• Data are collected at several points in time.
• Data can be collected/observed at different frequencies such as hourly, daily, weekly, monthly, quarterly, or annually.
• Ordering of records by time matters since there is a time dimension.
• Time series data allow us to identify and analyse trends or behaviours over time. Table 2 shows an upward trend in the number of individuals with higher education levels (e.g., Diploma, University) from 2017 to 2022, and a downward trend in the number of those with Secondary education or below.
• Other examples include interest rates (monthly), exchange rates (daily), GDP (annually), inflation (monthly, annual).

Table 2: Number of Singapore Residents aged 25 years and above by highest qualification attained, from 2017 to 2022

• Combines time series and cross-sectional data, but observations in each cross section do not necessarily refer to the same unit.
• For example, individuals across the years can be randomly sampled to obtain multiple years of cross-sectional data, and these datasets can be combined together.
• The main advantage of pooled data over cross-sectional data is that the former is typically a larger sample, since multiple cross-sectional data are combined from different time periods.

Table 3: Pooled cross-sectional data of individuals from 2015 to 2022, and their characteristics

Note: Records are “pooled” into the same table. The records may be from different periods of time.

• Combines cross-sectional and time series data, similar to pooled data. The difference is that the same cross-sectional units (e.g. individuals) are observed at several points in time (days, months, years, before and after event etc.). It is also known as panel data.
• Allows the observation of the same group over a period of time, and track the changes over the period. This is useful for detecting development trends or changes in the characteristics of interest. Hence, panel data are often used in studies that investigate the effects of certain events, policies or treatments. For example, the effects of a particular government policy on the wages of individuals can be studied by looking at the change in wages within individuals before and after policy implementation.

Table 4: Longitudinal data of individuals and their characteristics

Note: Each unit (person in this example) is observed for multiple periods of time.

Authors can unknowingly produce bad visualisations of data, or worse, be out to misinform their readers. It is important to be armed with knowledge to identify bad visualisations.

Using the chart on Average Monthly Real Earnings Per Employee against Mean Years of Schooling from the scatter plot above, data points for certain years could be omitted to give the impression that the mean years of schooling are not correlated with average real monthly income, as seen in the scatter plot below. This is known as truncated data.

Scatter plot of Average Monthly Real Earnings Per Employee against Mean Years of Schooling, with omitted data points

Scatter plot of Average Monthly Real Earnings Per Employee against Mean Years of Schooling, without omitted data points

Statistics from Office for National Statistics of United Kingdom (ONS) showed that death rates for the vaccinated were greater than the unvaccinated. These numbers could be wrongly used to argue that vaccination increases the risk of death.

Simpson’s Paradox refers to the observation of a trend that is present when data are aggregated, but disappears or reverses when the groupings are made clearer (e.g. grouping by age or vaccination status). The paradox arises because death rates increase significantly with age, such that mortality rates are higher for older folks as compared to younger folks, other things being equal. Older people are more likely to be vaccinated as compared to younger people in the same age range, and are also more likely to die from Covid-19 infection or other health reasons. Therefore, age is a confounding variable since it is positively related to both vaccination rates and death rates. It is age, rather than vaccinations that is driving up the death rates of vaccinated people.

The mortality rates shown in the line chart below is a crude measure of mortality, and do not take into account the age structure of the population. Accounting for the age structure of the population is important since it can influence the number of deaths. For example, the younger population will likely have fewer deaths than the older population, all else being equal.

Mortality Rates of Individuals by Vaccination Status in UK (Jan to Sep 2021)

Instead, age-standardised mortality rates^ can be used to meaningfully compare between populations with different age structures. Age-standardised mortality rates can be computed by first calculating the mortality rates within each specified age band, followed by taking the weighted average based on a standardised age distribution.

Suppose there are 2 countries – City A and City B. City A has a younger population compared to City B but has higher mortality rate for all age bands. For simplicity, assume that there are 3 age bands – young, middle, old.

Mortality Rates of City A and City B

The unadjusted overall mortality rate in City A is 9.2% (based on (0.3 x 8%) + (0.6 x 8%) + (0.1 x 20%) = 9.2%), lower than the 10.0% of City B, even though City A’s mortality rate at each age group is higher.

Age-Standardised Mortality Rates of City A and City B

To do age adjustments, take the weighted average of each countries’ mortality rate using a standardised set of age group proportions in table above. In this case, the mortality rate of City A becomes 11.6% (=(0.2 x 8%) + (0.5 x 8%) + (0.3 x 20%)), and this is higher than City B’s 8.0%.

Going back to the Covid-19 vaccination example from ONS, looking at the age-standardised death rates, the death rates of vaccinated are lower than those of the unvaccinated.

Age-Standardised* Mortality Rates of Individuals by Vaccination Status in UK (Jan to Sep 2021)

^For more information on age-standardised mortality rates for Singapore, please refer to the Statistics Singapore Newsletter article(778 KB).

*Age-standardised mortality rates per 100,000 people, standardised to the 2013 European Standard Population using 5-year age groups from age 10 and over.

The above information are cited from Office for National Statistics of United Kingdom (ONS) and the usage of the information is subjected to ONS's terms and conditions.