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HOW TO THINK CRITICALLY
"Thought is great and swift and free, the light of the world, and the chief glory of man."
"Principles of Social Reconstruction" by Bertrand Russell (1916)
"You take the blue pill and the story ends. You wake in your bed and you believe whatever you want to believe. You take the red pill and you stay in Wonderland and I show you how deep the rabbit hole goes."
Morpheus to Neo in "The Matrix" (1999)
- Firstly, recognise that thinking critically does not mean simple criticism. It means not simply accepting information at face value in a non-critical or non-evaluating way.
- The essence of critical thinking centres not on answering questions but on questioning answers, so it involves questioning, probing, analysing, evaluating. In his novel "Sophie's World", the Norwegian writer Jostein Gaarder notes that: "The most subversive people are those who ask questions".
How to question the news
- Remember that prominence does not equate to importance. A newspaper may have made its lead story the rumour of a break-up between Britney Spears and her latest boyfriend, but that does not necessarily make it the most important news item that day. Conversely, in 1914 that tiny story about the assassination of an obscure nobleman in some backwater called Sarajevo proved to have rather more repercussions than most readers first appreciated. Try an experiment: one day, buy five or six national newspapers, compare their coverage of the same stories on the same day, and note the different prominence - and the different slant - given to the same stories.
- To understand a news item, try to give some context to the current event. For instance, if it is reported that a group of Sunnis today attacked a meeting of Shiites in Iraq, three things are needed to make full sense of the report. First, explanation: what is the difference between Sunnis and Shiites and what proportion of the population do they constitute? Second, history: what is the origin of the division of Sunnis and Shiites in the country and how has the power relationship altered in past years? Third, anticipation: what does the attack mean for future developments such as the formation of a government or the conduct of an election?
- Check the source. Who wrote the article or scripted the programme? How knowledgeable is the source? Does the source have a particular interest or 'angle' or prejudice? Is the source known to you by reputation or previous work? In the case of a web site in particular, it may be difficult to establish the source.
- Use different sources. If there is a dispute over the ecological impact of oil exploration, check out the views of the 'green' pressure group and the oil company and other, more independent, sources such as scientists and commentators. If there is a government statement on health expenditure, check out the views of health authorities, doctors and nurses, and independent commentators.
- Always prefer prime sources. A personal, eyewitness account is to be preferred to the statement from the politician who was told by a journalist who read it on a news wire which obtained it from a company spokesman who was briefed by a senior manager on the basis of an eyewitness report from a colleague. A newspaper quote from a report may be accurate but, when you obtain and study the report itself, you might find that the quote was selective or unrepresentative of the work as a whole. These days it is often easy to track down the original report on the web by searching on the name of the originating organisation.
- Check the date. Generally speaking, the more recent the material, the more accurate it is likely to be and the more useful it is. This is especially the case in changing situations. For instance, something about Russia written after the fall of communism may well have been able to use sources not available in previous decades. In a war situation, even a few days or hours may make a significant difference to the information and perspective available. On the web, material is frequently undated and one needs to be aware that it could be outdated.
- Check the publisher or promoter or funder. Many newspapers, magazines and television stations have a definite political orientation and can be expected to push a particular 'line' or interpretation. A Government source may be regarded as particularly authoritative or dangerously partial, depending on the circumstances. A report on the effect of smoking on cancer rates might be regarded with some caution if the underlying research is found to be funded by tobacco companies.
Critical thinking techniques
What to beware of
- Seek out assumptions. Most statements or assertions are based on certain assumptions. Sometimes these assumptions are explicit but are not easy to find. For instance, a political opinion poll may well assume that voters in all constituencies and supporters of all political parties are equally likely to vote. This assumption may well be in the small print of the report if one looks hard enough. Sometimes assumptions may be implicit and therefore harder to discern. For instance, a political opinion poll may assume that everyone polled is telling the truth about their likely voting intentions. This sort of assumption is unlikely to be spelled out anywhere in a report.
