Alejandro Reyes, PhD

CrossFit Open 24.1 Statistics Recap

2023-03-05T00:00:00-08:00

The CrossFit Open is the largest participatory sport event on Earth, according to the official website, and it consists of three workouts spread over three weeks. The first workout of the CrossFit Open 2024 took place last weekend and participants in the Rx category had to perform the following exercises within maximum 15 minutes:

21 Dumbbell Snatches (arm 1) (50/35 lb)
21 Lateral Burpees Over Dumbbell
21 Dumbbell Snatches (arm 2) (50/35 lb)
21 Lateral Burpees Over Dumbbell
15 Dumbbell Snatches (arm 1) (50/35 lb)
15 Lateral Burpees Over Dumbbell
15 Dumbbell Snatches(arm 2) (50/35 lb)
15 Lateral Burpees Over Dumbbell
9 Dumbbell Snatches (arm 1) (50/35 lb)
9 Lateral Burpees Over Dumbbell
9 Dumbbell Snatches (arm 2) (50/35 lb)
9 Lateral Burpees Over Dumbbell

Global distribution of 24.1 scores

An impressive 366589 participants submitted a score to the CrossFit Open website: 62% of participants competed in the “Rx” category, 33% competed in the “scaled” category and 5% competed in the “foundations” category.

Figure 1: Distribution of completion times for 24.1.

Figure 1 shows the distribution of completion times for each category for male and female divisions. Across all categories, only
15% of athletes completed the workout in less than 10 minutes and 28% could not complete all the repetitions within the 15 minute mark. It was a very though workout!

How many seconds away are you from quarter-final scores?

Athletes that rank among the top 25% in the Rx category qualify to the quarterfinals. Table 1 shows how fast an athlete would have had to complete 24.1 in order to be within the top 25% in their age category.

Table 1: Completion time of the top 25% male athletes in 24.1
division	Age group	24.1 time
M	16-17	10M 23S
M	18-34	9M 23S
M	35-39	10M 12S
M	40-44	10M 59S
M	45-49	11M 45S
M	50-54	12M 36S

Table 2: Completion time of the top 25% female athletes in 24.1
division	Age group	24.1 time
F	16-17	10M 55S
F	18-34	10M 14S
F	35-39	10M 46S
F	40-44	11M 20S
F	45-49	11M 53S
F	50-54	12M 36S

For example, I am a 35-year-old male and I completed the Rx workout in 13:43, meaning that I’m more than two minutes away from being a quarter-final athlete!

Comparing scores between CF boxes

Figure 2 shows a comparison of completion times between: - CF boxes with at least ten athletes in the CF Open leaderboard that had the best average scores worldwide (blue) - CF boxes in Basel, where I live and work out (red) - CF boxes in the rest of the world (green)

Figure 2: Distribution of completion times of top 8 world boxes and basel boxes.

It is interesting that in the Rx category, the completion times of male athletes from my CF box (CF HelvetiX) are very similar to those of CF boxes across the rest of the world. However, the completion times of female athletes from CF HelvetiX are much closer to the world’s top eight boxes.

Conclusion

If you have to bet for someone in Basel to qualify to the CF Games quarter finals, bet on a CF HelvetiX female athlete!

Brecha de género en investigación reflejada en los resultados de la convocatoria SNI 2020

2020-11-01T00:00:00-07:00

Los resultados de la convocatoria del Sistema Nacional de Investigadores del año 2020 se acaban de publicar. ¿Cómo se refleja la brecha de género en investigación en los resultados de la convocatoria?

Hace algunos meses, hice un blogpost en el que analicé cómo la brecha de género en ingestigación se refleja en el Sistema Nacional de Investigadores (SNI) del Consejo Nacional de Ciencia y Tecnología (CONACYT). Entre otras cosas, noté que el sesgo es evidente en todas las areas de investigación del SNI y el sesgo es mayor conforme aumenta el rango del SNI. En algunas ramas de investigación, el porcentaje de mujeres en los rangos mayores es menor al 10%. ¡Terrible!

La Dra. Álvarez-Buylla, directora de CONACYT, ha expresado su preocupación por la brecha de género que existe en el SNI y su compromiso a mejorar la situación actual. Dado que los resultados de la convocatoria del SNI del 2020 fueron publicadas hace algunos días, me dio curiosidad ¿Qué tanto se ve reflejado la brecha de género en investigación en los resultados de la convocatoria del SNI 2020? A continuación presento un análisis “dominguero”. El código está disponible en este repositorio de GitHub.

