2 Statistical Ideas to help your Critical Thinking using COVID-19 as an example

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Being isolated from home during the COVID-19 outbreak made me recall my days in my final year in high school, Palmerston North Boys’ High School. In our final year, we were lucky enough to do introductory courses through Massey University, one of these courses was a brief dive into statistics.

To most people, statistics is a tedious allotment of numbers in congested tables producing confusing line graphs and bar charts. However, I learnt from my time in high school that statistics is far greater than this. It is a form of critical thinking allowing the understanding of the relationship between numbers and understanding these numbers in relation to the real world.

Statistics is so important and powerful; it is the judge and jury for most discipline in science – the understanding of how we and the world works.

Statistical knowledge is important as it helps you critically analyze the data being laid out in front of you. So, by reading this I hope to empower you with some tools to further your ability to critically think, and if you knew all this already, then please let me know that I am right.

We will use the recent COVID-19 outbreak and how the numbers have been treated by the media, looking at two principles: Simpson’s Paradox and confounding variables.

As a disclaimer, the events of COVID-19 are changing daily. It is likely the data here may change and I would encourage you to check a trusted source like the World Health Organisation (WHO) to keep updated on what is going on. The statistical principles, however, are timeless. Also, thanks to Jason Dhana and John Boyle for curating and collecting data about the cases of COVID19 for New Zealand – it has been incorporated into the featured image for this post.

The mortality rate is 3.4%

On the 3rd of March 2020, the Director-General of WHO – at the time of writing – Dr. Tedros Adhanom Ghebreyesus, announced that the mortality rate caused by the novel coronavirus or 2019-nCoV was 3.4%1.

Portrait of Dr. Tedros Adhanom Ghebreyesus, Director-General of WHO at the time of publication of this post, sourced from WHO

The mortality rate is simply given by deaths divided by those infected. Multiplying this value by one-hundred gives us a percentage value.

Mortality Rate
Mortality Rate equation

A number like 3.4% would indicate that for every 100 persons, roughly 3 to 4 individuals are predicted to die from this virus. 

Can we use this reliable to represent every one of all ages?

Before we look at the data closely, I am going to introduce the principle of Simpson’s Paradox. This usually happens when we combine all the data together; we lose its true message. This can lead to conclusions that are actually the opposite of reality.

A famous example of this is the University of California, Berkeley (UC) being accused of gender bias. The accusation claimed that overall there were more male accepted applications compared to female applications; therefore, male applicants were being unfairly favoured over female applicants. However, when looking closely at admission for each particular faculty, there were higher admissions for female students than male students.

It was a case where the overall admission did not represent the more specific faculty admissions. There were simply more male applicants which caused bias in the data2.

For our COVID-19 example, it’s not extreme of a case where we see a reversal in trend but we do see some misrepresentation of the data and where misunderstandings can take place.

Table data sourced from Coronavirus Age, Sex, Demographics (COVID-19) – Worldometer (accessed on 2nd of April 2020 at 11:50 am NZT)

Please note that if you were to total the percentages in this table, it will not add to 100 percent. The reason for this is individual mortality rates are specific to that particular age group. Instead of dividing the total deaths by total infected, we are looking at total deaths for that particular age group divided by those infected in that age group.

We can see the 3.4% overall rate is grossly underestimating the deaths in the older population and vice-versa, it overestimates death in the younger population.

This can result in two incorrect mindsets:

  • A younger person may think that they are in the 3 to 4 out of the 100, where their actual chance of death is a lot lower.
  • On the flip side – and possibly more importantly – an elderly member could become more complacent, thinking the percentage of 3.4% is quite low, where the actual rate for this age group is higher

We can see that the general mortality rate does not represent everyone. It is important to not generalise data as this ignores factors like age. On top of this, co-morbidity, which is another disease that a person may have reducing life expectancy, such as lung problems, diabetes, and high blood pressure can also increase the chance of mortality from the virus, which is masked by generalisation.

Masks or No Masks

Statistics aims to model the relationship between two variables. However, what may seem an obvious causal link may have an underlying hidden variable at play. An example of this can be related to mask-wearing and the spread of infection.

Graph sourced from Masks Save Lives – COVID-19 (accessed on 2nd April 2020 at 11:50 am NZT)

The authors of the website have diligently highlighted the distinct trajectories of two groups. The group of countries that are considered low mask-wearers had higher rates of infection compared to those countries that instigated high mask-wear.

So, can we conclude that wearing masks will slow the rate of infections?

What we are seeing here is a correlation: high mask wear and low infection rate.

However, as always, we need to take a closer look especially what other methods these high mask-wearing countries took to reduce spread.