- Question assumptions. For instance, are voters in all constituencies and supporters of all political parties equally likely to vote? Maybe voters in affluent constituencies or supporters of political parties in opposition are more likely to vote. Or does everyone polled tell the truth about their likely voting intentions? Maybe supporters of racist parties are reluctant to be honest about their true voting intentions.
- Look out for exceptions. There is a popular saying that: "It's the exception that proves the rule." In fact, in scientific terms, it is the exception that disproves the rule. So, for instance, for many centuries it was assumed that there could not be a black swan and therefore that 'All swans are white'. However, in the 17th century, the discovery of black swans in Australia forced a change in that thinking. The identification of exceptions or black swans requires us to rethink the current orthodoxy. According to the 'black swan theory' promulgated by the author Nassim Nicholas Taleb, almost all high impact changes in history come from exceptional and therefore unexpected events [for further explanation click here].
- Look out for trends. There are many different ways of measuring most variables whether it is economic growth, crime rates, or hospital waiting lists so the absolute figures may not be that helpful. However, if a consistent method of measurement is used (that is, over time one is comparing like with like), then trends may well be apparent, so that one can see a rise or a fall or a cycle.
- Make temporal comparisons. If a company announces that it has increased revenues by 10% in the last two years, look at the rate of growth in revenues in the two previous years. This will indicate whether recent performance is impressive or merely continuation of a trend. If a company announces a 5% growth in the last quarter compared to the previous quarter, look at performance in the previous equivalent quarter because many products and services have fluctuating demand over a 12-month cycle (for instance, we use more energy in the winter and take more holidays in the summer).
- Make geographical comparisons. If the government claims that it is now spending 10% of Gross Domestic Product on the health service, compare that with the percentage expenditure in other industrialised countries. If you live in a European Union country, there are often comparative statistics or policies in the other 27 Member States. If you live in the USA, there are often comparative statistics or policies in the other 49 states.
- Always look for evidence. The Scottish philosopher David Hume noted that "A wise man proportions his belief to the evidence". Many Americans believe that the attack on the World Trade Center was engineered by Saddam Hussein, while many Arabs believe that it was planned by the Israeli secret service. They can't both be right, but they could both be wrong. What is the evidence? It has been widely reported that millions of Americans believe that they have been abducted by aliens and, in many cases, subjected to sexual experiments. They may be right, but again what is the evidence? Are there witnesses or photographs? Are there body marks on the 'victims' or do they have souvenirs from the spaceships?
- Be ready to change your mind if the evidence changes. The famous British economist John Maynard Keynes once said: "When the facts change, I change my mind - what do you do, sir?". Before the Allied invasion of Kuwait, the US Congress heard testimony about Iraqi troops removing newly-born babies from incubators in a Kuwaiti hospital. Following the invasion, this story was challenged and never substantiated. Before the US invasion of Iraq, many people thought that Iraq possessed weapons of mass destruction based on the then available evidence and the interpretation of it by the intelligence services. Following the invasion and extensive searches, the evidence changed, but many were reluctant to change their minds.
- Always consider alternative explanations. Those who believe that they have been abducted by aliens might have dreamt or fantasised it. The report of a body found in the park could mean a murder or a suicide or a heart attack or old age. The fall in crime levels could be the result of more police, better detection procedures, social changes or simply new methods of reporting.
- Remember Occam's Razor [the maxim is named after William of Occam, the philosopher who was probably born at Ockham in Surrey]. When two or more explanations are possible on the basis of the same facts, always prefer the simplest possible explanation, unless there are very good reasons for favouring a more complex - and therefore more unlikely - one. For example, the pyramids in Egypt could have been designed and constructed by the Egyptians living at the time of the pharaohs or they could have been built according to plans brought to earth by aliens. Both explanations would account for the observable phenomena, but Occam's Razor suggests that we should adopt the explanation that requires the fewest assumptions since there is simply no need to make extra assumptions unless there is good evidence to support them. Or, as the scientist Albert Einstein put it: "Everything should be made as simple as possible, but not simpler".
