Ordering of the 'individuals'

Many basic statistical methods assume that the 'individuals' in a data matrix are unordered — any rearrangement of the rows would give the same information. For example, the weights of 20 loaves of bread sampled from a supermarket would form an unordered data set.

However sometimes the rows of the data matrix are ordered, usually by time. For example, the number of admissions at a hospital accident and emergency clinic might be recorded each day for a year. The resulting data are a discrete numerical variable whose values are time-ordered — the ordering of the values holds useful information that will help us understand the data. These kinds of data are called time series.

For a preliminary exploration of ordered data, it is often useful to examine them as though they were unordered, but a full analysis should take account of the ordering.

Examples

In both of the data sets below, the data were time-ordered. In the camp site example, the number of tents was recorded on 12 successive days, whereas in the second example, the insurance claims were recorded annually between July 2001 to June 2013.

Camp site use on 12 days
  Weather   Tents
Cloudy
Sunny
Rainy
Cloudy
Sunny
Rainy
Rainy
Rainy
Cloudy
Sunny
Cloudy
Sunny
62
46
51
79
44
60
72
55
78
63
81
53
Maritime insurance claims
  Weather pattern for year   Claims (thousands),
July-June
Ordinary
El Nino
Ordinary
El Nino
La Nina
El Nino
La Nina
Ordinary
El Nino
La Nina
La Nina
Ordinary
62
46
51
79
44
60
72
55
78
63
81
53

It would be possible to ignore the ordering of the camp-site data and perform a preliminary analysis as though they were unordered. (But this would ignore the fact that some days were at weekends.)

This may also be a reasonable initial analysis of the insurance claim data, but it is more important to take account of the possibility of an overall increase in shipping over the period.

To include the time-ordering of the data in the data matrix, a new variable can be added, as shown below.

Camp site use on 12 days
Day Weather Tents
1
2
3
4
5
6
7
8
9
10
11
12
Cloudy
Sunny
Rainy
Cloudy
Sunny
Rainy
Rainy
Rainy
Cloudy
Sunny
Cloudy
Sunny
62
46
51
79
44
60
72
55
78
63
81
53
Maritime insurance claims
Year starting July Weather pattern for year Claims (thousands),
July-June
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Ordinary
El Nino
Ordinary
El Nino
La Nina
El Nino
La Nina
Ordinary
El Nino
La Nina
La Nina
Ordinary
62
46
51
79
44
60
72
55
78
63
81
53

The 'time' variable contains all information about the ordering of the data so the data matrix can otherwise be treated as 'unordered'.