Aclaración Nov 2, 2020: El análisis está enfocado en ver como se refleja en los resultados de la convocatoria un problema de desigualdad de oportunidades de muchos años. Este análisis no analiza sesgos de los evaluadores o de las decisiones de la convocatoria SNI 2020.

Procesamiento de datos

El código a continuación, baja el pdf con los resultados de la convocatoria del SNI del año 2020, captura los datos del documento y formatea los datos para poder analizarlos.

library(tabulizer)
library(gender)
library(magrittr)
library(ggplot2)
library(cowplot)
theme_set(theme_cowplot())
location <- "https://www.conacyt.gob.mx/images/SNI/2020/RESULTADOS_SNI_CONVOCATORIA_2020_INGRESO_O_PERMANENCIA.pdf"

# Extract the table
sniResFile <- "sni_results.rds"
if( !file.exists(sniResFile) ){
  out <- extract_tables(location)
  saveRDS( out, file=sniResFile )
}

sni2020 <- readRDS( sniResFile )
sni2020 <- lapply( sni2020, function(x){
  x[,!colSums(x == "") == nrow(x)]
} )
stopifnot(all(sapply(sni2020, ncol) == 5) )
sni2020 <- Reduce( rbind, sni2020 )
sni2020 <- sni2020[sni2020[,5] != "Nacional",]
sni2020 <- sni2020[sni2020[,5] != "",]

sni2020 <- sni2020 %>%
  janitor::row_to_names(1) %>%
  as.data.frame() %>%
  dplyr::rename(lvl=`Nivel  otorgado`) %>%
  dplyr::mutate( 
    firstFirstName=gsub("(\\S+)\\s.*", "\\1", Nombre), 
    lvl=factor( dplyr::case_when( 
      lvl == "Investigador Nacional Nivel I" ~ "SNI I",
      lvl == "Investigador Nacional Nivel II" ~ "SNI II",
      lvl == "Investigador Nacional Nivel III" ~ "SNI III",
      grepl("Prórroga", lvl) ~ "Prórroga",
      grepl("Candidato", lvl) ~ "Candidato",
      TRUE ~ lvl
    ), levels=c("Prórroga", "Candidato", "SNI I", 
                "SNI II", "SNI III") ) )

Usando el paquete gender, podemos predecir el género de cada investigador con base en sus nombres de pila.

gender_df <- gender(unique(sni2020$firstFirstName)) %>%
  dplyr::select( name, gender ) %>%
  dplyr::rename( firstFirstName=name )

sni2020 <- sni2020 %>%
  dplyr::select( CVU, firstFirstName, lvl ) %>%
  dplyr::left_join( gender_df ) %>%
  dplyr::group_by( lvl, gender ) %>%
  dplyr::summarise(number=dplyr::n())

percAssigned <-
  round(100*(1-sum(sni2020$number[is.na(sni2020$gender)])/sum(sni2020$number)))

Este paquete puede predecir el género de 96% de los investigadores, es decir, 9145 de un total de 9478 investigadores.

Resultado

El gráfico a continuación, muestra el porcentage de mujeres (eje de las \(y\)) en cada categoría del SNI (eje de las \(x\)), ordenado con respecto al rango de la categoría. Los rangos más altos están hacia la derecha del gráfico.

sni2020 %>%
  dplyr::filter( !is.na(gender) ) %>%
  tidyr::pivot_wider( names_from="gender", values_from="number" ) %>%
  dplyr::mutate( 
    tot=sum(female+male), 
    fracFemales=100*female/tot, 
    lab=sprintf("%d%%", round(fracFemales))) %>%
  as.data.frame() %>%
  ggplot( aes( lvl, fracFemales, group = 1, label=lab) ) +
  geom_point() +
  geom_line() +
  geom_text(nudge_x = -0.2, nudge_y = -2) +
  ylim(25, 75) +
  geom_hline(yintercept=51, col="red", alpha=0.8, linetype="dashed") +
  labs(x="Nivel SNI", y="% de mujeres", title="Resultados SNI 2020") +
  panel_border(colour="black") +
  theme( axis.line=element_blank(), axis.text.x=element_text(angle=25, hjust=1) )

El gráfico muestra el sesgo de género en investigación reflejado en la convocatoria del SNI 2020. La población de mujeres en el mundo es del 51% (la línea roja en el gráfico), y es evidente que el porcentaje de mujeres está muy por debajo del 51% en todos los rangos y el porcentaje decrece conforme el rango del SNI aumenta. Sólo un tercio de los investigadores del máximo nivel son mujeres.