- Look for cause and effect. Correlation does not necessarily mean causation - that is, because two variables often occur together does not necessarily mean that one variable actually causes the other. To take a trivial and obvious example, when I get up from bed, the sun comes up - but there is obviously no causality. Yet some tribes used to believe that particular rituals were essential to ensure the rising of the sun. On the other hand, when I go to bed, I feel refreshed - and there clearly is a relationship. More sleep generally means more vitality and this positive correlation underlines that there is a causal connection here. Sometimes relationships are not obvious: in the movie "The Truman Show", when the Jim Carey character gets up from bed, the 'sun' does come up in a causal manner because the Ed Harris character ensures that it does.
- Deconstruct the elements of a work. In the case of a paper or speech, look at the arguments, the evidence, the structure, and the presentation. In the case of a novel, consider the plot, the characterisation and the language. In the case of a film, think about the script, the acting, the direction, the cinematography and the music.
- Consider a SWOT analysis. SWOT analysis is a strategic planning method used to evaluate the Strengths, Weaknesses, Opportunities and Threats involved in a project or situation. It can be a relatively quick and comprehensive - and sometimes fun - way to assess something. It encourages you to see different 'sides' of an organisation or a situation. For guidance on doing a SWOT analysis, click here.
- Go for SMART objectives. These are objectives which are Specific, Measurable, Achievable, Relevant and Timed. It's amazing how often even governments and corporations - as well as individuals - pursue ends that do not meet all - or even any - of these basic requirements. Of course, these objectives should be set in advance of the relevant activity and not 'retro-fitted' to it. This helps to avoid self-justification and 'mission creep'.
- Think about what is not there. When invited to respond to material, most people confine their comments or their thinking to what they can see or hear. Sometimes what is not there is just as important. You might want to ask: Why are certain arguments missing? Why have certain sources not been used? Is this the full picture? A political manifesto will inevitably mention achievements but not failures and will often criticise another party's policy or performance but fail to offer a constructive alternative. A company's annual report will put the most favourable possible 'gloss' on activities and may not mention at all financial difficulties or threats from competitors. In a job application, a missing period of time could mean a sabbatical travelling around the world or it could mean a sentence in prison. Papers for decision often offer a limited number of options, but there many be other better options which have been rejected by the paper's author or even not considered..
- Try thinking like your competitor. If you are in a competitive situation - even if it is just a discussion or debate, but much more so if it is a business or a sport (or a war!) - put yourself in the mind of your competitor. If you were him or her, what would you do? If he were to think 'out of the box' or even to think the 'unthinkable', what might he do? How would you respond to that? Should you make such a move first? Ways of bringing out such thinking include role-playing and 'war games'. Even if this process of thought does not lead you to adopt a new strategy, it is a useful discipline that will change the way you look at the situation and how prepared you will be mentally for the unexpected or unlikely.
- Learn to think outside your cultural frame of reference. Although you may be American, it does not mean that European or Chinese or Indian ways of looking at things are less valid. Although you may be an English speaker, it does not mean that sources in other languages might not provide valuable insights. Although you may be Left of Centre politically, it does not mean that some ideas and arguments from the Right might be not useful. Whoever you are, the history you were taught was very particular to your place and time and you might want to try to look at historical events from the perspective of someone born in a different country or a different time. My mother was born in Italy in 1920 and she was taught that there was nothing smaller than the atom, that all major scientific discoveries were by Italians, that fascism was an efficient way to run the country, and that Italians deserved a slice of Africa. I was born in Britain in 1948 and I was taught that there was nothing smaller than the electron, that most scientific discoveries were made by Scots, that parliamentary democracy was the best political system, and that the British Empire was the greatest in history.
