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A landmark 2015 report that cast doubt on the results of dozens of published psychology studies has exposed deep divisions in the field, serving as a reality check for many working researchers but as an affront to others who continue to insist the original research was sound. On Thursday, a group of four researchers publicly challenged the report, arguing that it was statistically flawed and, as a result, wrong.The 2015 report, called the Reproducibility Project, found that less than 40 studies in a sample of 100 psychology papers in leading journals held up when retested by an independent team. The new critique by the four researchers countered that when that team’s statistical methodology was adjusted, the rate was closer to 100 percent.

Graphs can be as manipulative as words. Using tricks such as cutting axes, rescaling things, changing data from positive to negative, etc. Sometimes putting zero on the y-axis is wrong. So to be sure that you are communicating the right things, you need to evaluate the message that people are taking away. There are no absolute rules. It all depends on what you want to communicate.

The bottom line is that humans are very bad at understanding probability. Everyone finds it difficult, even I do. We just have to get better at it. We need to learn to spot when we are being manipulated.

If we’re going to rely on science as a means for reaching the truth — and it’s still the best tool we have — it’s important that we understand and respect just how difficult it is to get a rigorous result

Scientists’ overreliance on p-values has led at least one journal to decide it has had enough of them. In February, Basic and Applied Social Psychology announced that it will no longer publish p-values.

P-hacking and similar types of manipulations often arise from human biases. “You can do it in unconscious ways — I’ve done it in unconscious ways,” Simonsohn said. “You really believe your hypothesis and you get the data and there’s ambiguity about how to analyze it.” When the first analysis you try doesn’t spit out the result you want, you keep trying until you find one that does.

Gerd Gigerenzer's test In 2006 and 2007 Gigerenzer gave a series of statistics workshops to gynaecologists, and kicked off every session with the same question: A 50-year-old woman, no symptoms, participates in routine mammography screening. She tests positive, is alarmed, and wants to know from you whether she has breast cancer for certain or what the chances are. Apart from the screening results, you know nothing else about this woman. How many women who test positive actually have breast cancer? What is the best answer? nine in 10 eight in 10 one in 10 one in 100 Gigerenzer then supplied the doctors with data about Western women of this age. (His figures were based on US studies from the 1990s, rounded up or down for simplicity - recent stats from Britain's National Health Service are slightly different.) The probability that a woman has breast cancer is 1% ("prevalence") If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity") If a woman does not have breast cancer, the probability that she nevertheless tests positive is 9% ("false alarm rate") In one session, almost half the gynaecologists said the woman's chance of having cancer was nine in 10. Only 21% said that the figure was one in 10 - which is the correct answer.

After the Charlie Hebdo attack, a Paris imam went to the scene and condemned the murders. "These victims are martyrs, and I shall pray for them with all my heart," said Hassen Chalghoumi (above). He was also quoted as saying that 95% of victims of terrorism are Muslim. How accurate is this statistic?

Are the 85 richest people in the world as wealthy as the world's poorest half? A number of listeners got in touch to ask about this fact, widely reported around the world, from the Washington Post to CNN. The figure comes from a report by British aid charity Oxfam. It got lots of attention, so the charity produced another figure for the UK, stating that the five richest families had more wealth than the poorest 20%. But how were these figures calculated?

In universities around the world, semesters end with students filling out similar surveys about their experience in the class and the quality of the teacher. Student ratings are high-stakes. They come up when faculty are being considered for tenure or promotions. In fact, they're often the only method a university uses to monitor the quality of teaching. Recently, a number of faculty members have been publishing research showing that the comment-card approach may not be the best way to measure the central function of higher education.

When people face an uncertain situation, they don’t carefully evaluate the information or look up relevant statistics. Instead, their decisions depend on a long list of mental shortcuts, which often lead them to make foolish decisions.

Perhaps our most dangerous bias is that we naturally assume that everyone else is more susceptible to thinking errors, a tendency known as the “bias blind spot.” This “meta-bias” is rooted in our ability to spot systematic mistakes in the decisions of others—we excel at noticing the flaws of friends—and inability to spot those same mistakes in ourselves.

Not even he believes that the various flaws that bedevil decision-making can be successfully corrected. The most damaging of these is overconfidence: the kind of optimism that leads governments to believe that wars are quickly winnable and capital projects will come in on budget despite statistics predicting exactly the opposite. It is the bias he says he would most like to eliminate if he had a magic wand. But it “is built so deeply into the structure of the mind that you couldn’t change it without changing many other things”.

In the right (or wrong) hands, bar graphs and pie charts can become powerful agents of deception, tricking you into inferring trends that don’t exist, mistaking less for more, and missing alarming facts. The best measure of a chart’s honesty is the amount of time it takes to interpret it, says Massachusetts Institute of Technology perceptual scientist Ruth Rosenholtz: “A bad chart requires more cognitive processes and more reasoning about what you’ve seen.”