Men have more perceived power in the public domain, however, this domain has a lower preference weighting than the private domain where women have more power than men.

From Weighting power by preference eliminates gender differences by Sverker Sikström, Laura Mai Stoinski, Kristina Karlsson, Lotta Stille, and Johan Willander  From the Abstract:

Power can be applied in different domains (e.g., politics, work, romantic relationships, family etc.), however, we do not always reflect on which domains we have power in and how important power in these domains is. A dominant idea is that men have more power than women. This notion may be biased because the concept of power is associated with public life. We introduce the concept of preference-weighted power (PWP), a measure of power that includes different domains in life, weighted by the domains’ subjective importance. Two studies investigated power from this perspective. In Study 1, participants generated words related to power, which were quantified/categorized by latent semantic analysis to develop a semantic measure of the power construct. In Study 2, we computed a PWP index by weighting the participants' self-rated power in different power domains with the importance of having power in that domain. Together the studies suggest that men have more perceived power in the public domain, however, this domain has a lower preference weighting than the private domain where women have more power than men. Finally, when preferences for power in different domains were considered, no gender differences were observed. These results emphasize gender difference in different domains and may change how we perceive men’s and women’s power in our society.

It has the usual weaknesses of most such studies.  Sample size is half-way decent but not randomized and with 20% more female participation than male.  Word clouds in particular are still a somewhat low consensus measure. 

I regard this as interesting and possibly indicative but not much more.  

But they are exploring something which I do think is important and which also undermines much of the corrupting Critical Theory palaver.  

Critical theory, among its many other deep failings, sanctions a pretty limited series of identity and takes not account of evolution of identities or the transactional nature of many of those identities.  CT coercively wants to determine my identities for me without taking into account my actual identities.  CT wants me to define myself as straight male and as white.

The reality is that most of us don't think about our identity very much and when we do, it is usually very context and transactionally determined.  CT misses out two or three other obvious and prevalent identities - class and religion.  Then the floodgates open - neighborhood, profession, personality profile, education attainment, avocations, familial status, age, etc.  There are an infinitude of relevant and often high impact identities which never breach the limited pantheon of CT.

I think of this alternative to the stick figure representation of identity in CT as the Dynamic Identity Stack (DIS).  "Dynamic" reflecting that the identities we orient around change to some extent as we age, sometimes softening, sometimes hardening, and sometimes demonstrating one or more disjoints.  "Dynamic" also reflects that even within a day, depending on the context and circumstances we wear multiple masks, multiple identities.  At the office I am the responsible professional, at home I am the spouse and parent, at church I am the faithful congregant, with my college buddies I am the witty guy in the group, etc.

Dynamic Identity Stack introduces marvelous variance and slips the clumsy shackles of imposed identity coerced in Critical Theory.  Human variation is the enemy of imposed uniform identity and why CT struggles outside of environments where there is financial support and no accountability for outcomes.  CT is a worldview depending on subsidies from the productive.

This study by Sikström, et al, captures some of that identity diversity.  They don't signal quite the diversity of identity discussed above.  They merely add two to the pot - Professional Identity and Domestic Identity.  As an aside they are using perceived power as their unit of measure but perceived competence, perceived prestige, etc. are other measures.  We can assess someone as high in perceived power and equally perceive them as low in competences.

We introduce the concept of preference-weighted power (PWP), a measure of power that includes different domains in life, weighted by the domains’ subjective importance. 

[snip]

Together the studies suggest that men have more perceived power in the public domain, however, this domain has a lower preference weighting than the private domain where women have more power than men. 

 While they might not add much in terms of reliable data, they add a lot in terms of refinement of identity models particularly b y acknowledging that there are more identities than just race and gender.