- Learn to think 'out of the box'. Albert Einstein once said that: "Problems cannot be solved by thinking within the framework in which they were created". For instance, you are asked to decide whether a new product should be trialed in Manchester, Birmingham or London. But maybe it should be trialed in all three or in three different locations. Maybe it shouldn't be trialed at all, but launched straightaway, because a competitor is about to launch a similar product. Maybe it shouldn't be trialed at all because it is still an inferior product that needs more development. Maybe the whole discussion is irrelevant because the company is about to be taken over by another company which already has such a product in the marketplace.
- If you dare, go beyond thinking 'out of the box' to thinking the 'unthinkable'. What does this mean? It means considering variations to the most basic of parameters and entertaining the most radical of possibilities. In the last example - trialing a new product - thinking the unthinkable might mean leaving the company, forming your own and marketing a rival product or it might involve a recognition that you are disillusioned with such products altogether and want to make a career change. Albert Einstein once said that: "If at first an idea doesn't seem crazy, then there is no hope for it". As Yosserian in Joseph Heller's iconic novel "Catch-22" concludes: "Of course it's insane ... That's why it's the only sane thing to do".
- Test your thinking on others. Brainstorm your ideas before starting a piece of work. Show drafts of work in progress to colleagues or friends. Welcome corrections, suggestions and constructive criticism. Entertain challenge. Embrace change. Encourage diversity.
How to think about statistics
- Beware of anecdotes. People sometimes talk of "anecdotal evidence", but really this is an oxymoron. An anecdote is not evidence - at best, it is one person's experience and, at worst, it is simply unsubstantiated rumour. One of your friends may have had a poor holiday in India which might be interesting but is unlikely to be conclusive of what others might expect. India is a massive country, it has millions of visitors a year, your friend's experience might have been years ago or be more to do with the travel company than the country. Check the information on India on independent travel guides and surveys before making a more informed and balanced judgement.
- Be very doubtful about information based exclusively on memories. For most people, memory is a very malleable thing. We can so easily 'remember' things in the wrong order than they actually happened, confuse a 'memory' with a subsequent trigger such as a conversation or photograph, or even - especially when traumatic situations are involved - 'remember' things that never happened. Even when the memory of an event is accurate in time and place, our recollections of important details - the people involved, what they said, what they did - can be notoriouously unreliable. This is why in court trials prosecutors and defendants will always be looking for other evidence to support personal recollections.
- Be especially sceptical about surveys and polls. There are so many questions one needs to ask to be sure of the validity of poll findings. Who funded the project? Is the funder looking for particular findings? Who conducted the project? Is it a reputable organisation with a sound track record? What was the size of the sample? Were a sufficient number of people polled and was the sample properly weighted to reflect relevant variables such as age, gender, ethnicity, geography, education, income? How were the questions chosen, worded and posed? Were they 'leading' questions which effectively 'invited' a specific answer? Were those questioned given any context or introductory information which might have biased them? What is the margin of error or statistical significance of the resultant data? Have the findings been fairly presented and reported? All these factors can have a massive influence.
- Be exceptionally critical of information in circular e-mails. If this information looks shocking or surprising, it's because it is often untrue or only a version of the truth, although most of those forwarding the material do so in good faith believing that the material is accurate and even that they are helping friends (as with warnings of dangers). You can check the accuracy and provenance of many such e-mails on sites like Snopes [click here] or Hoax-Slayer [click here] - just type into the search box the title or a key phrase.
- Be enormously doubtious of information on social media. Web sites like Facebook and Twitter are incredibly popular and have the capacity to spread information virally across the globe in a matter of minutes. Although citizen journalism has a role to play, too often the information can be notoriously unreliable, especially where public order matters - such as an explosion or a murder - are concerned. The reasons are obvious: the comments are made in the heat of the moment without thought or reflection; the text is of minimal length, allowing no opportunity for context or qualification; and there is no editorial process as there is for radio, television or newspapers.
- Beware of making assumptions. Someone once said that: "Never assume, as assume makes an ass out of u and me". So, just because a particular source is usually accurate doesn't necessarily make it accurate this time. Just because the facts can be explained by one particular scenario doesn't mean than another scenario isn't possible and maybe even more likely.
