Understand Data Basics

Correlation is a statistical measure that indicates the extent to which the value of two or more variables move in relation to each other. Positively correlated variables tend to move in the same direction, while negatively correlated variables tend to move in opposite directions with one another. However, it may not necessarily be the case that the change in one variable causes the change in the other. On the other hand, causation means that the change in one variable causes the other variable to change.

The figure below illustrates the difference between correlation and causation. Hot sunny weather would cause an ice-cream to melt and cause sunburn (with prolonged sun exposure). Melting ice-cream and getting a sunburn are correlated, where they tend to occur together in the hot sunny weather. If the presence of the hot sunny weather was ignored, it would be wrongly concluded that melting ice-cream causes sunburn!

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 in this graphs and charts, 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.

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.

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.

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.

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

*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.