Este análisis no demuestra que el sesgo observado proviene de las evaluaciones del SNI, lo observado es probablemente un reflejo del sesgo que existe en la población de investigadores. De cualquier forma, ¡Mucho trabajo es necesario para mejorar esta situación!

Reproducibilidad

sessionInfo()

## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.4
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] cowplot_1.1.0   ggplot2_3.3.2   magrittr_1.5    gender_0.5.4   
## [5] tabulizer_0.2.2
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.5          pillar_1.4.6        compiler_4.0.3     
##  [4] tools_4.0.3         digest_0.6.27       lubridate_1.7.9    
##  [7] evaluate_0.14       lifecycle_0.2.0     tibble_3.0.4       
## [10] gtable_0.3.0        pkgconfig_2.0.3     png_0.1-7          
## [13] rlang_0.4.8         yaml_2.2.1          xfun_0.19          
## [16] rJava_0.9-13        genderdata_0.5.0    withr_2.1.2        
## [19] dplyr_1.0.2         stringr_1.4.0       knitr_1.30         
## [22] janitor_2.0.1       generics_0.1.0      vctrs_0.3.4        
## [25] grid_4.0.3          tidyselect_1.1.0    glue_1.4.2         
## [28] snakecase_0.11.0    R6_2.4.1            rmarkdown_2.5      
## [31] farver_2.0.3        tidyr_1.1.2         purrr_0.3.4        
## [34] tabulizerjars_1.0.1 scales_1.1.1        ellipsis_0.3.1     
## [37] htmltools_0.5.0     colorspace_1.4-1    labeling_0.3       
## [40] stringi_1.5.3       munsell_0.5.0       crayon_1.3.4

Sesgos de género en el SNI de CONACYT

2020-02-13T00:00:00-08:00

El Sistema Nacional de Investigadores (SNI), es un programa del Consejo Nacional de Ciencia y Tecnología de México (CONACYT) que tiene como objetivo reconocer el trabajo de las personas que se dedican a la ciencia en México. Como investigadores, nosotros aplicamos y podemos recibir distinciones que simbolizan la calidad y prestigio de nuestras contribuciones científicas. Las distinciones que podemos recibir son:

Candidato a Investigador Nacional
Investigador Nacional con tres niveles
Investigador Emérito

Hace unos meses, escribí un blog post acerca de un análisis de la brecha salarial de género en puestos académicos de la UNAM en el 2019. Dudo que la Dra. Álvarez-Buylla, directora del CONACYT, haya leído mi blog post. Sin embargo, la Dra. Álvarez-Buylla escribió el día siguiente en twitter:

Me preocupa mucho la brecha de género; este y otros problemas del Sistema Nacional de Investigadores deben corregirse. A 35 años de su creación, es momento de pensar colectivamente en su transformación virtuosa.
#CienciaPorMéxico pic.twitter.com/j5tDP3SeE9
— María Elena Álvarez-Buylla Roces (@ElenaBuylla) December 11, 2019

The gender wage gap is the average difference in income between men and women. According to the Organisation for Economic Cooperation and Development, in 2018 the gender wage gap was 13.5% globally and 14% in Mexico ¹. The reasons behind the wage gap include discrimination, occupational segregation and gender roles established by society. Research studies have estimated that gender wage gaps may not disappear before 2109 ².

The National Autonomous University of Mexico (UNAM, for its acronym in Spanish) is one of the biggest universities in Latin America. More than 10,000 researchers work in UNAM’s laboratories. Because UNAM is funded by taxpayers, the University is required to release all information about contracts and wages of each faculty member. These data are available in the UNAM’s transparency website.

The current blog post describes a documented data analysis that addresses the question: Is UNAM paying its male and female faculty equally? The code to reproduce this analysis can be found in my Github account.