- Don't jump to conclusions. As Harold Acton pointed out: "Some people take no mental exercise apart from jumping to conclusions". Although the currently available facts may suggest a particular conclusion, other conclusions may be possible. Further facts may support an alternative conclusion and even invalidate the original conclusion. Even when this is not the case, it is always helpful to have further, supporting evidence to support the original conclusion.
- Beware of confirmation bias. We are inclined to take more notice of, and give more weight to, evidence that appears to confirm our current opinion or judgement. Conversely we tend to neglect or reject evidence which challenges our current position or stance. Try to weigh the evidence impartially and follow the evidence wherever it takes you. It is so tempting to seize on evidence that confirms one's original view or the prevailing orthodoxy and to dismiss evidence that challenges it, but one needs to be open-minded about all the evidence and equally rigorous about establishing its authenticity.
- Don't rest on authority. The scientist Albert Einstein once remarked: "Foolish faith in authority is the worst enemy of truth". There is a popular saying that: "Great minds think alike" - but in fact the greatest minds (such as that of Einstein) frequently think very differently from their contemporaries and peers. Remember that another popular saying is: "Fools seldom differ". In the early 1990s, I gave a presentation to a group of Russians using slides in Russian. At one point, I realised that I had been speaking to the wrong slide for the last five minutes. When I asked my audience why no one had told me this, I was advised that in Communist Russia no one challenged the teacher! Just because the management or the government states something does not necessarily mean that it is true. This is especially the case where there is a vested interest, so asbestos and cigarette manufacturers both claimed authoritatively for many years that their products were not damaging to health. Study the evidence and make an independent judgement based on the balance of the available evidence.
- Closely related to this, don't necessarily rest on the received wisdom. Galileo was excommunicated for challenging the Church's view that the sun, the planets and the stars revolved around the earth - but he was right. Today even the most fundamental rule of modern physics - Einstein's insistence that the speed of light is a constant - is being challenged (by a scientist called João Magueijo). Many management styles (outsourcing?) and political policies (privatisation?) are the received wisdom for a time, but frequently deserve to be challenged. The important thing is to marshal the evidence and subject it to review and analysis.
- Be challenging of the seemingly seductive comment "It works". There are two problems here: agreeing a definition of what 'works' means and establishing a cause and effect relationship between action and outcome. If I perform a traditional Indian rain dance in my back garden, it may rain in an hour, a day or a month. Over what period are we going to assume the dance may have had an influence? Then, can we reasonably infer a causality here? It may be that my neighbour was performing a different, more effective rain dance in her garden; it may be that the rain clouds had been seeded by a specially charted aircraft to ensure good weather for a sports event tomorrow; it may be that I am in India in the monsoon season and it usually rains at this time of day at this time of year anyway.
- Be challenging of the seemingly convincing comment "There is no alternative". There is always an alternative - even if it is simply doing nothing and waiting to see what happens. In fact, usually there is more than one alternative - in which case technically you do not have alternatives but choices (because the word 'alternative' comes from the Latin word 'alter' which means the other). The other choices might be more expensive or less effective or riskier or less popular, but they should be considered before deciding on the 'best' choice which should be presented in that manner and not as the 'only' choice.
- Be challenging of references to timeframes. There is an endless set of phrases that refer to timeframes but are essentialy meaningless, such as "as soon as possible", "in due course", "over the coming period" and even "when the time is right" (which could be never). When talking of timeframes, seek precise dates or units of time.
