A level subject choices

Ofsted have recently published statistics relating to the subject choices of students starting A levels in England in 2013/2014. (For those unfamiliar with A levels, they are the qualifications taken between the ages of 16 and 18, students usually pick 3–4 subjects for the first year, which is known as AS, and normally slim down to 3 for the second year, A2; university admissions are based upon A level results). This is part of an effort to understand what drives students to pick different subjects and particularly science. Engaging students in science is a challenge, although many enjoy it or can achieve well in tests, then can struggle to see that it is for them. In Physics, we have a particular problem recruiting girls, which means we are not getting the best mix of people. I was interesting in having a look at the subject choices, so I’ve put together a few graphs.

Subject popularity

The most popular subjects at AS level are:

  1. English,
  2. Mathematics,
  3. Psychology.

English and Maths make sense, as they’ll be familiar from previous study and are of general applicability. I was surprised that Psychology came third, since it’ll be a new subject; the top ten consists of subjects familiar from pre-16 education, with the exception of the two social sciences, Psychology and Sociology (8). Physics comes in at number 7, behind both Biology (4) and Chemistry (6). This makes me sad, but at least Physics is still one of the most popular choices.

The distribution of student numbers is show in the graph below. I’ve not quite figured out what the distribution of student numbers should be, but it’s roughly exponential. There are too many subjects to label individually, so I’ve grouped them roughly by subject area. The main sciences (Biology, Chemistry and Physics) all do rather well, but modern languages are languishing towards the bottom of the list (top is French at 21). The smallest subjects have been grouped together into Other categories, these make up the bottom of the distribution, but in amongst them are Classical studies (29), German (30), and Accounting & finance (31).

Subjects ranking

Student numbers in the most popular subjects at AS level (in England 2013/2014). Data from A level subject take-up.

Gender differences

The report also lists the numbers of boys and girls taking each subject. I know that Physics is male-dominated, but I didn’t know how this compared to other subjects. To quantify the imbalance, I’m going to define the asymmetry as

\displaystyle \mathrm{Asymmetry} = \frac{\mathrm{No.\ of\ girls}\ -\ \mathrm{No.\ of\ boys}}{\mathrm{No.\ of\ students}}.

This is 0 if there are equal numbers of boys and girls, and is ±1 if completely made up of boys (−1) or girls (+1). Overall, more girls than boys are taking A levels, giving an total asymmetry of 0.0977. That’s not great, but we’ll see it’s smaller than is typically the case for individual subjects.

The most male-dominated subjects are:

  1. Computing (−0.8275),
  2. Physics (−0.5446),
  3. Further mathematics (−0.4569).

The most female-dominated subjects are:

  1. Sociology (0.5084),
  2. Art & design (0.4896),
  3. French (0.4531).

We see that Physics is in pretty poor shape, being the second most asymmetric subject overall. However, Computing is really out in a league of it’s own: there are almost 11 boys for every girl in the subject! That is not healthy. The most balanced subjects are:

  1. Geography (0.0056),
  2. Chemistry (−0.0167),
  3. Government & politics (−0.0761).

These are the only subjects with asymmetries smaller than the overall population of students. The gender balance in Chemistry shows that the Physical sciences don’t need to be male-dominated; however, this could equally reflect the compromise between male-dominated Physics and female-dominated Biology (0.2049).

The graph below plots the number of students taking a subject and its asymmetry. There’s no real trend with student numbers, it’s not the case that it’s easier for smaller subjects to become biased or that it’s easier for larger subjects to develop a reputation.

Asymmetry and number of students

Scatter plot of the number of students and gender asymmetry of AS subjects (in England 2013/2014). Higher points are more female dominated and lower points are more male dominated. The dashed line indicates gender parity and the dotted line indicates the average for all subjects. Data from A level subject take-up.