UNAM’s wages data

All UNAM’s wage data is publicly available. I downloaded the data corresponding to the year 2019 and saved them as tab-separated file. I did some additional data wrangling to remove non-ASCII characters and have nicer column names.

library(magrittr)

###perl -pi -e 's/[^[:ascii:]]//g' UNAM_Remuneracion-profesores_2019-09-11_21.41.55.txt 
payData <- read.delim("UNAM_Remuneracion-profesores_2019-09-11_21.41.55.txt")
payData <- payData[,vapply( payData, function(x){length(unique(x))}, numeric(1)) > 1]
payData <- payData %>%
  dplyr::rename( 
    unidad_academica=`Unidad.acadmica`, 
    nombre=`Nombre.completo.del.profesor.a`,
    apellido_paterno=`Primer.apellido.del.profesor.a`,
    apellido_materno=`Segundo.apellido.del.profesor.a`,
    contrato=`Tipo.o.nivel.de.contratacin`,
    pago_bruto=`Remuneracin.bruta`,
    pago_neto=`Remuneracin.neta`,
    estimulos=`Estmulos.correspondientes.a.los.niveles.de.contratacin`,
    pago_total=`Monto.total.percibido`)

payData <- payData %>%
  dplyr::mutate_at( 
    c("pago_bruto", "pago_neto", "pago_total"), 
    function(x){as.numeric(gsub("\\$|,", "", as.character(x)))})
payData$id <- sprintf("investigador%0.9d", seq_len(nrow(payData)))

payData$academic_title <- payData$contrato
payData$academic_title <- gsub( "^\\S+ (.*)$", "\\1", payData$academic_title )

These data contain information for 12,720 researchers, including full names, monthly salaries, academic ranks and academic departments.

Women constitute 45% of UNAM’s faculty

Then, I aimed at assigning gender to each faculty member based on their first names. In my first attempt, I created catalogs of masculine and feminine names by scraping data from Wikipedia (the code for that can be found here). But I was pointed to an R package called gender, which uses US social security and census data to assign a gender to names. I used the gender package because it was better and cleaner than my name catalogs.

In Mexico, it is common for people to have more than one first name and names like “María José” can be tricky, since “María” is a feminine name, “José” is a masculine name and the combination of the two, “María José”, is a name given to women. In these cases, I considered both the gender of the first first name and the consensus gender of the individual names. In general, these two strategies gave almost identical results. For researchers with a single first name, the assignment was straightforward. For researchers with more than one first name, I selected the gender of the first first name or the consensus gender of the names whenever the first first name was uninformative. Note that in my analysis, gender defaults to “man” and “woman” and as a result, I failed to include people who experience their gender identity as falling outside these two categories.

namesDf <- as.data.frame(payData[,c("nombre", "id")])
namesDf$nombre <- strsplit( as.character(payData$nombre), " " )
namesDf <- tidyr::unnest(namesDf, cols = c(nombre))
namesDf <- namesDf %>% 
  dplyr::mutate( nameOrder=ave(id, id, FUN=seq_along) )

library(gender)
gendersPackage <- gender( unique(namesDf$nombre), 2012 )[,c("name", "gender")]

gendersPackage <- gendersPackage %>%
  dplyr::mutate( gender=gsub("^female", "Female", gsub("^male", "Male", gender) ) ) %>%
  dplyr::select( name, gender ) %>%
  dplyr::rename( nombre=name )

namesDf <- dplyr::left_join( namesDf, gendersPackage )

genderFirstName <- namesDf %>% 
  dplyr::filter( nameOrder == 1 ) %>%
  dplyr::select( id, gender )

genderConsensus <- namesDf %>%
  dplyr::group_by( id, gender ) %>%
  dplyr::summarize( cnt=dplyr::n() ) %>%
  na.omit() %>%
  reshape2::dcast( id ~ gender, value.var="cnt", fun.aggregate = length) %>%
  dplyr::mutate( 
    genderConsensus=dplyr::case_when(
      Male > Female ~ "Male", 
      Female > Male ~ "Female",
      (Male == Female & Female > 0) ~ "Ambiguous",
      is.numeric(Male) ~ "Unknown" )
  )

genderAssignment <- dplyr::full_join( genderConsensus, genderFirstName )

genderAssignment$genderFinal <- with( genderAssignment, 
               ifelse( genderConsensus %in% c("Ambiguous", "Other"), 
                       gender, genderConsensus ) )

payData <- payData %>% 
  dplyr::left_join( genderAssignment[,c("id", "genderFinal")] ) %>%
  dplyr::rename( gender=genderFinal ) %>%
  dplyr::select( -pago_bruto )

payData$gender[is.na(payData$gender)] <- "Unknown"

Using this approach, I could assign a gender to 12,320 faculty members, or 97% of UNAM’s academics. Of those, 5,498 (45%) were females. This estimate of the percentage of female faculty is consistent with UNAM’s reports.

