Erik Gahner Larsen

Potpourri: Statistics #52

How to improve your figures #1: Don’t use the y-axis to mislead

There are good reasons to think carefully about the y-axis when you design figures, including considerations on whether to start your y-axis at zero or not. In this post, I provide a simple piece of advice: when presenting bar charts on a linear scale, start at 0. Not 0.38. Not 0.31. Not 0.04. 0.

The figure below, from Hanel et al. (2018), depicts the same data in three panels. It shows how the same data can be presented in different ways with implications for how we perceive differences between groups.

In the first panel, we see the distributions of the two groups. In the second panel, we see that the y-axis starts at 4.6. In that figure, it looks like the value for Poland (the red bar) is three times greater than the value for the UK (the blue bar). In the third panel, relative to the second panel, we see a much better presentation of the two groups with a y-axis starting at zero.

Despite the fact that bar charts with arbitrary and non-zero starting y-axes are problematic, I see it again and again in scientific publications. Take for example this new article in the American Political Science Review, where the bar charts use the y-axis to mislead. Specifically, they leave the impression of a greater difference between the two groups than is supported by the data:

For another example, take this new article in Political Communication where the bar chart conveniently starts at 4.00% to give the impression of a large difference between the groups. (On a sidenote, I can’t believe how unlucky the authors were. The only statistical finding in the article is the finding that wasn’t preregistered.)

Alas, journals and books are filled with examples of bar charts that use the y-axis to mislead. The general issue is that these figures do not comply to the principle of proportional ink: “The sizes of shaded areas in a visualization need to be proportional to the data values they represent.”

This is not to say that y-axes should always start at zero. On the contrary, there are many cases where figures should definitely not start at zero (see this article from Quartz and this video from Vox for more information). However, when creating a bar plot, the best way to improve your figure is to comply to the principle of proportional ink. Start at 0.

Do men face more discrimination?

An article in the Daily Mail presents the argument that men face more discrimination than women. Similarly, RT writes: “Contrary to everything you’ve ever been told, in most developed countries men are actually more disadvantaged than women, according to new research published in one of the world’s leading scientific journals.” And Yahoo Finance writes “that men actually face more discrimination than women”. The story also made it all the way to Fox News.

The coverage builds upon a new article published in PLOS ONE, “A simplified approach to measuring national gender inequality“. The article begins with a critique of existing indices and especially the popular The Global Gender Gap Index (GGGI, an index I also criticised in a post last year). The authors of the article focus in particular on one aspect of the GGGI, namely that no country (by definition) can be more favourable towards women than to men. As they formulate their critique: “there is no defensible rationale for truncating scores on an ‘equality’ measure when they disadvantage boys or men.”

Based on this, they develop a measure of national gender inequality tapping into three specific dimensions: 1) educational opportunities, 2) life expectancy and 3) life satisfaction. They call this the BIGI, the Basic Index of Gender Inequality. The objective of the index is to pay attention to measures where women perform as well as or better than men. It is, for example, a well-known fact that women tend to live longer than men.

In Figure 1 in the article, the authors present deviation from gender parity across the 134 countries in the sample (missing data is illustrated with a black colour):

What can we learn from this analysis? Here is the main finding of the article that is getting the most attention in the media coverage: “In 91 (68%) of the 131 countries, men were on average more disadvantaged than women, and in the other 43 (32%) countries, women were more disadvantaged than men. The international median of the BIGI is -0.017 (SD = 0.062), that is, nearly a two percent deviation from parity, favoring women.”

While I believe it is great to put emphasis on dimensions where men face problems to a greater extent than women, I do believe there are noteworthy limitations in the study that are lost in the coverage. These limitations are significant and when taken into account, there is no support for the conclusion that men are discriminated more than women.

First and most importantly, the selling point of the study – i.e. the simplified approach – is also the main limitation. The study focuses on a limited set of indicators, selected in favour of men (in other words, to show numbers where women are doing better than men in a lot of countries), that are not necessarily providing a representative picture of gender inequality in a comparative perspective. Accordingly, it is misleading to draw conclusions about whether men in general are more disadvantaged than women.