Normally, I’d expect there to be scatter in a quantity like asymmetry: some values high, some low, but more clustering in the middle than out in the extremes. Looking at the plot above, this doesn’t seem to be the case. There are relatively few subjects in the middle, but there seem to be two clusters, one at small positive asymmetries and another at small negative asymmetries. I’ve plotted the distribution of subject asymmetries below. To make it clearer to view (and to make a nice smooth, continuous distribution), I’ve smeared out the individual subjects. These means I’m actually plotting the density of subjects per unit of asymmetry, rather than the number of subjects: if you work out the area under the curve, that gives the number of subjects in that range. (For those who care, I’ve convolved with a Gaussian kernel with a standard deviation of 0.1, and made sure to renormalise them so that the total area is correct).

Asymmetry distribution.

Smoothed distribution of gender asymmetry for AS subjects (in England 2013/2014). Left is male dominated and right is female dominated. The area under the curve gives the number of subjects. The diamonds mark the locations of individual subjects. Data from A level subject take-up.

It does appear that there are two peaks: one for boys’ subjects and another for girls’. Computing is off being a clear outlier. However, if I turn up the smoothing (using a standard deviation of 0.3), this disappears. This always happens if you smooth too much…

Asymmetry distribution.

Heavily smoothed distribution of gender asymmetry for AS subjects (in England 2013/2014). Left is male dominated and right is female dominated. The area under the curve gives the number of subjects. The diamonds mark the locations of individual subjects. Data from A level subject take-up.

It looks like this is one of the cases where I should really do things properly and I should come back to look at this again later.

Regardless of whether my suspicion of there being two clusters of subjects is correct, there does appear to be a spectrum of subjects, with some being as perceived as for boys and others for girls. This differentiation exists already exists at age 16—even for subjects like Psychology and Sociology that have not been studied previously. It seems that these stereotypes are ingrained from an earlier age.

Computing and Psychology role models

Ada, Countess of Lovelace, mathematician and first computer programmer (and superheroine), and Sigmund Freud, neurologist and founder of psychoanalysis. Evidence that there really shouldn’t be divides in Computing, Psychology or any other subject.

Continuation

As well as looking at how many students take AS, we can look at how many continue to A2. The report gives the percentage that continue for both boys and girls. The distribution of all continuation percentages is shown below, again with subjects grouped by area. The average progression across all subjects is 72.7%.

Continuation ranking

Percentage continuation from AS to A2 for different subjects (in England 2013/2014). The dotted line indicates the average. Data from A level subject take-up.

The top subjects for continuation to A2 are:

  1. Other modern languages (90.4%),
  2. Drama (82.7%),
  3. Media/film/TV studies (81.4%).

Other modern languages is the smallest subject in terms of student numbers, but has the highest continuation: I guess those who opt for it are dedicated to seeing it through. However, there doesn’t seem to be a correlation between student numbers and continuation. English, the most popular subject, comes in just below Media/film/TV studies with 81.2%. The bottom subjects for continuation are:

  1. Other social sciences (45.9%),
  2. Accounting & finance (59.7%),
  3. Computing (61.4%).

I don’t know enough about these subjects to know if there might be a particular reason why just taking them for one year might be useful. In contrast to Other modern languages, German (62.7%), French (64.1%) and Spanish (65.8%) have some of the lowest continuation rates (coming in just above Computing). Physics also does poorly, with only 67.8% continuing, below both Chemistry (71.0%) and Biology (72.2%). For comparison, Further mathematics has 68.3% continuation and Mathematics has 75.4%. I would expect continuation to be lower for subjects that students find more difficult (possibly with the biggest jump from GCSE).

Now, let’s have a look at the difference in progression between the genders. In the figure below, I plot the difference in the percentage progression between boys and girls,

\mathrm{Difference} = \mathrm{Percent\ girls\ continuing}\ -\ \mathrm{Percent\ boys\ continuing},

versus the asymmetry. The two quantities show a clear correlation: more girls than boys progress in subjects that are female dominated and vice versa. Gender asymmetry gets worse with progression.

Asymmetry and progression

Scatter plot of the gender asymmetry and difference in percentage progression of AS subjects (in England 2013/2014). Left is male dominated and right is female dominated. Higher points have a higher proportion of girls than boys continuing and lower points have a higher proportion of boys than girls continuing. Data from A level subject take-up.