High-rank positions are mostly occupied by men

I found a significant difference between the wages earned by women and men (\(p = 2.9 * 10^{-13}\)). On average, male faculty earn 3,080 Mexican pesos (MXN) more than female faculty. The plot below shows the distribution of wages for each gender.

library(cowplot)
library(ggplot2)
theme_set(theme_cowplot())

payData %>%
  dplyr::filter( gender %in% c("Male", "Female") ) %>%
  ggplot( aes( pago_total, col=gender ) ) +
  geom_density() +
  geom_segment(
    aes(x = x1, y = y1+.2e-5, xend = x1, yend = y1),
    data = data.frame(x1=c(70000, 125000), y1=c(1.2e-5, .2e-5) ),
    inherit.aes=FALSE,
    arrow = arrow(length = unit(0.03, "npc") ) ) +
  labs(y="Density", x="UNAM's monthly salary (MXN)", col="") +
  scale_colour_manual(values=c(Female="#e41a1c", Male="#377eb8"))

These distributions show several modes, and there are two peaks towards the higher-ranking salaries that are higher for men than for women (see the arrows). These patterns suggest that higher-rank positions are occupied by men.

Thus, I plotted the percentage of women in each academic title as a function of the average salary in that title.

library(cowplot)
theme_set(theme_cowplot())

contractSummary <- payData %>%
  dplyr::filter( gender %in% c("Male", "Female") ) %>%
  dplyr::group_by( academic_title ) %>%
  dplyr::summarise( num=dplyr::n(), avePay=mean( pago_total ) ) %>%
  dplyr::arrange( desc(avePay) )

payPerGenderSumm <- payData %>%
  dplyr::filter( gender %in% c("Male", "Female") ) %>%
  dplyr::group_by( academic_title, gender ) %>%
  dplyr::summarise( num=dplyr::n() ) %>%
  tidyr::pivot_wider(names_from="gender", values_from="num", values_fill=list(num=0)) %>%
  dplyr::mutate( femalePercent=100*(Female/(Male+Female) )) %>%
  dplyr::right_join( contractSummary ) %>%
  dplyr::ungroup() 

payPerGenderSumm %>%
#  dplyr::filter( num > 3 ) %>%
  ggplot( aes( avePay/1000, femalePercent) ) +
  geom_point() +
  geom_hline(yintercept=50, col="red") +
  ylim(0, 100) +
  labs(x="Monthly salary (x 1,000 MXN)", y="Percentage of women")

In the plot above, the split between man and women is centered around 50% for most positions. But among the top 6 academic titles that are better paid, the percentage of women is way below 50%.

The code below pulls the contracts where the average salary is above 50,000 MXN per month. For all contracts except one, the percentage of women is below 40%. The academic titles in this list are the most prestigious positions such as Emeritus Faculty and Investigadores/Profesores Titulares (equivalent to full professors in the US system).

payPerGenderSumm %>%
  dplyr::filter( avePay > 50000) %>%
  dplyr::select( academic_title, num, femalePercent, avePay )

## # A tibble: 7 x 4
##   academic_title                           num femalePercent  avePay
##                                                 
## 1 INVESTIGADOR EMERITO                      66          15.2 128744.
## 2 PROFESOR EMERITO                          43          27.9 126215.
## 3 INVESTIGADOR TITULAR C TIEMPO COMPLETO   792          30.2  73496.
## 4 PROFESOR TITULAR C TIEMPO COMPLETO      1671          39.6  71001.
## 5 PROFESOR TITULAR B TIEMPO COMPLETO       763          43.1  55514.
## 6 INVESTIGADOR TITULAR B TIEMPO COMPLETO   614          36.3  54739.
## 7 PROFESOR EXTRAORDINARIO                    1           0    50389.