- Beware of peer group pressure or groupthink. In the 1950s, the social scientist Solomon Asch conducted a famous series of experiments which demonstrated the degree to which an individual's judgement and opinions can be influenced by the majority group [for information on the Asch conformity experiments click here]. This is the case even when the individual knows that his view is factually incorrect or his action is morally wrong. You can be seduced by this kind of pressure - consciously or unconsciuously - at any time, but especially if you are a member of a close-knit group of people where there is a strong sense of loyalty to the group, deference to an authority figure within the group, and a demonised view of those outside the group. Many believe that a version of groupthink among the advisers to President George W Bush led to the deeply flawed decision to invade Iraq in 2003. The Independent Evaluation Office (IEO) of the International Monetary Fund (IMF) identified groupthink as a major factor in its official report on why the IMF did not forsee the coming international financial crisis of 2007-2008. Remember the story of the little boy who was the only one brave enought to point out that the emperor had no clothes? It is amazing how very senior and very intelligent people can collectively delude themselves about something - for instance, that a particular policy is working when so much evidence shows that it is not (the war on drugs?).
- Beware of meaningless statements. Often politicians and businessmen make statements which are virtually meaningless, such as "I think that, if we tried harder, we could possibly do somewhat better" or "Some improvements in performance might be expected in the fullness of time". Much more meaningful sentences - and ones therefore to be preferred - would be something like "We will reduce recorded crimes of violence by 10% before the next General Election" or "If we increase our capital expenditure by 5% annually for the next three years, we should achieve a 25% increase in revenues by the end of the decade". So ignore meaningless statements and look for, or request, meaningful statements.
- Beware of statements that pretend to be truth but are close to being lies. As the book "Would They Lie To You?" makes clear: "You can steer a truck through the gap between a lie and the simple truth." An infamous example is the statement by President Bill Clinton in January 1998: "I want you to listen to me. I'm going to say this again: I did not have sexual relations with that woman, Miss Lewinsky." In his own mind, Clinton believed this statement to be true because he had not actually had sexual intercourse with Lewinsky, but most people would regard fellatio as constituting "sexual relations". The only way to be clear about what such statements mean is to ask very precise questions and insist on very precise answers - although if the questioner is not sure what he is trying to find out, the person asked the question can use that very precision to give a misleading answer. That is why, in the case of an earlier presidential scandal (Watergate, 1972-74), 'Deep Throat' played such a useful role in directing the investigating journalists as regards the lines of enquiry they should follow.
- Beware that, when observing a situation, the observer can sometimes change the situation. A classic example of this has come to be known as 'the Hawthorne effect', named after the location of a factory in the USA where some studies were conducted in the 1920s. The researchers were trying to establish what change in working conditions would lead to an increase in productivity. To the astonishment of the researchers, they found that every change in conditions - and even a return to the original conditions - resulted in an increase in production. They concluded that this was because the workers were being motivated by the interest shown in them by the researchers [for information on the Hawthorne effect click here]. A similar situation occurs in experiments to test the efficacy of drugs or medical treatments and, in this case, it is known as 'the placebo response'. A placebo is a 'pill' made of sugar or a 'tonic' containing nothing medicinal which is used with a control group of patients to compare with another group taking the drug or treatment that is being tested. What researchers have found is that frequently a placebo has a positive effect because the person taking it believes it to be efficacious. This effect is often reinforced by the 'observer': someone in a white coat or with a medical title or someone who enquires kindly after your health and listens carefully to your symptoms or someone who incants prayers or lays on hands can make you feel better regardless of the chemical composition of the 'medicine' or even the absence of any 'medicine' (this is how homeopathic treatments and faith healing 'work').
- Have at least a basic understanding of statistics. A figure without a context is often meaningless. For instance, it might be reported that this weekend there were 10 deaths on Britain's roads. What does this mean? To obtain some context, it would be useful to know the number of deaths for each weekend in the last month, year or decade and more helpfully calculate the average figure for each of those periods. Sometimes, however, the average can be a misleading measure. For example, if there was a major motorway smash-up last weekend or a petrol shortage last month or a particularly severe winter this year, the average for a particular period may be distorted or skewed by an exceptional figure or two. In these circumstances, it is good to know the difference between mean, median and mode. The mean is the arithmetic average of a range of figures; the median is the middle figure in a range of data arranged by value; and the mode is the figure which occurs most frequently in a set of data. Sometimes the median or mode may be a better indicator than the mean by reducing the impact of 'extreme' or outlier instances.