The subjects with the largest differences in continuation are:

  1. Physics (−14%),
  2. Other science (−12%),
  3. Psychology (11%).

That’s a really poor show for Physics. This polarising trend is not surprising. People like to be where they feel they belong. If you’re conspicuously outnumbered, you’re more likely to feel uncomfortable. Data show that girls are more likely to continue with Physics in all-girls schools. Also, as we’ve seen, there seems to be a clustering of boys’ subjects and girls’ subjects, and developing these reputations can make it difficult for people to go against stereotypes. This impacts both how people view themselves and others, potentially impacting perceived competence (e.g., for Physics, Gonslaves 2014a, 2014b). These cultural biases are something we need to work against if we’re going the get the best mix of students (I guess it’s good we have all these Psychologists and Sociologists to help figure this out).

I’d recommend trying the excellent (and adorable) Parable of the Polygons to see how biases can become magnified.

Summary

At A level, some subjects are favoured by boys or by girls. This imbalance gets larger during the transition from AS to A2. Physics is one of the most popular subjects at AS level, but lags behind the other main sciences. It has a poor gender ratio, which notably gets worse going from AS to A2. Physics is (arguably) the the most awesome subject, so we should do more to show that is for everyone. If you’d like to play around the data (and don’t fancy typing it out yourself), I have it available via Google Drive.

(For disclosure: I took Geography at AS, and Physics, Maths and Further maths at A2).

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Parameter estimation for binary neutron-star coalescences with realistic noise during the Advanced LIGO era

The first observing run (O1) of Advanced LIGO is nearly here, and with it the prospect of the first direct detection of gravitational waves. That’s all wonderful and exciting (far more exciting than a custard cream or even a chocolate digestive), but there’s a lot to be done to get everything ready. Aside from remembering to vacuum the interferometer tubes and polish the mirrors, we need to see how the data analysis will work out. After all, having put so much effort into the detector, it would be shame if we couldn’t do any science with it!

Parameter estimation

Since joining the University of Birmingham team, I’ve been busy working on trying to figure out how well we can measure things using gravitational waves. I’ve been looking at binary neutron star systems. We expect binary neutron star mergers to be the main source of signals for Advanced LIGO. We’d like to estimate how massive the neutron stars are, how fast they’re spinning, how far away they are, and where in the sky they are. Just published is my first paper on how well we should be able to measure things. This took a lot of hard work from a lot of people, so I’m pleased it’s all done. I think I’ve earnt a celebratory biscuit. Or two.

When we see something that looks like it could be a gravitational wave, we run code to analyse the data and try to work out the properties of the signal. Working out some properties is a bit trickier than others. Sadly, we don’t have an infinite number of computers, so it means it can take a while to get results. Much longer than the time to eat a packet of Jaffa Cakes…

The fastest algorithm we have for binary neutron stars is BAYESTAR. This takes the same time as maybe eating one chocolate finger. Perhaps two, if you’re not worried about the possibility of choking. BAYESTAR is fast as it only estimates where the source is coming from. It doesn’t try to calculate a gravitational-wave signal and match it to the detector measurements, instead it just looks at numbers produced by the detection pipeline—the code that monitors the detectors and automatically flags whenever something interesting appears. As far as I can tell, you give BAYESTAR this information and a fresh cup of really hot tea, and it uses Bayes’ theorem to work out how likely it is that the signal came from each patch of the sky.

To work out further details, we need to know what a gravitational-wave signal looks like and then match this to the data. This is done using a different algorithm, which I’ll refer to as LALInference. (As names go, this isn’t as cool as SKYNET). This explores parameter space (hopping between different masses, distances, orientations, etc.), calculating waveforms and then working out how well they match the data, or rather how likely it is that we’d get just the right noise in the detector to make the waveform fit what we observed. We then use another liberal helping of Bayes’ theorem to work out how probable those particular parameter values are.

It’s rather difficult to work out the waveforms, but some our easier than others. One of the things that makes things trickier is adding in the spins of the neutron stars. If you made a batch of biscuits at the same time you started a LALInference run, they’d still be good by the time a non-spinning run finished. With a spinning run, the biscuits might not be quite so appetising—I generally prefer more chocolate than penicillin on my biscuits. We’re working on speeding things up (if only to prevent increased antibiotic resistance).