Interestingly, several part-time senior positions are mostly occupied by men.

payPerGenderSumm %>%
  dplyr::filter( femalePercent < 40, grepl("MEDIO TIEMPO", academic_title ) ) %>%
  dplyr::select( academic_title, femalePercent, avePay )

## # A tibble: 8 x 3
##   academic_title                            femalePercent avePay
##                                                  
## 1 PROFESOR TITULAR C MEDIO TIEMPO                    13.0 12438.
## 2 PROFESOR TITULAR B MEDIO TIEMPO                    15.4 10695.
## 3 PROFESOR TITULAR A MEDIO TIEMPO                    32.3  9482.
## 4 TECNICO ACADEMICO TITULAR A MEDIO TIEMPO            0    7995.
## 5 PROFESOR ASOCIADO B MEDIO TIEMPO                   18.2  7779.
## 6 INVESTIGADOR ASOCIADO B MEDIO TIEMPO                0    7350.
## 7 PROFESOR ASOCIADO A MEDIO TIEMPO                   10    6900.
## 8 TECNICO ACADEMICO AUXILIAR A MEDIO TIEMPO          26.7  5629.

The analysis shows an overall difference of male faculty earning more money than female faculty. This difference is explained by male faculty members having higher academic titles than female faculty members.

Women earn 542 MXN more than men with the same contract

Then I asked a sligthly different question: is there a gender pay gap for faculty members who have the same contract?

To answer this question, I fitted a linear model

\[y_{i} = \beta_{0} + \beta_{1}^{female}x_{1i} + \sum_{j=2}^{q} {\beta_{j}^{contract}x_{ji}} + \epsilon_{i}, \]

where \(y_{i}\) is the salary of individual \(i\) and \(q\) is the number of possible contracts. \(\beta_{0}\) is the intercept term, which estimates the mean salary for men that have a contract that is arbitrarily selected as base level. \(x_{1i}\) is a dummy variable that is equal to \(1\) if individual \(i\) is a female and is equal to \(0\) if individual \(i\) is a male. \(x_{ji}\) are \(q-1\) dummy variables that are equal to 1 if individual \(i\) has a contract \(j\) and are equal to \(0\) if individual \(i\) does not have contract \(j\). \(\epsilon_{i}\) is the error term that is normally distributed.

The coefficient of interest in the model is \(\beta_{1}^{female}\), which estimates the difference in salary that women receive compared to men after adjusting for salary differences between different contracts, which are estimated by the \({\beta}_{j}^{contract}\) coefficients.

testable <- as.character( payData %>%
  dplyr::filter( gender %in% c("Male", "Female") ) %>%
  dplyr::group_by( contrato ) %>%
  dplyr::summarise( num=dplyr::n() ) %>%
  dplyr::filter( num > 15 ) %>%
  dplyr::pull( contrato ) )

minN <- min( payData[payData$contrato %in% testable,] %>%
  dplyr::group_by( gender, contrato ) %>%
  dplyr::summarise( n=dplyr::n() ) %>%
  dplyr::pull( n ) )

stopifnot( minN > 0 )

fit <- lm( pago_total ~ contrato + gender,
          data={
            dplyr::filter(payData, gender %in% c("Male", "Female"), contrato %in% testable ) %>%
              dplyr::mutate( gender=factor(gender, levels=c("Male", "Female"))) } )

coefFemale <- coefficients(fit)[["genderFemale"]]
coefFemale

## [1] 541.6868

pvalLm <- broom::tidy(anova(fit)) %>%
  dplyr::filter( term == "gender" ) %>%
  dplyr::pull(p.value)
pvalLm

## [1] 0.0001195584

The \(p\)-value of an analysis of variance indicates that there is a significant difference in the salaries that women earn compare to men that are employed with the same contracts. The resulting \(\beta_{1}^{female}\) coefficient indicates that women earn 542 MXN more than men. I found this result to be counterintuitive given that historically, due to discrimination, men typically earn more than women.