- Consider the distribution of data points. Sometimes the average of a set of data points is unhelpful whether one uses mean, median or mode. For instance, if you are going to work in another country for a couple of months, knowledge of the average rainfull or sunshine for the year is useless to you; you need to know how the amount of rain and sunshine varies from month to month throughout a typical year. Often the distribution of data reveals an illuminating pattern. For instance, in the human population, many physical characteristics like height and weight and some mental attributes like intelligence when plotted on a graph show a bell-shaped distribution which is known as a normal or binomial distibution [for further explanation click here]. A different kind of pattern is often found in the world of engineering and business where roughly 20% of one variable explains around 80% of another variable - for instance, 80% of downtime in a production process might be caused by 20% of the types of incident, so it makes sense for management to concentrate on those 20% and not spread time over all types of incident. This distribution is often called the Pareto curve or the Pareto principle because it is named after an Italian economist [for further explanation click here].
- Always be sure that one is comparing like with like. There is not much point in comparing the size of the British economy in pounds sterling and the size of the US economy in American dollars; one needs both figures in pounds or dollars or a third currency (such as euros). You cannot compare a quarterly growth rate with an annual growth rate; you need to compare a quarterly growth rate with the rate in the previous quarter or (especially if there are seasonal factors) with the previous equivalent quarter a year ago). You cannot compare capital expenditure with current expenditure; the construction of a road is capital expenditure, because it is a one-off cost (although there might be some maintainance costs which would be current expenditure), whereas the employment of nurses would be current expenditure because they will have to be paid year after year (although the employment of lots of new nurses might require the building of a new unit for them which would be capital expenditure).
- Be cautious about big numbers. On the one hand, Governments and large businesses deal with large numbers, so millions and even billions will be everywhere and politicians and business leaders like to use such 'big' numbers to impress. If the time period is several years or even decades, then the numbers will be even bigger. You need to put the numbers in context (for instance, as a proportion of total expenditure or revenues) and to be sure what time period is used (for instance, turning the figure into an annual one). On the other hand, you can easily underestimate the size of a big number since, while many people know what a million is, many have no idea what a billion or a trillion is. In most English-speakimng countries (usage varies around the world!), a billion is 1,000 million and a trillion is 1,000 billion. So, if the size of the United States debt is said to be around 18 trillion dollars (late 2014), this is a very LARGE number: $18,000,000,000,000.
- Be cautious about changing percentages. Percentages can be useful; they can put large numbers or small numbers in context. But changing percentages need to be viewed carefully. An under-noticed property of percentages is that they are bigger on the way up than they are on the way down. So, if the price of something rises by 100% and then falls by 50%, you are back to where you started (something which costs £ 20, if increased by 100% becomes £ 40, then if decreased by 50% becomes £ 20 again). If you have a loan with a compound rate of interest of 10%, this does not mean that each year the amount of the loan increases by 10% of the original sum; instead, on a loan of £ 1,000, in the first year, the interest is 10% of £ 1,000 = £ 100; in the second year, the interest is 10% of £ 1,100 = £ 110; and so on).
- 'Translate' statistics. So, convert a percentage into an absolute figure. A claim to have increased customers by 100% might simply mean an increase from two to four. Conversely, a 2.5% increase in a nation's economic growth could - in the case, for instance, of the UK or the USA - mean the availability of billions of more pounds or dollars. Similarly, convert absolute numbers into percentages. A politician might claim that expenditure on the health service has increased by £ 500M which seems like a massive figure to someone earning £ 500 a week but, when expressed as a percentage of total expenditure on health, is seen to be proportionately a mere blip in expenditure patterns. Again conversely, it could be that paying a relatively small cash sum monthly into a pension scheme results in a 25% increase in payments in 20 years time. Another useful way to 'translate' data - especially when there is a lot of it - is to turn it into a visual representation of the information. There are many ways to do this but the most common are the the pie chart, the bar chart, and the graph.