In this paper, we were interested in what you could work out quickly, while there’s still chance to catch any explosion that might accompany the merging of the neutron stars. We think that short gamma-ray bursts and kilonovae might be caused when neutron stars merge and collapse down to a black hole. (I find it mildly worrying that we don’t know what causes these massive explosions). To follow-up on a gravitational-wave detection, you need to be able to tell telescopes where to point to see something and manage this while there’s still something that’s worth seeing. This means that using spinning waveforms in LALInference is right out, we just use BAYESTAR and the non-spinning LALInference analysis.

What we did

To figure out what we could learn from binary neutron stars, we generated a large catalogue of fakes signals, and then ran the detection and parameter-estimation codes on this to see how they worked. This has been done before in The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo which has a rather delicious astrobites write-up. Our paper is the sequel to this (and features most of the same cast). One of the differences is that The First Two Years assumed that the detectors were perfectly behaved and had lovely Gaussian noise. In this paper, we added in some glitches. We took some real data™ from initial LIGO’s sixth science run and stretched this so that it matches the sensitivity Advanced LIGO is expected to have in O1. This process is called recolouring [bonus note]. We now have fake signals hidden inside noise with realistic imperfections, and can treat it exactly as we would real data. We ran it through the detection pipeline, and anything which was flagged as probably being a signal (we used a false alarm rate of once per century), was analysed with the parameter-estimation codes. We looked at how well we could measure the sky location and distance of the source, and the masses of the neutron stars. It’s all good practice for O1, when we’ll be running this analysis on any detections.

What we found

  1. The flavour of noise (recoloured or Gaussian) makes no difference to how well we can measure things on average.
  2. Sky-localization in O1 isn’t great, typically hundreds of square degrees (the median 90% credible region is 632 deg2), for comparison, the Moon is about a fifth of a square degree. This’ll make things interesting for the people with telescopes.

    Sky localization map for O1.

    Probability that of a gravitational-wave signal coming from different points on the sky. The darker the red, the higher the probability. The star indicates the true location. This is one of the worst localized events from our study for O1. You can find more maps in the data release (including 3D versions), this is Figure 6 of Berry et al. (2015).

  3. BAYESTAR does just as well as LALInference, despite being about 2000 times faster.

    Sky localization for binary neutron stars during O1.

    Sky localization (the size of the patch of the sky that we’re 90% sure contains the source location) varies with the signal-to-noise ratio (how loud the signal is). The approximate best fit is \log_{10}(\mathrm{CR}_{0.9}/\mathrm{deg^2}) \approx -2 \log_{10}(\varrho) +5.06, where \mathrm{CR}_{0.9} is the 90% sky area and \varrho is the signal-to-noise ratio. The results for BAYESTAR and LALInference agree, as do the results with Gaussian and recoloured noise. This is Figure 9 of Berry et al. (2015).

  4. We can’t measure the distance too well: the median 90% credible interval divided by the true distance (which gives something like twice the fractional error) is 0.85.
  5. Because we don’t include the spins of the neutron stars, we introduce some error into our mass measurements. The chirp mass, a combination of the individual masses that we’re most sensitive to [bonus note], is still reliably measured (the median offset is 0.0026 of the mass of the Sun, which is tiny), but we’ll have to wait for the full spinning analysis for individual masses.

    Mean offset in chirp-mass estimates when not including the effects of spin.

    Fraction of events with difference between the mean estimated and true chirp mass smaller than a given value. There is an error because we are not including the effects of spin, but this is small. Again, the type of noise makes little difference. This is Figure 15 of Berry et al. (2015).

There’s still some work to be done before O1, as we need to finish up the analysis with waveforms that include spin. In the mean time, our results are all available online for anyone to play with.

arXiv: 1411.6934 [astro-ph.HE]
Journal: Astrophysical Journal; 904(2):114(24); 2015
Data release: The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo
Favourite colour: Blue. No, yellow…

Notes

The colour of noise: Noise is called white if it doesn’t have any frequency dependence. We made ours by taking some noise with initial LIGO’s frequency dependence (coloured noise), removing the frequency dependence (making it white), and then adding in the frequency dependence of Advanced LIGO (recolouring it).