To find out the reason for these wage gaps, I analyzed the difference in pay in each contract. For each contract, I tested whether there were differences in salaries between male and female faculty members.

contractSummary <- payData %>%
  dplyr::filter( gender %in% c("Male", "Female") ) %>%
  dplyr::group_by( contrato ) %>%
  dplyr::summarise( num=dplyr::n(), avePay=mean( pago_total ) ) %>%
  dplyr::arrange( desc(avePay) )

payPerGenderSumm <- payData %>%
  dplyr::filter( gender %in% c("Male", "Female") ) %>%
  dplyr::group_by( contrato, gender ) %>%
  dplyr::summarise( num=dplyr::n() ) %>%
  tidyr::pivot_wider(names_from="gender", values_from="num", values_fill=list(num=0)) %>%
  dplyr::mutate( femalePercent=100*(Female/(Male+Female) )) %>%
  dplyr::right_join( contractSummary ) %>%
  dplyr::ungroup() 

differentPays <- payData %>%
  dplyr::filter( gender %in% c("Male", "Female"), contrato %in% testable ) %>%
  dplyr::mutate(gender=factor(gender, levels=c("Female", "Male"))) %>%
  dplyr::group_by( contrato ) %>%
  dplyr::group_map( ~ cbind( 
    broom::tidy( t.test( pago_total ~ gender, data=.x )),
    contrato=unique( .x$contrato ), stringsAsFactors=FALSE), keep=TRUE ) %>%
  dplyr::bind_rows() %>%
  dplyr::select( estimate, estimate1, estimate2, conf.low, conf.high, contrato, p.value ) %>%
  dplyr::mutate( q.value = p.adjust( p.value, method="BH")) %>%
  dplyr::filter( q.value < 0.1 ) %>%
  dplyr::left_join(  payPerGenderSumm[,c("contrato", "avePay")] ) %>%
  dplyr::mutate( aveDiff=(100*estimate1/estimate2) - 100 )

nrow(differentPays)

## [1] 2

Two full-time contracts, Investigador Titular B and Profesor Titular C, were significant at a false discovery rate of 10%. The plot below shows the distributions of wages for these two contracts.

library(cowplot)
theme_set(theme_cowplot())
payData %>%
  dplyr::filter( 
    contrato == dplyr::pull(differentPays, contrato), 
    gender %in% c("Male", "Female") ) %>%
  dplyr::mutate( contrato = gsub(" TIEMPO COMPLETO|^\\S+ ", "", contrato) ) %>%
  ggplot( aes(pago_total/1000, col=gender ) ) +
  geom_density() +
  facet_wrap( ~contrato ) +
  theme(legend.pos="top", axis.line=element_blank()) +
  labs(x="Monthly salary (x 1,000 MXN)", y="Density", col="") +
  panel_border(colour="black", size=1) +
  scale_colour_manual(values=c(Female="#e41a1c", Male="#377eb8"))

In these two positions, the average salary of women is 3.4% and 2% higher than that of men, respectively.

The plot below shows the differences between the salaries of women compared to men (\(y\)-axis) for each contract (represented as a dot) plotted as a function of the average salary of the contract (\(x\)-axis). The points are color-coded according to the percentage of women in that contract. The vertical solid lines represent the 95% confidence intervals of the mean differences. Dots above the horizontal dotted line indicate that the average salary is higher for women than men, and dots below the horizontal dotted line indicate that the average salary of women is lower compared to that of men.

library(cowplot)
theme_set(theme_cowplot())

cols <- c( colorRampPalette( c("#b2182b", "#f4a582", "#bababa"), bias=0.5)(100),
   rev(colorRampPalette( c( "#2166ac", "#92c5de", "#bababa"), bias=0.5)(100) ) )

payData %>%
  dplyr::filter( gender %in% c("Male", "Female"), contrato %in% testable ) %>%
  dplyr::mutate(gender=factor(gender, levels=c("Female", "Male"))) %>%
  dplyr::group_by( contrato ) %>%
  dplyr::group_map( ~ cbind( 
    broom::tidy(t.test( pago_total ~ gender, data=.x )),
    contrato=unique( .x$contrato ), stringsAsFactors=FALSE ), keep=TRUE ) %>%
  dplyr::bind_rows() %>%
  dplyr::select( estimate, conf.low, conf.high, contrato, p.value ) %>%
  dplyr::mutate( q.value = p.adjust( p.value, method="BH")) %>%
  dplyr::left_join( payPerGenderSumm ) %>%
  ggplot( aes( avePay/1000, estimate/1000, col=femalePercent) ) +
  geom_errorbar(aes(ymin=conf.low/1000, ymax=conf.high/1000), width=.1) +
  geom_point() + 
  scale_colour_gradientn(colours=cols,  limits=c(0, 100)) +
  geom_hline(yintercept=0, col="black", alpha=0.95, linetype="longdash") +
  annotate("text", x=27, y=6.5, label="   ↑ Women earn more", color = "black") +
  annotate("text", x=27, y=-6.5, label=" ↓ Men earn more  ", color = "black") +
  ylim(-6.5, 15) +
  labs(x="Monthly salary (x 1,000 MXN)", 
       y="Difference in salary\n( Women - Men )",
       col="% of women")

