are full of angles.
around the house
like vicious swans,
at piles of shoes
and tangled thoughts,
at the disarray.
in the night
like a swallow
with the burr
of a wing,
with a memory,
with the swoop
of a hip-bone,
with the slow,
of two cigarettes
thinning the gloom,
curing the darkness
You need to be very still
To hear the concert of your body
To think about what you contain
Salt and water
Know what it’s doing
Back to earth
It is a quiet thing
This is where our riches are
We are all red inside
Brimming with love
All fluid and quiet and fire.
Hume’s (1739) Treatise famously argued that we cannot infer an “ought” from an “is”. This has presented an enduring problem for science: how should we produce a set of recommendations for what should be done following the results of a study? If a new cancer treatment dramatically improves remission rates, should study authors simply shrug, present the results, and leave the recommendations to politicians? What if a treatment causes significant harms – can we recommend that the treatment be banned? Or suppose we have ideas for future studies that should be carried out and want to summarise them in the conclusions…? Even doing this would be ruled out by Hume.
The solution, if it is one, is that any recommendations require a set of premises stating our values. These values necessarily assert something beyond the evidence, for instance that if a treatment is effective then it should be provided by the health service. In practice, such values are often left implicit and assumed to be shared with readers. But there are interesting examples where it is apparently possible to draw an is-ought inference without assuming values.
One example, due to Mavrodes (1964), begins with the premise
If we ought to do A, then it is possible to do A.
This seems reasonable enough. It would, for instance, be horribly dystopian to require that people behave a particular way if it were impossible for them to do so. Games like chess and tennis have rules that are possible – if they were impossible then it would make playing the games challenging. Let’s see what happens if we apply a little logic to this premise.
Sentences of the form
If A, then B
are equivalent to those of the contrapositive form
If not-B, then not-A
This can be seen in the truth table below, where 1 denotes true and 0 denotes false. The values of the last two columns are equivalent:
|A||B||not-A||not-B||If A, then B||If not-B, then not-A|
Together, this means that if we accept the premise
If we ought to do A, then it is possible to do A,
and the rules of classical logic, we must also accept
If it is not possible to do A, then it is not the case that we ought to do A.
But here we have an antecedent that is an “is” and a consequent that is an “ought”: logic has licenced an is-ought!
Worry not: there has been debate in the literature… See Gillian Russell (2021) for a recent analysis.
Mavrodes, G. I. (1964). “Is” and “Ought.” Analysis, 25(2), 42–44.
Russell, G. (2021). How to Prove Hume’s Law. Journal of Philosophical Logic. In press.
Here’s an interesting paper (Greenland & Moore, 2021) that used our (Fugard & Potts, 2015) quantitative model for choosing a sample size for a thematic analysis. The authors also had a probability sample – very rare to see in published qualitative research.
Key ingredients: they had a sample frame (students who dropped out of open online university courses and their phone numbers); they wanted a comprehensive typology of reasons for drop out and suggestions for retaining students; and they could complete each interview within an average of 15 minutes (emphasis on average: some must have been longer).
Here are the authors’ conclusions:
“This study’s research design demonstrates the value of using a larger qualitative probability-based sample, in conjunction with in-depth interviewer probing and thematic analysis to investigate non-traditional student dropouts. While prior qualitative research has often used smaller samples (Creswell, 2007), recent studies have highlighted the need for more rigorous sample design to enable subthemes within themes, which is the key purpose of thematic analysis (eg, Nowell et al., 2017). This study’s sample moved beyond simple thematic saturation rationale, with consideration of the level of granularity required (Vasileiou et al., 2018). That is, 226 participants had a 99% probability of capturing all relevant dropout reason subthemes, down to a 5% incidence level or frequency of occurrence (Fugard & Potts, 2015). This study therefore presents a definitive typology of non-traditional student dropout in open online education.”
It’s exciting to see a rigorous and yet pragmatic qualitative study.
Fugard, A. J. B. & Potts, H. W. W. (2015). Supporting thinking on sample sizes for thematic analyses: A quantitative tool. International Journal of Social Research Methodology, 18, 669-684. (There’s an app for that.)
Greenland, S. J., & Moore, C. (2021). Large qualitative sample and thematic analysis to redefine student dropout and retention strategy in open online education. British Journal of Educational Technology.
