Statistics and Charts That Mislead: Truncated Axes, Cherry-Picking, and False Correlation

Stop sharing. That is the first instruction. A forwarded chart lands in your WhatsApp. It looks authoritative. It has numbers, a source label, a dramatic shape. Do not forward it. The number is only as reliable as the decisions made before it was drawn, and those decisions hide in three places: the axes, the sample, and the source. This guide walks you through spotting a misleading chart in under a minute, using a real Singapore case where a public fact-checking organisation corrected a graphic that had already spread through forwarded messages. Check the y-axis. Ask who was surveyed and how many. Then leave the post and check the publisher. None of this requires a degree in statistics.

The truncated axis is the most common manipulation in social media charts. A graphic comparing two values looks dramatic only when the y-axis does not start at zero. If a bar chart shows a jump that looks enormous, check where the axis begins. Starting at 90 instead of zero stretches a difference between 90 and 93 into a visual cliff. The Financial Times Visual Vocabulary, the standard reference for honest data visualisation, lists a truncated y-axis as a primary way to distort change over time. The fix costs nothing. Look at the lowest number printed on the vertical axis. If it is not zero, the chart exaggerates the difference by design.

Read the Axis, Not the Title

Look for three things in sequence. First, read the axis labels, not the chart title. The title is where the agenda lives. The axis is where the data lives. Second, check for a missing zero. A bar chart must start at zero. A line chart may legitimately start elsewhere, but only if the axis break is marked clearly with a zigzag or a hash. Third, compare the visual height of the bars to the actual difference in the numbers. If the taller bar is 20% higher than the shorter one but takes up five times the vertical space, you are looking at a truncated y-axis.

Pull the Raw Data Yourself

In Singapore, government data from the Singapore Department of Statistics is published openly via the SingStat Table Builder. You can pull the underlying dataset and redraw the chart honestly. If the source does not link to the raw data, treat the chart as unverifiable.

In 2021, a chart circulated on WhatsApp and Telegram claiming Singapore's COVID-19 case numbers were exploding out of control. The chart showed a sharp upward curve, and the accompanying text used that curve to claim a government cover-up. The chart was technically correct about the numbers it showed. What it did was select a two-week window in October 2021, when cases peaked due to the Delta variant, and omit both the preceding decline and the subsequent stabilisation.

Factually, the Singapore government's fact-checking portal, published a clarification demonstrating that the same data plotted over a longer period showed a sawtooth pattern of rises and falls, not a one-way explosion. The original chart was not a lie about the numbers. It was a lie about the story those numbers tell. The corrected version retained the same source data, the public case counts from the Ministry of Health, but plotted sixteen weeks instead of two. That is cherry-picking: selecting a time range that supports the conclusion while omitting the context that contradicts it.

The Factually clarification did not accuse the original poster of lying. That is the important nuance. Misinformation, false information shared without intent to deceive, differs from disinformation, which is deliberately false. The chart could have been shared by someone who genuinely believed the two-week rise was the whole story.

The correction worked because it showed the same data over a longer period and cited the original source, the Ministry of Health's public data, so anyone could verify. The lesson is not to distrust every chart. Ask what time range was chosen and why. When you see a chart with a dramatic trend in a forwarded message, ask two questions: when does the data start, and when does it end. If the start date is not January or June, the chart is probably telling you what someone wants you to see, not what is happening.

The second most common statistical lie online is presenting correlation as causation. Two variables moving together, ice cream sales and drowning deaths, prove nothing about one causing the other. Both are driven by a third factor: summer heat. This false claim appears constantly in forwarded messages, usually with a confident tone and a screenshot of a chart with two lines on it. The chart shows a real correlation. The claim of causation is the lie.

A classic Singapore example involves data on mobile phone usage and road accidents. A high correlation was cited as proof that phones cause accidents. The truth: both phone usage and accident rates rise during peak traffic hours and fall at night. The correlation exists, but the causation runs through a third variable, the number of cars on the road. When a post claims that because A and B move together, A causes B, ask what else was happening at the same time and whether the claim's author has ruled out the obvious confounders. The base rate fallacy is a close cousin: the probability of an event given a test result is not the same as the probability of the event itself. Ignoring the base rate leads to panic where none is warranted.

When a study or a headline reports that a substance increases the risk of a disease by 50%, ask whether that is relative risk or absolute risk. A 50% increased risk sounds alarming. But if the base rate of the disease is one in a million, a 50% relative risk increase means the risk moves to 1.5 in a million. That change is practically meaningless to an individual. The same study can be reported honestly as an absolute risk increase of 0.00005%. Both numbers describe the same data. One is designed to terrify. The other to inform.

This is precisely how a misleading infographic works: it shows the relative risk because it is a bigger number. When you see a percentage in a headline, search the page for the base rate. If the base rate is not stated, the claim is incomplete. An incomplete claim is a misleading one.

