primary key (a criteria for 2nd normal form) and no other columns in the table.
Issues with our Example Data Model
Let’s review what we have done so far with our database. You’ll see that I’ve found one transitive dependency:
CustomerCity relies on CustomerPostalCode which relies on CustomerID
Generally speaking a postal code applies to one city. Although all the columns are dependent on the primary key, CustomerID, there is an opportunity for an update anomaly as you could update the CustomerPostalCode without making a corresponding update to the CustomerCity.
We’ve identified this issue in red.
Fix the Model to 3NF Standards
In order for our model to be in third normal form, we need to remove the transitive dependencies. As we stated our dependency is:
CustomerCity relies on CustomerPostalCode which relies on CustomerID
It is OK that CustomerPostalCode relies on CustomerID; however, we break 3NF by including CustomerCity in the table. To fix this we’ll create a new table, PostalCode, which includes PostalCode as the primary key and City as its sole column.
The CustomerPostalCode remains in the customer table. The CustomerPostalCode can then be designated a foreign key. In this way, through the relation, the city and postal code is still known for each customer. In addition, we’ve eliminated the update anomaly.
To better visualize this, here are the Customer and PostalCode tables with data.
Now each column in the customer table is dependent on the primary key. Also, the columns don’t rely on one another for values. Their only dependency is on the primary key.
The same holds true for the PostalCode table.
At this point our data model fulfills the requirements for the third normal form. For most practical purposes this is usually sufficient; however, there are cases where even further data model refinements can take place. If you are curious to know about these advanced normalization forms, I would encourage you to read about BCNF (Boyce-Codd Normal Form).
Can Normalization Get out of Hand?
Can database normalization be taken too far? You bet! There are times when it isn’t worth the time and effort to fully normalize a database. In our example you could argue to keep the database in second normal form, that the CustomerCity to CustomerPostalCode dependency isn’t a deal breaker.
I think you should normalize if you feel that introducing update or insert anomalies can severely impact the accuracy or performance of your database application. If not, then determine whether you can rely on the user to recognize and update the fields together.
There are times when you’ll intentionally denormalize data. If you need to present summarized or complied data to a user, and that data is very time consuming or resource intensive to create, it may make sense to maintain this data separately.
Several years ago I developed a large engineering change control system which, on the home page, showed each engineer’s the parts, issues, and tasks requiring their attention. It was a database wide task list. The task list was rebuilt on-the-fly in real-time using views. Performance was fine for a couple of years, but as the user base grew, more and more DB resources were being spent to rebuild the list each time the user visited the home page.
I finally had to redesign the DB. I replaced the view with a separate table that was initially populated with the view data and then maintained with code to avoid anomalies. We needed to create complicated application code to ensure it was always up-to-date.
For the user experience it was worth it. We traded off complexity in dealing with update anomalies for improved user experience.