This comes up a lot – here’s my take:
The distinction between sex and gender seems straightforward. Sex refers to biology, e.g., chromosomes and genitalia. Gender refers to psychosocial processes, e.g., roles and expression. However, they are more complex than this neat division. Like happiness and pain, gender is partly ontologically subjective. Gender identity is ‘deeply felt’ and ‘not necessarily visible to others’ (American Psychological Association, 2015, p. 862).
Sex has social facets. The classic sociological work Doing Gender by West and Zimmerman (1987, p. 127) illustrates how a sex category is assigned at birth:
Sex is a determination made through the application of socially agreed upon biological criteria for classifying persons as females or males. […] Placement in a sex category is achieved through application of the sex criteria, but in everyday life, categorization is established and sustained by the socially required identificatory displays that proclaim one’s membership in one or the other category. In this sense, one’s sex category presumes one’s sex and stands as proxy for it in many situations […].
This assigned sex category affects children’s social life in a variety of arbitrary ways, e.g., how they are dressed and expectations about behaviour, and feeds into the development of gender. For the majority of social contexts where sex category is applied, chromosomes and genitals are concealed and irrelevant.
Gender has biological facets: minds do gender identity and are embodied in the brain and nervous system, so even the phenomenology of gender identity has a biological correlate somewhere (Serano, 2013, pp. 138–168). There is emerging evidence that gender identity is a complex trait that is part-heritable and polygenic. A recent systematic review suggests that its heritability is likely in the range 30−60% (Polderman et al., 2018).
The interwoven biopsychosocial nature of sex and gender has led some scientists to use the combined concept sex/gender (e.g., Rippon et al., 2014). This does not mean that the multiplicity of facets blend into an amorphous blob. It does mean that it is important to clarify what particular facets are intended when discussing measurement and theory: chromosomes, genitalia, gender identity, socialisation, etc. The view of sex as only biological and gender as only psychosocial is too simplistic to progress theorising.
Fugard, A. (2020). Should trans people be postmodernist in the streets but positivist in the spreadsheets? A reply to Sullivan. International Journal of Social Research Methodology, 23, 525–531. [Preprint here]
“This Conceptual Framework for Public Mental Health is an interactive web-based tool that brings together evidence from academic research, reports, and practitioner and public consultations to map out the factors affecting mental health across all stages of a person’s life, including links to key evidence and lived experiences.”
If you’re using propensity score weighting (e.g., inverse probability weighting), one question that will arise is how big a sample you need.
Solutions have been proposed that rely on a variance inflation factor (VIF). You calculate the sample size for a simple design and then multiply that by the VIF to take account of weighting.
But the problem is that it is difficult to choose a VIF in advance.
Austin (2021) has developed a simple method (R code in the paper) to estimate VIFs from c-statistics (area under the curve; AOC) of the propensity score models. These c-statistics are often published.
A larger c-statistic means a greater separation between treatment and control, which in turn leads to a larger VIF and requirement for a larger sample.
Picture illustrating different c-statistics.
The magnitude of the VIF also depends on the estimand of interest, e.g., whether average treatment effect (ATE), average treatment effect on the treated (ATET/ATT), or average treatment effect where treat and control overlap (ATO).
Austin, P. C. (2021). Informing power and sample size calculations when using inverse probability of treatment weighting using the propensity score. Statistics in Medicine.
If we try to eliminate pay gaps by monitoring only single characteristics like gender or ethnicity, we can still end up with pay gaps between combinations of characteristics. One way to do this would be to appoint white women and Black men to senior management positions, but not appoint any Black women.
The idea of an intersection comes from set theory and describes where two sets overlap. For instance, the intersection of the set of Black people and the set of women is the set of Black women.
Intersectionality is a broad framework that promotes the study and elimination of oppression and exploitation of people in terms of combinations of characteristics.
Is intersectionality a theory, explaining why this form of discrimination occurs? Here’s Patricia Hill Collins (2019, p.51), a leading scholar in this area:
“Every time I encounter an article that identifies intersectionality as a social theory, I wonder what conception of social theory the author has in mind. I don’t assume that intersectionality is already a social theory. Instead, I think a case can be made that intersectionality is a social theory in the making.”
Collins, P. H. (2019). Intersectionality As Critical Social Theory. Duke University Press.