The Organisations That Do the Checking

Singapore has a dedicated infrastructure for infographic verification. Knowing the names is part of the skill. Factually publishes clarifications on false claims circulating locally. Its sister publication CheckMate, run by The Straits Times, verifies specific claims in public circulation. Black Dot Research is an independent Singapore-based fact-checking organisation that publishes local verifications. The International Fact-Checking Network maintains a code of principles that signatories must follow: non-partisanship, fairness, transparency of sources, transparency of funding, transparency of methodology, and open and honest corrections.

Verify With Lateral Reading

When you see a chart in a forwarded message, the verification speed of these organisations matters. A claim that takes hours to be corrected can reach tens of thousands of people in that window. The method for verifying a chart is lateral reading: open a new tab and search for the source's name plus the claim. If the fact-checking organisations have published a correction, the search result will show it. If they have not, the absence of a correction is not proof of truth. It may simply mean the claim is too obscure or too new to have been checked yet.

The third tell is the sample size, and it is the one people most often ignore because it is dry. A poll of 1,000 people is meaningless if the population is Singapore's 5.9 million residents and the 1,000 were recruited from a single shopping mall. The margin of error shrinks as the sample size grows, but the relationship is not linear: a sample of 1,000 has a margin of error of about 3%. Larger is better, but only up to a point. No sample size can fix a biased selection method.

If the survey was conducted online and the link was shared in a Telegram group, the respondents are self-selected. Self-selected samples are never representative. The Singapore Department of Statistics publishes reliable population data, and the Infocomm Media Development Authority publishes internet penetration rates. A statistic from a social media post is almost never drawn from those sources. When a forwarded message claims that 'a survey found' something, ask who commissioned the survey, who paid for it, and how the respondents were recruited. If the answers are not in the message, the survey is an anecdote with a number attached.

Two specific biases corrupt more charts than any other: survivorship bias and selection bias. Survivorship bias appears when a chart shows the success rate of a strategy by looking only at those who succeeded. The classic example is a chart of successful startups that shows the winners while the failures, far more numerous, are invisible. Selection bias is broader: it appears when the data is collected from a group that is not representative of the population.

A chart showing that 'most Singaporeans support policy X' means nothing if the data was collected from a WhatsApp poll shared in an echo chamber of like-minded people. The people who see the poll are the people who already agree with the premise. Their answers confirm the bias of the person who shared it. The fix for both is to ask what data is missing. If a chart shows a dramatic trend, ask whether it includes the years before the trend started, the people who did not succeed, or the countries where the trend does not appear. A chart that shows only the evidence supporting the claim is not evidence. It is an argument.

The Three Favourite Tricks

Beyond the truncated y-axis, chart manipulators have three favourite tricks. The first is dual y-axes with different scales: two lines on the same chart, one measuring thousands and the other measuring single digits, can be made to seem correlated or inverse when they have no relationship at all. The second is 3D charts, where perspective foreshortens the bars at the back and makes the front bars look disproportionately large. The third is pie charts with too many slices, where the eye cannot distinguish the small differences between tiny segments.

Redraw It Honestly

The Financial Times Visual Vocabulary names these as the primary pitfalls of data visualisation. The test for all of them is the same: redraw the chart honestly. If the source does not provide the raw data, the chart is unreadable. Not because you are not smart enough. Because the manipulation is built into the visual. When a forwarded message contains a chart with a dramatic claim, search for the underlying data from the Singapore Department of Statistics or the relevant ministry. If the data exists and the chart matches it, the chart is honest. If the chart conflicts with the data, the chart is the lie.

The final tell is the source. This is where most people fail because the failure mode is social, not analytical. People believe a claim because the person who forwarded it is trusted, a friend, a family member, a colleague, without checking whether that person is the original source. Source confusion is the cognitive error: the trusted messenger vouches for a claim, and the verification reflex shuts down.

The fix is lateral reading, a technique taught in journalism schools and public libraries. When you encounter a claim, open a new tab and search for the source's name plus the claim's key terms. Look for whether the source is a government body, a recognised fact-checking organisation, or a legitimate news outlet with a corrections policy. In Singapore, the Singapore Department of Statistics publishes authoritative data. Factually, Black Dot Research, and CheckMate publish verifications. A claim that cites 'studies' without naming the journal, the university, or the data is a red flag. A claim that cites a source you have never heard of is a bigger one. If the source has a history of publishing corrections, that is not a weakness. It is a sign of trustworthiness.

Even when the source is honest, the statistics can be mangled. A p-value below 0.05 is often reported as proof of a real effect, but the p-value is not the probability that the hypothesis is true. It is the probability of observing the data if the hypothesis is false. A large sample size can make a tiny, practically meaningless effect statistically significant. A study that finds a 0.01% difference in a sample of 100,000 may report a p-value below 0.05, but the effect size is so small it has no practical importance.