The chirp mass: Gravitational waves from a binary system depend upon the masses of the components, we’ll call these m_1 and m_2. The chirp mass is a combination these that we can measure really well, as it determines the most significant parts of the shape of the gravitational wave. It’s given by

\displaystyle \mathcal{M} = \frac{m_1^{3/5} m_2^{3/5}}{(m_1 + m_2)^{1/5}}.

We get lots of good information on the chirp mass, unfortunately, this isn’t too useful for turning back into the individual masses. For that we next extra information, for example the mass ratio m_2/m_1. We can get this from less dominant parts of the waveform, but it’s not typically measured as precisely as the chirp mass, so we’re often left with big uncertainties.

BritGrav 15

April was a busy month. Amongst other adventures, I organised the 15th British Gravity (BritGrav) Meeting. This is a conference for everyone involved with research connected to gravitation. I was involved in organising last year’s meeting in Cambridge, and since there were very few fatalities, it was decided that I could be trusted to organise it again. Overall, I think it actually went rather well.

Before I go on to review the details of the meeting, I must thank everyone who helped put things together. Huge thanks to my organisational team who helped with every aspect of the organisation. They did wonderfully, even if Hannah seems to have developed a slight sign-making addiction. Thanks go to Classical & Quantum Gravity and the IOP Gravitational Physics Group for sponsoring the event, and to the College of  Engineering & Physical Sciences’ marketing team for advertising. Finally, thanks to everyone who came along!

Talks

BritGrav is a broad meeting. It turns out there’s rather a lot of research connected to gravity! This has both good and bad aspects. On the plus side, you can make connections with people you wouldn’t normally run across and find out about new areas you wouldn’t hear about at a specialist meeting. On the negative side, there can some talks which go straight-over your head (no matter how fast your reaction are). The 10-minute talk format helps a little here. There’s not enough time to delve into details (which only specialists would appreciate) so speakers should stick to giving an overview that is generally accessible. Even in the event that you do get completely lost, it’s only a few minutes until the next talk, so it’s not too painful. The 10-minute time slot also helps us to fit in a large number of talks, to cover all the relevant areas of research.

Open quantum gravitational systems

Slide from Teodora Oniga’s BritGrav 15 talk on gauge invariant quantum gravitational decoherence. There are not enough cats featured in slides on gravitational physics.

I’ve collected together tweets and links from the science talks: it was a busy two days! We started with Chris Collins talking about testing the inverse-square law here at Birmingham. There were a couple more experimental talks leading into a session on gravitational waves, which I enjoyed particularly. I spoke on a soon-to-be published paper, and Birmingham PhDs Hannah Middleton and Simon Stevenson gave interesting talks on what we could learn about black holes from gravitational waves.

Detecting neutron star–black hole binaries

Slides demonstrating the difficulty of detecting gravitational-wave signals from Alex Nielsen’s talk on searching for neutron star–black hole binaries with gravitational waves. Fortunately we don’t do it by eye (although if you flick between the slides you can notice the difference).

In the afternoon, there were some talks on cosmology (including a nice talk from Maggie Lieu on hierarchical modelling) and on the structure of neutron stars. I was especially pleased to see a talk by Alice Harpole, as she had been one of my students at Cambridge (she was always rather good). The day concluded with some numerical relativity and the latest work generating gravitational-waveform templates (more on that later).

The second day was more theoretical, and somewhat more difficult for me. We had talks on modified gravity and on quantum theories. We had talks on the properties of various spacetimes. Brien Nolan told us that everyone should have a favourite spacetime before going into the details of his: McVittie. That’s not the spacetime around a biscuit, sadly, but could describe a black hole in an expanding Universe, which is almost as cool.

The final talks of the day were from the winners of the Gravitational Physics Group’s Thesis Prize. Anna Heffernan (2014 winner) spoke on the self-force problem. This is important for extreme-mass-ratio systems, such as those we’ll hopefully detect with eLISA. Patricia Schmidt (2105 winner) spoke on including precession in binary black hole waveforms. In general, the spins of black holes won’t be aligned with their orbital angular momentum, causing them to precess. The precession modulates the gravitational waveform, so you need to include this when analysing signals (especially if you want to measure the black holes’ spins). Both talks were excellent and showed how much work had gone into the respective theses.

