Are women Nobel Prize winners younger than men on average?
By: Tiantian Yuan
Tags: Blogging, Data Visualization, Data Science, Critical Thinking, Statistics

The positive correlation between the age and year is present for most fields except ‘Peace’, which has a negative correlation. If we exclude the ‘Peace’ category, Figure 1 would look like this (Figure 4). The difference between the Male and Female groups is now less pronounced. We can treat the Peace category separately (Table 1 below).

Figure 4: Similar to Figure 1, but excluding recipients from the Peace category. The male and female groups have now a very similar linear regression relation.

Statistical tests:

Pearson test for the correlation. To quantify the statistical significance of the age vs. award year correlation for each category, we can use Pearson tests. The Pearson coefficient r ranges from -1 to 1 and is sensitive to outliers. A perfect positive (negative) correlation will have r = 1 (-1), and 0 means no correlation. The p value indicates the statistical significance of the null hypothesis that there is no linear correlation between the age and year. The smaller the p, the more significant the correlation.

Table 1: Pearson tests for the correlation between the age and year. The correlation coefficient (r) and significance level (p) are calculated for different samples and categories (Figure 1, 3, 4).

The Pearson tests confirms what we have already seen in Figure 1, 3 and 4 statistically: that the correlation between the age and year is significant, and the Peace category has a negative correlation. When dividing the Peace recipients into Male and Female groups, the statistical significance of the linear relation becomes too weak to draw confident conclusions (based on the p-value).

A few words about the p-value. The p value is widely used in statistics. It is a popular index in evaluating machine learning models too. It is easy to calculate, but does not say much about the real uncertainties of parameters (that is where the more computationally expensive Bayesian statistics shine). The debates about the use of p value in hypothesis testing are never ending. I find it super useful to have some intuitions about p so that you can stand your own ground in those debates.

Here are my intuitions. p stands for probability. A p value of 0.07–0.12 is akin to a probability of getting the same side of a coin 3–4 times in a row in the coin-tossing game; it is uncommon but possible in the statistical fluctuations of our Universe. A p value of 0.01–0.03 is like landing the same side of a coin 6–7 times in a row, which is bizarre and begs for an investigation. This is why many people choose a p value of less than 0.02 or even 0.005 as a threshold to claim a signal or reject a null hypothesis. Of course, if you are looking for those extremely rare events in the Universe, as rare as throwing a coin 20 times and get the same side 20 times, then, feel free to set an extremely low p value (0.000001) to claim your signal. The ‘flexibility’ in threshold of p is where most debates about p values come from. But the little p is a powerful number when it is used in the right context. I recommend this recent paper and podcast for good insights about p.

Kolmogorov–Smirnov (KS) test for the age distribution difference. The effort so far is to establish the correlation between the age and year, so that we can answer our question most intelligently. However, if we want the simplest answer, and ignore the dependence of age on the year, then it is only a one-step analysis.

We can use the p-value of the KS test to evaluate the statistical significance of the null hypothesis that two age distributions are from the same parent sample. When p drops to a very low (<0.005) number, we reject the null hypothesis.

So the simple answer we seek is in Figure 5, where the age distribution of the male and female recipients are shown. The KS test yields p=0.3655, meaning no difference in the two distributions. Using the coin tossing analogy again, a p=0.36 is as random as throwing a coin 2 times and getting the same side 1 or 2 times. So, we can not reject the hypothesis that the age distribution (including the mean and the spread) of the male and female groups is the same. If the title of this article is more precisely phrased as ‘Are women recipients younger than men for the sample of all Nobel winners in the past 120 years?’. Then the answer is no.

Figure 5: The age probability density function of the Female and Male recipients of all categories from 1901 to 2020. A Kernel density estimation (KDE) is used to smooth the age data with a Gaussian kernel, producing a continuous density estimate of the underlying age distributions.

But wait. Didn’t the commenter in the story used data from ‘recent years’ as evidence? Maybe the age distributions have changed in recent years? We can loop over the years and plot the KS p-value as a function of the starting year of our sample (Figure 6). Indeed, the male and female age distributions start to differ significantly after the year 1990.

Figure 6: Left: KS test’s p value as a function of different starting year used in composing the age sample. The decreasing p implies that the difference between the male and female age groups is getting larger with time. Right: The age probability distribution function for the subsample of years 1990–2020. The year 1990 is chosen as it is the first year after which the p value drops to lower than 0.005 (left). The vertical dash lines show the mean age of two distributions.

So if the comment was that “women seem to win Nobel Prizes at relatively younger ages than men in recent years”, then it is supported by this statistical analysis. And the recent years count from 1990. Owing to the small numbers of women recipients, we do not divide the years further into more subsamples.

There is one last piece to figure out. The mean age of the female group (58) is smaller than that of the male group (66) (Figure 6). How significant is this mean? The p-value evaluates the distribution function as a whole; it does not yield a specific probability for the mean. This problem can be phrased as what are the odds of a randomly selected woman being younger than a randomly selected man from the 1990–2020 recipient pool. We can get this number by randomly selecting the recipients from the distributions in Figure 6 tens of thousands of times, and count the number of times that a woman is younger (algorithms can be found in the GitHub code). As I am bored of my own writing, I think I should just show the numbers in Table 2.

Table 2: The odds (2nd row) that a randomly selected woman recipient from the specific sample pool (top rows) is younger than a randomly selected man. Here STEM means Physics, Chemistry, Medicine, and Economics combined. The STEM categories suffer the most from small number statistics and can only be combined for analysis.

Conclusions:

The answer to the title of this article is no. But if we add an extra condition to the question, “Are women Nobel Prize winners younger than men on average in recent years?” Then the answer is yes (I didn’t see this coming), and the odds of that yes are summarised in Table 2.

Personally, I am not sure how much value there is in asking this question or writing this article. Two valuable things that I get from this analysis: 1) I should not reject a claim based on how hand-wavy it is, 2) The only useful statistics in the Physics category is that I cannot do statistics with 4 women (3 individuals as Marie Curie won twice) vs 206 men. Science knows no gender. We have such a long way to go.

Thanks for reading, and feel free to comment and cross-validate!