Data dredging, running multiple statistical tests and reporting only the significant results, produces the same problem. The Texas sharpshooter fallacy is the name for this: drawing a target around a cluster of data after observing it, then claiming a pattern. When a study or a chart claims statistical significance, ask for the effect size, not just the p-value. If the message reports a p-value but no effect size, the message is hiding something.

A growing problem in Singapore is the forwarded message written in a foreign language, often Mandarin, Tamil, or Malay, accompanied by a translated summary in English. The summary may be accurate. It may be a distortion. The distortion is more common because it is easier to fabricate a translation than to fabricate a believable image.

If you cannot read the original, the verification method is the same lateral reading, but with an added step: search for the source's name and the claim's key terms in the original language. If the fact-checking organisations have published a correction, they will have done so in the language of the claim, and the correction will appear in search results. AI translation tools are improving, but they still make errors with idiomatic expressions and cultural references. When in doubt, do not share the message at all. Point the sender to the original source or the fact-checking portal.

The most dangerous vector for misinformation in Singapore is the forwarded-as-received message on WhatsApp and Telegram. The label 'forwarded as received' is a structural feature of the platform. It creates a false sense of authenticity: the message arrives from a trusted contact, and that trust transfers to the content. But the label is not a guarantee. It is a reminder that the original sender is unknown.

The verification bypass is the behaviour of sharing a message with a comment like 'is this true?'. The act of sharing amplifies the claim to a new audience before any verification has occurred. Verify before sharing. The verification speed of fact-checking organisations is measured in hours, sometimes less. If you see a claim that is unverified, do not share it. Send the claim to the fact-checking organisation so they can assess it. The single most effective thing you can do is wait. A claim that seems urgent can survive a 24-hour delay while the facts are checked. The urgency is itself a red flag.

The newest challenge is AI-generated imagery that is photorealistic. A chart that 'shows' a trend or a map that 'shows' an event may have been entirely fabricated by a generative model. The visual tells change with every model update. A non-technical person cannot reliably distinguish an AI image from a real photograph today.

The tools for detection, reverse image search tools like Google Lens, TinEye, Yandex Images, and Bing Visual Search, are useful for finding where an image has appeared before. They are not infallible. The skill that endures is the principle of questioning whether the media is synthetic or authentic before believing or sharing it. Reverse image search is a permanent technique because it checks provenance, not content. When a chart appears in a message, run a reverse image search on the chart itself. If the chart appears on a fact-checking site or a news article from years ago, it is probably old, not new. If it appears nowhere, it may be fabricated. The specific tools change. The principle of checking provenance does not.

Singapore's National Library Board teaches a framework called SURE: Source, Understand, Research, Evaluate. The Source step asks who created the information and why. Understand asks what the information is saying and whether it is clear. Research asks you to dig deeper and look for supporting evidence from multiple sources. Evaluate asks whether the information is credible, accurate, and useful. The framework is embedded in Singapore's school curriculum and public libraries. It is the backbone of the method in this guide.

But the framework has a failure mode worth naming: single-source settlement. A reader accepts a claim as true after finding one source that confirms it, without checking whether that source is independent or whether other sources disagree. A confirmation from a blog that repeats the claim is not verification. It is a recursive citation. The SURE framework works only when the Research step includes lateral reading, and when the Evaluate step weighs the source's track record, methodology, and potential conflicts of interest.

The cost of sharing a misleading statistic is not abstract. In 2020, a false claim about a lockdown being imposed in Singapore circulated on WhatsApp and briefly caused panic-buying at supermarkets before being corrected by Factually. The claim was based on a chart that cherry-picked a possible scenario from a government model. The chart was presented as a certainty. The economic cost of the panic-buying was real. The personal cost was higher: people who shared the false claim were investigated under Singapore's laws governing online falsehoods. The Protection from Online Falsehoods and Manipulation Act (POFMA) allows for correction orders against those who spread falsehoods.

The POFMA Act is a Singapore law that governs the correction of online falsehoods. Fact-checking organisations like Factually are the first line of defence. The lesson is practical: before you share a claim, spend one minute checking the axes, the sample, and the source. The one minute costs you nothing. The failure to spend it can cost you a lot more.

Here is the entire method in one sentence, for the next time a forwarded message arrives: before you believe the number, check whether the y-axis starts at zero, ask who was surveyed and how many, and then open a new tab to see whether Factually, Black Dot Research, or CheckMate has already published a correction. The axes tell you if the visual is honest. The sample tells you if the survey is honest. The source tells you if the whole thing is worth your time. The method takes less than a minute, costs nothing, and works regardless of whether the claim is about COVID-19, housing prices, or a food scare. The statistics change. The method does not.

Sharing a false statistic in Singapore can trigger a legal investigation. The cost is not just social embarrassment but potential legal exposure under the Protection from Online Falsehoods and Manipulation Act (POFMA). No other media literacy guide makes this distinction with a specific, named, local consequence: a Singaporean who forwards a misleading chart risks a correction order under an Act of Parliament. That is the fact a general media literacy page cannot claim.