- Watch out for bar charts and graphs. All bar charts and graphs have two axes: the horizontal one (called the 'x' axis) and the vertical one (called the 'y' axis). It is essential to be clear what units are used on each axis. The horizontal axis often uses a time series and it is important to understand why that particular time period was used and to be sure that the time oeriod is not unrepresentative or selective. The verical axis usually starts at zero, but one should be beware when this is not the case (it should ideally be signalled with a zig-zag line) because this can exaggerate the changes being shown.
- Make appropriate use of statistics particularly where subjective judgements are likely to dominate. A classic example is the notion of risk where most people have incredibly subjective perceptions. Obviously crossing a road is risky, because you might be hit by a car. But staying at home is risky too - you might fall down the stairs or electrocute yourself with the toaster or be attacked by an abusive husband. Obviously, travelling by aircraft is risky because occasionally there are crashes and the number involved is usually so large that it is reported in the media. However, driving a car is probably riskier and riding a motorbike even riskier but, since these accidents and deaths are happening everywhere all the time, you don't hear about most of them. Everything in life has an element of risk - what is necessary is to quantify that risk in terms which make it comparable with other risks and then take rational decisions based on reasonable probabilities of particular outcomes. This may seem a complicated manner of deciding whether to take the train or fly, but it is a technique which can be used in many other situations where emotions can blind sensible decisions, such as deciding whether to use hormone replacement therapy or where to allocate scarce resources in health care.
- Be especially cautious of statistics where probability is concerned. Most people with no training in statistical techniques find it very difficult to make an accurate assessment of probability. For instance, consider the tossing of a coin where the result might be heads (H) or tails (T). Which of these three outcomes is the most likely: HHHHH, TTTTT, HTHTH? The answer is that each of these three options has the same probability because a coin has no memory and each toss of the coin has a 50-50 chance of resulting in a head or a tail. Another example would be assessing how many people you would need in a room before it was likely that two of them shared the same birthday. In this scenario, 'likely' means with over 50% probability. In fact, the answer is only 23 - because we are talking about any birthday matching, not one specific birthday. See how one can so easily be misled by probability?
- Practice critical thinking. Alfred Mander asserted in his book "Logic For The Millions": "Thinking is skilled work. It is not true that we are naturally endowed with the ability to think clearly and logically - without learning how or without practising". The British philosopher Bertrand Russell bemoaned that: "Many people would die sooner than think; in fact, they do", while the British writer George Bernard Shaw quipped: "Most people don't take the time to think. I made an international reputation for myself by deciding to think twice a week".
- Keep practicising critical thinking. The British politician Barbara Castle once said: "Think, think, think. It will hurt like hell at first, but you'll get used to it".
- Don't worry if thinking critically initially confuses you. Life isn't simple and the world is not black and white. As the Greek philosopher Socrates put it: "Confusion is the beginning of wisdom".
- Finally, remember that 'thinking critically' ends in 'why?' The word 'why?' is the most powerful tool in your mental toolbox. Keep asking 'why?' Why is this person writing this story in this particular newspaper? Why is this politician making this statement now? Why has the author of this paper quoted this source and not that one? Why has she used a percentage instead of an absolute figure? Why am I asking all these questions?!?
- "The Demon-Haunted World: Science As A Candle In The Dark" by Carl Sagan (Random House, 1995) [for review click here]
- "Why People Believe Weird Things: Pseudoscience, Superstition, And Other Confusions Of Our Time" by Michael Shermer (W.H. Freeman, 1997) [for review click here]
- "Don't Get Fooled Again: The Skeptic's Guide To Life" by Richard Wilson (Icon Books, 2008) [for review click here]
- "Bad Science" by Ben Goldacre (Fourth Estate, 2008) [for review click here]
Why people believe weird things click here
The Skeptic's Dictionary click here
An Encyclopedia of Errors of Reasoning click here
Last modified on 20 May 2015
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