For example, South Korea implemented extensive testing, following up with tracing contact with those who were sick. South Korea was prepared after exposure to the MERS-CoV outbreak3.

Another example is Japan. Japan comparatively tested far less than South Korea. But could fewer tests mean less positive results? This is a question that is difficult to answer. The people of Japan are regarded for their high maintenance of cleanliness, which requires high societal contribution, which could also translate to high compliance when it comes to crisis, but there is no certainty with this either4.

In the end, we cannot really say definitively that wearing masks will reduce infection spread, because there are so many variables at play. We mask-wearing in this case a confounding variable. I am postulating that high use of masks is indicative of widespread public compliance to hygiene and that this widespread public compliance to hygiene, which includes hand washing, isolating if ill, wearing masks, may be the key factor in reducing spread; mask-wearing is just what we see so it is what we think will be the cause.

WHO has left out its recommendation of mask-wearing opting for the following ways to reduce the spread of 2019-nCoV5:

  1. Wash hand frequently
  2. Maintain social distancing
  3. Avoid touching face and mouth
  4. Practice respiratory hygiene – cough into the arm
  5. Seek medical care early if you have a fever, cough and difficulty breathing
  6. Stay informed and follow advice from the healthcare provider

Masks should be worn6:

  • if you are healthy, you only need to wear a mask if you are taking care of someone who is suspected of having the 2019-nCoV infection, or
  • if you are coughing or sneezing yourself.
  • Note that masks are effective when hand washing is performed regularly.

Furthermore, the transmission of 2019-nCoV is similar to that of influenza7.

As current understanding, the 2019-nCoV are released in large droplets (>5-10 μm), where people in close contact (less than 1 m) are exposed. These droplets when they settle on surfaces can result in indirect transmission if another person touches this surface and then their face.

This is in opposition to airborne pathogens, like the bacteria responsible for Tuberculosis8, where these pathogens linger in the air for a long period of time.

This is in accordance with WHO recommendation to wash hands, social distance and limit touching of one’s face. 

We must remember that masks are a scarce resource 9

The economic principle of scarcity means that we have to be educated about how we prioritise our resources, like masks.

WHO’s recommendations, I would consider as ‘big wins’ in reducing infection spread and work well in public health campaigns as this can be practiced without much strain on resources. 

This allows proper allocation of resources, allowing hospitals, doctors clinics, and essential workers to be well stocked with masks.

From the data, are we effective in recommending masks, a strained resource, for everyone? Or put our focus into public awareness of handwashing, distancing and limiting face touching allowing masks to be allocated more appropriately?


We covered Simpson’s paradox, where the generalisation of mortality rate for 2019-nCoV hides how the mortality rate is for particular age groups causing misrepresentation.

Finally, the true variable can be masked by another more obvious, confounding variable. It is most likely the social policies the countries adopt and not just mask-wearing alone results in the distinct reduction in infection rates that we are seeing.

I am hoping, day-by-day, that we get over the COVID-19 pandemic and be back to normal life soon. In the meantime, I am hoping these two statistical principles have empowered you with the ability to decipher data better.

We can use these principles and extend this beyond the realm of COVID-19, as we will get out of this soon.

  1. WHO Director-General’s opening remarks at the media briefing on COVID-19 – 3 March 2020[]
  2. Sex Bias in Graduate Admissions: Data from Berkeley[]
  3. Coronavirus cases have dropped sharply in South Korea. What’s the secret to its success?[]
  5. (COVID-19) Advice for public | WHO[]
  6. (COVID-19) advice for the public: When and how to use masks | WHO[]
  7. Modes of transmission of virus causing COVID-19: implications for IPC precaution recommendations | WHO[]
  8. Chapter 2: Transmission and Pathogenesis of Tuberculosis | Core Curriculum on Tuberculosis: What the Clinician Should Know | Centre of Disease Control and Prevention[]
  9. Rational use of face masks in the COVID-19 pandemic | The Lancet[]

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2 thoughts on “2 Statistical Ideas to help your Critical Thinking using COVID-19 as an example”

  1. For me this is a very frustrating topic because of the lack of logic in what many people in the media are saying. I have been doing a lot of research online recently to find out for myself whether I thought everyone should be wearing masks or not during this pandemic. Like yourself, I was very confused at the start due to mixed messages being portrayed in the media and different countries or organisations recommending different things. What I have concluded for myself in this situation is that one must not ignore scientific data but when there is a lack of reliable data to go by one should use common sense and logic. Also, people should err on the side of caution during a pandemic like this. Hence, I think people should wear masks out in public in crowded places if you have to go out.

    Do masks act as a barrier and reduce the amount of respiratory droplets and hence the viral load that you may be exposed to? Yes.
    Do masks reduce the viral load significantly enough that you won’t get infected? That probably depends on the type of mask you are wearing and whether you are wearing it properly.