For 70% of the contracts (23 out of 33), the average salary was higher for women than for men. This explains why the \(\beta_{1}^{female}\) coefficient is significant in the linear model. However, the 95% confidence intervals overlap with the zero line for 30 of the contracts, which is why only two contracts, Investigador Titular B and Profesor Titular C, are significant in the contract-wise tests after multiple-testing correction.

Conclusions

My analysis shows that among UNAM’s faculty members, men earn on average 7% more than women faculty. This wage gap is explained by the high-rank academic titles being occupied mostly by men. For example, only 15% of UNAM’s research faculty members with the highest academic titles, Investigadores Emeritos, are women.

When I tested for differences in wages between male and female faculty with the same contracts, I found that women earn on average 1% more than men with the same contract. This difference is more pronounced in two contracts, Investigador Titular B and Profesor Titular C, where women earn 3.4% and 2% more than men, respectively.

In the academic positions where the percentage of men is high, which tend to be senior positions, the few women in those positions earn more than men on average. This is very intriguing and I don’t have an explanation for it. One hypothesis is that men are promoted more often than women. In this scenario, female researchers would remain in lower-rank positions for longer and thus would accumulate more salary increases.

The biggest problem, however, is the lack of representation of women in senior faculty positions: in order to reach gender equality, UNAM should promote more women to the higher-rank academic titles.

Session Information

sessionInfo()

## R version 3.6.1 (2019-07-05)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Mojave 10.14
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] cowplot_1.0.0 ggpubr_0.2.3  ggplot2_3.2.1 gender_0.5.3  magrittr_1.5 
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.3       pillar_1.4.2     compiler_3.6.1   plyr_1.8.4      
##  [5] tools_3.6.1      zeallot_0.1.0    digest_0.6.22    lattice_0.20-38 
##  [9] nlme_3.1-142     evaluate_0.14    lifecycle_0.1.0  tibble_2.1.3    
## [13] gtable_0.3.0     pkgconfig_2.0.3  rlang_0.4.1      cli_1.1.0       
## [17] yaml_2.2.0       xfun_0.11        genderdata_0.5.0 withr_2.1.2     
## [21] dplyr_0.8.3      stringr_1.4.0    knitr_1.26       generics_0.0.2  
## [25] vctrs_0.2.0      grid_3.6.1       tidyselect_0.2.5 glue_1.3.1      
## [29] R6_2.4.1         fansi_0.4.0      rmarkdown_1.17   tidyr_1.0.0     
## [33] purrr_0.3.3      reshape2_1.4.3   backports_1.1.5  scales_1.0.0    
## [37] codetools_0.2-16 htmltools_0.4.0  assertthat_0.2.1 colorspace_1.4-1
## [41] ggsignif_0.6.0   labeling_0.3     utf8_1.1.4       stringi_1.4.3   
## [45] lazyeval_0.2.2   munsell_0.5.0    broom_0.5.2      crayon_1.3.4

Alejandro Reyes, PhD

CrossFit Open 24.1 Statistics Recap

CrossFit Open 24.1 Statistics Recap

Alejandro Reyes

Global distribution of 24.1 scores

How many seconds away are you from quarter-final scores?

Comparing scores between CF boxes

Conclusion

Brecha de género en investigación reflejada en los resultados de la convocatoria SNI 2020

Brecha de género en investigación reflejada en los resultados de la convocatoria SNI 2020

Alejandro Reyes

Procesamiento de datos

Resultado

Reproducibilidad

Sesgos de género en el SNI de CONACYT

Sesgos de género en el SNI de CONACYT

Alejandro Reyes

UNAM’s faculty gender pay gap in the year 2019

Alejandro Reyes

UNAM’s wages data

Women constitute 45% of UNAM’s faculty

High-rank positions are mostly occupied by men

Women earn 542 MXN more than men with the same contract

Conclusions

Session Information

References