The meeting closed with the awarding of the best student-talk prize, kindly sponsored by Classical & Quantum Gravity. Runners up were Viraj Sanghai and Umberto Lupo. The winner was Christopher Moore from Cambridge. Chris gave a great talk on how to include uncertainty about your gravitational waveform (which is important if you don’t have all the physics, like precession, accurately included) into your parameter estimation: if your waveform is wrong, you’ll get the wrong answer. We’re currently working on building waveform uncertainty into our parameter-estimation code. Chris showed how you can think about this theoretical uncertainty as another source of noise (in a certain limit).

There was one final talk of the day: Jim Hough gave a public lecture on gravitational-wave detection. I especially enjoyed Jim’s explanation that we need to study gravitational waves to be prepared for the 24th century, and hearing how Joe Weber almost got into a fist fight arguing about his detectors (hopefully we’ll avoid that with LIGO). I hope this talk enthused our audience for the first observations of Advanced LIGO later this year: there were many good questions from the audience and there was considerable interest in our table-top Michelson interferometer afterwards. We had 114 people in the audience (one of the better turn outs for recent outreach activities), which I was delighted with.

Attendance

We had a fair amount of interest in the meeting. We totalled 81 (registered) participants at the meeting: a few more registered but didn’t make it in the end for various reasons and I suspect a couple of Birmingham people sneaked in without registering.

Looking at the attendance in more detail, we can break down the participants by their career-level. One of the aims of BritGrav is to showcase to research of early-career researchers (PhD students and post-docs), so we ask for this information on the registration form. The proportions are shown in the pie-chart below.

Attendance at BritGrav 15 by career level

Proportion of participants at BritGrav 15 by (self-reported) career level.

PhD students make up the largest chunk; there are a few keen individuals who are yet to start a PhD, and a roughly even split between post-docs and permanent staff. We do need to encourage more senior researchers to come along, even if they are not giving talks, so that they can see the research done by others.

We had a total of 50 talks across the two days (including the two thesis-prize talks); the distribution of talks by career level as shown below.

Talks at BritGrav 15 by career level

Proportion of talks at BritGrav 15 by (self-reported) career level. The majority are by PhD students.

PhDs make up an even larger proportion of talks here, and we see that there are many more talks from post-docs than permanent staff members. This is exactly what we’re aiming for! For comparison, at the first BritGrav Meeting only 26% of talks were by PhD students, and 17% of talks were by post-docs. There’s been a radical change in the distribution of talks, shifting from senior to junior, although the contribution by post-docs ends up about the same.

We can also consider at the proportion of participants from different institutions, which is shown below.

Attendance at BritGrav 15 by institution

Proportion of participants at BritGrav 15 by institution. Birmingham, as host, comes out top.

Here, any UK/Ireland institution which has one or no speakers is lumped together under “Other”, all these institutions had fewer than four participants. It’s good to see that we are attracting some international participants: of those from non-UK/Ireland institutions, two are from the USA and the rest are from Europe (France, Germany, The Netherlands and Slovenia). Birmingham makes up the largest chunk, which probably reflects the convenience. The list of top institutions closely resembles the list of institutions that have hosted a BritGrav. This could show that these are THE places for gravitational research in the UK, or possibly that the best advertising for future BritGravs is having been at an institution in the past (so everyone knows how awesome they are). The distribution of talks by institution roughly traces the number of participants, as shown below.

Talks at BritGrav 15 by institution

Proportion of talks at BritGrav 15 by institution.

Again Birmingham comes top, followed by Queen Mary and Southampton. Both of the thesis-prize talks were from people currently outside the UK/Ireland, even though they studied for their PhDs locally. I think we had a good mix of participants, which is one of factors that contributed to the meeting being successful.

I’m pleased with how well everything went at BritGrav 15, and now I’m looking forward to BritGrav 16, which I will not be organising.