    Washing your hands and disinfecting surfaces are the most important things to be doing during this pandemic. Masks may be a tool to reduce the chance of contracting the virus by small amount. But hey, every little bit counts right? Washing your hands does not prevent an asymptomatic carrier of the virus from accidentally spitting out a bit of saliva while talking or coughing/sneezing near you. It is up to you to look after your own health.

    Early on in this pandemic, I was already hearing on the news that this COVID-19 could be transmitted from asymptomatic carriers of the virus. At the time, there may not have been sufficient evidence to scientifically prove that this was true but if that were the case would you not err on the safe side and advise people to take caution as there may be asymptomatic people spreading the disease? As you already know, the WHO suggests that, with the current available evidence, COVID-19 transmission is mostly via respiratory droplets. There appears to be lacking evidence that the virus could be air-borne in our everyday settings but is not totally ruled out and in my opinion this is where we have to take caution. We don’t know what we don’t know.

    Onto social distancing, which has been huge everywhere…
    On the WHO website they advise people to “maintain social distancing” by maintaining “at least 1 metre (3 feet) distance between yourself and anyone who is coughing or sneezing.” This statement seems to suggest that asymptomatic people do not necessarily have to maintain the 1m distance between each other. Yet, on the Australian Department of Health website, it advises people “to keep 1.5 metres away from others”, which suggests that people should keep the 1.5m distance even from asymptomatic people and I know that that is what we are being told here. But why? Does this mean that the Australian government is suggesting that this virus could be transmitted from one person to another just by being close to someone even if they are not symptomatic? Yet, mask-wearing in public is discouraged for asymptomatic people. Where is the logic in that?
    A document published by the Australian Health Department on 06/03/2020 states that “you do not need to wear a mask if you are healthy”. How do you know if you are healthy or not? On 06/03/2020, people already knew that there was an incubation period for COVID-19 so this is very frustrating once again.

    I totally agree that the medical staff who are directly dealing with patients with COVID-19 should be prioritised when it comes to accessing masks. But that does not mean the the general public should be discouraged to wear masks. I think this is definitely an ethical question. Having said that, I think it is best that the general public leave the N95 respirator type masks to be used by health professionals dealing directly with COVID-19 patients.
    I was very disappointed that what seemed to be driving the recommendations from various organisations, especially early on as things seem to be somewhat changing now, regarding masks was the lack of supply of masks rather than genuine concern for the health of the public. This is very concerning.

    As an optometrist, who is still working full time currently, I do not feel safe interacting with patients in my room during this pandemic without a mask and my colleagues who I have spoken to seemed to agree. Yet, I am told that we are not “required” to wear a mask in practice though we “may wish to use one given the proximity to patients.” These guidelines seem somewhat vague to me. So decided for myself to wear a mask in clinic. I don’t think anyone will be able to criticise my actions for wearing a mask in an optometry room as going overboard. We are supposed to keep 1.5m away from each other in Australia. Nowhere does it say that this does not apply if you are in an optometry practice.
    At an optometry webinar that I watched in late March, the message regarding masks was that we did not have to wear a mask if the patient was asymptomatic.
    The Royal College of Ophthalmologists UK released on the 1st of April that “clinicians should wear surgical masks” behind the slit lamp and the RANZCO advised on the 2nd of April that “where practical, doctors, staff and patients should wear masks”.

    The WHO stated in a document released on the 19th of March that wearing masks may “create a false sense of security that can lead to the neglect of other essential measures, such as hand hygiene practices” and that “using a mask incorrectly may hamper its effectiveness in reducing the risk of transmission.” While all of this is true this statement sounds very discouraging. I wonder why the WHO released this statement. It was probably due to the shortage of masks. Wearing masks was not popular anyway in many parts of Europe and the US at this time. It was not like everyone was already wearing masks and that this was becoming a concern for the WHO that people may become complacent because they were wearing masks. If they were so concerned that wearing masks would make people become complacent about other measures, such as washing hands then I think that people should be encouraged to wear masks properly and to carry on washing hands, not discouraged to wear them in case they cannot learn how to wear a mask properly.

    The CDC in the US now seem to be recommending people in public to cover themselves with cloth face masks so the view on mask-wearing is changing. I am not saying that wearing masks will definitely protect you from the virus but this seems to be the sensible thing to be doing if we are taking a “better safe than sorry” approach.

    1. Hi Ryan,

      This is a fantastic post. You come up with a convincing argument.

      It makes me want to rewrite what I wrote, but I think I will keep it as is for what I initially wrote and thought about at the time.

      Thank you for your comment once again, Ryan.


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