Missing Data

Overview

Teaching: 15 min
Exercises: 15 min

Questions

• How do databases represent missing information?

• What special handling does missing information require?

Objectives

• Explain how databases represent missing information.

• Explain the three-valued logic databases use when manipulating missing information.

• Write queries that handle missing information correctly.

Real-world data is never complete — there are always holes. Databases represent these holes using a special value called null. null is not zero, False, or the empty string; it is a one-of-a-kind value that means “nothing here”. Dealing with null requires a few special tricks and some careful thinking.

To start, let’s have a look at the Visited table. There are eight records, but #752 doesn’t have a date — or rather, its date is null:

SELECT * FROM Visited;

Null doesn’t behave like other values. If we select the records that come before 1930:

SELECT * FROM Visited WHERE dated < '1930-01-01';

we get two results, and if we select the ones that come during or after 1930:

SELECT * FROM Visited WHERE dated >= '1930-01-01';

we get five, but record #752 isn’t in either set of results. The reason is that null<'1930-01-01' is neither true nor false: null means, “We don’t know,” and if we don’t know the value on the left side of a comparison, we don’t know whether the comparison is true or false. Since databases represent “don’t know” as null, the value of null<'1930-01-01' is actually null. null>='1930-01-01' is also null because we can’t answer to that question either. And since the only records kept by a WHERE are those for which the test is true, record #752 isn’t included in either set of results.

Comparisons aren’t the only operations that behave this way with nulls. 1+null is null, 5*null is null, log(null) is null, and so on. In particular, comparing things to null with = and != produces null:

SELECT * FROM Visited WHERE dated = NULL;

produces no output, and neither does:

SELECT * FROM Visited WHERE dated != NULL;

To check whether a value is null or not, we must use a special test IS NULL:

SELECT * FROM Visited WHERE dated IS NULL;

or its inverse IS NOT NULL:

SELECT * FROM Visited WHERE dated IS NOT NULL;

Null values can cause headaches wherever they appear. For example, suppose we want to find all the salinity measurements that weren’t taken by Lake. It’s natural to write the query like this:

SELECT * FROM Survey WHERE quant = 'sal' AND person != 'lake';

but this query filters omits the records where we don’t know who took the measurement. Once again, the reason is that when person is null, the != comparison produces null, so the record isn’t kept in our results. If we want to keep these records we need to add an explicit check:

SELECT * FROM Survey WHERE quant = 'sal' AND (person != 'lake' OR person IS NULL);

We still have to decide whether this is the right thing to do or not. If we want to be absolutely sure that we aren’t including any measurements by Lake in our results, we need to exclude all the records for which we don’t know who did the work.

In contrast to arithmetic or Boolean operators, aggregation functions that combine multiple values, such as min, max or avg, ignore null values. In the majority of cases, this is a desirable output: for example, unknown values are thus not affecting our data when we are averaging it. Aggregation functions will be addressed in more detail in the next section.

Sorting by Known Date

Write a query that sorts the records in Visited by date, omitting entries for which the date is not known (i.e., is null).

Solution

SELECT * FROM Visited WHERE dated IS NOT NULL ORDER BY dated ASC;

id	site	dated
619	DR-1	1927-02-08
622	DR-1	1927-02-10
734	DR-3	1930-01-07
735	DR-3	1930-01-12
751	DR-3	1930-02-26
837	MSK-4	1932-01-14
844	DR-1	1932-03-22

NULL in a Set

What do you expect the query:

SELECT * FROM Visited WHERE dated IN ('1927-02-08', NULL);

to produce? What does it actually produce?

Pros and Cons of Sentinels

Some database designers prefer to use a sentinel value to mark missing data rather than null. For example, they will use the date “0000-00-00” to mark a missing date, or -1.0 to mark a missing salinity or radiation reading (since actual readings cannot be negative). What does this simplify? What burdens or risks does it introduce?

Key Points

• Databases use a special value called NULL to represent missing information.

• Almost all operations on NULL produce NULL.

• Queries can test for NULLs using IS NULL and IS NOT NULL.