Second, and related, the study argues that the approach “avoids the difficulties of choosing and weighing indices that are relevant in some contexts but not others, and often may reflect life choices rather than restricted opportunities”. I would argue that simply getting rid of most indicators is not a suitable solution to the challenge of finding relevant indices. As an example, the authors mention that “the ratio of male to female national politicians is only relevant to the tiny proportion of people who choose a political career”. This is incorrect as several studies demonstrate the implications and relevance of having female politicians beyond the career trajectories of the respective politicians (e.g. Anzia and Berry 2011, Clayton et al. 2019, Gilardi 2015, Ladam et al. 2018, and Mendelberg et al. 2013).

Third, I would not make conclusions about the state of gender (in)equality in different countries based on the BIGI. Saudi Arabia, for example, is one of the countries with a relatively high level of overall average gender parity. Granted, I do not know a lot about gender equality and discrimination in Saudi Arabia, but I am reluctant about calling the country a national gender equality pioneer. While the authors provide some post hoc reflections on why Saudi Arabia takes up such a good place, I see no convincing case for taking these scores serious.

Fourth, even if we want to compare countries, we are unable to say whether there are any statistically significant differences between the countries. It can be difficult to compare the scores on the index in substantial terms, and we are unable to say whether any country is actually significantly more equal than any other country.

Fifth, and related, one of the measures used to create the index is the overall life satisfaction data from the Gallup World Poll. However, they do not take any measurement error or uncertainty into account in any of the estimates. Accordingly, while they argue that the life satisfaction score is culturally independent, I do believe additional work is needed before the index scores are useful for what the researchers use it for. Furthermore, the use of survey data significantly limits the data availability and quality. In brief, I am not convinced that the life satisfaction data is of an equal quality and equally representative in the 134 surveyed countries, and we are limited in the spatial and temporal coverage of the index.

Sixth, in connection to the media coverage described above, the study says nothing about discrimination at all. Even if we do not take any of the limitations outlined so far into account, we cannot say anything about actual discrimination. In other words, the news coverage of the study is extremely misleading.

Overall, while I appreciate the objective of providing a better measure of gender inequality in a comparative setting, I do believe that the limitations outlined above render the index useless for actual policy recommendations. As I told the Danish newspaper Weekendavisen the other day, it is important to look at gender inequalities across different countries, but I cannot see the usefulness of this particular index in its current form.

Nyt bogkapitel: Analyse af adfærd via eksperimenter

Har sammen med Pelle Guldborg Hansen skrevet et kapitel om analyse af adfærd via eksperimenter til bogen ‘Metodekogebogen – 129 analysemetoder fra humaniora og samfundsvidenskab’, redigeret af Mie Femø Nielsen og Svend Skriver.

Bogen er, som titlen antyder, en samling af 129 opslag om metoder med relevans for humaniora og samfundsvidenskab. En beskrivelse af bogen fra infomaterialet:

Du får i klar tekst at vide, hvad du skal gøre trin for trin. Hvor begynder du? Hvad skal du være opmærksom på undervejs? Hvilken type resultater kan en konkret metode give dig, og cirka hvor meget tid skal du bruge?

Bogen giver dig inspiration til at forsøge dig med andre metoder, så du kan lave analyser og opnå overraskende indsigter. Det bliver nemmere at udføre ambitiøse, veltilrettelagte og spændende undersøgelser. Resultatet er ny viden både til dig og det omkringliggende samfund.

Den kan købes her, her, her og her.

Det skrantende køn i Weekendavisen

Jeg udtalte mig i Weekendavisen omkring en ny undersøgelse af ligestilling mellem mænd og kvinder i et komparativt perspektiv. Jeg citeres blandt andet for følgende:

»Selvfølgelig er det relevant at se på forskelle mellem kønnene i Danmark, når det gælder sundhed, uddannelse og livstilfredshed, men det bliver fuldstændig meningsløst, når man antyder, at vi skal kigge på Bahrain for at gøre tingene bedre,«

Artiklen kan læses på print og online.