6  Question asking experiment

We conducted an experiment in which we instructed session hosts assigned to manipulated sessions to either direct the first question of the Q&A to a woman or to a man. Here, we test whether this condition (first question asked by a man vs a woman) significantly affects the probability that women asks questions in the rest of the Q&A, the probability of a woman raising their hand, and/or the probability of a woman getting chosen to ask their question. Our hypothesis is that if women engagement is encouraged by female participation, women ask more questions in the condition where women started the Q&A.

To address this question, we build binomial GLMMs with condition as a fixed effect. The model structure is similar to the question-asking models used in section XXXX.

6.1 Manipulated data

First, we focus on manipulated sessions only, where we exclude situations where the host could not make a choice or if the gender proportion in the audience or the gender of the questioner was unknown (or disagreed upon between observers).

We assess the significance of the condition using an LRT as well as a Wald test.

### Asking questions

man_ask_null <- glmer(gender_questioner_female ~ (1|session_id/talk_id), data = data_analysis_tr, family = binomial, offset = boot::logit(audience_women_prop))

man_ask <- glmer(gender_questioner_female ~ -1 + condition + (1|session_id/talk_id), data = data_analysis_tr, family = binomial, offset = boot::logit(audience_women_prop))

# LRT
drop1(test="Chisq",man_ask) 

Single term deletions

Model:
gender_questioner_female ~ -1 + condition + (1 | session_id/talk_id)
          npar    AIC    LRT Pr(Chi)
<none>         294.73               
condition    1 294.87 2.1355  0.1439

summary(man_ask)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + condition + (1 | session_id/talk_id)
   Data: data_analysis_tr
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   294.7    308.3   -143.4    286.7      216 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.5555 -0.9521  0.6339  0.9046  1.4779 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0        0       
 session_id         (Intercept) 0        0       
Number of obs: 220, groups:  talk_id:session_id, 90; session_id, 38

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)   
conditionF  -0.6561     0.2039  -3.219  0.00129 **
conditionM  -0.2514     0.1880  -1.337  0.18112   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
           cndtnF
conditionM 0.000 
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_man_ask <- collect_out(model = man_ask, null = man_ask_null,  name = "QA_mani_asking", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_man_ask %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_mani_asking
AIC	294.732
n_obs	220
lrt_pval	0.144
lrt_chisq	2.135
n_factors	2
est_conditionF	-0.656
est_probabitily_conditionF	0.342
lowerCI_conditionF	-1.056
higherCI_conditionF	-0.257
pval_conditionF	0.001
zval_conditionF	-3.219
est_conditionM	-0.251
est_probabitily_conditionM	0.437
lowerCI_conditionM	-0.62
higherCI_conditionM	0.117
pval_conditionM	0.181
zval_conditionM	-1.337

### Raising hands

# remove when no hands when were raised, only men or only women
data_analysis_tr_hands <- subset(data_analysis_tr, hands_total > 0 & !is.na(hands_women) & !is.na(hands_men) & 
  !is.na(hands_total))

man_hands_null <- glmer(cbind(hands_women, hands_men) ~  (1|session_id/talk_id), data = data_analysis_tr_hands, family = binomial, offset = boot::logit(audience_women_prop))

man_hands <- glmer(cbind(hands_women, hands_men) ~ -1 + condition + (1|session_id/talk_id), data = data_analysis_tr_hands, family = binomial, offset = boot::logit(audience_women_prop))

summary(man_hands)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: 
cbind(hands_women, hands_men) ~ -1 + condition + (1 | session_id/talk_id)
   Data: data_analysis_tr_hands
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   330.6    343.9   -161.3    322.6      200 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.6465 -0.7914 -0.1532  0.9407  1.6499 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0.11951  0.3457  
 session_id         (Intercept) 0.01973  0.1405  
Number of obs: 204, groups:  talk_id:session_id, 85; session_id, 38

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)    
conditionF  -0.9191     0.2038  -4.510 6.48e-06 ***
conditionM  -0.6171     0.1752  -3.523 0.000427 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
           cndtnF
conditionM 0.000 

m_qa_man_hands <- collect_out(model = man_hands, null = man_hands_null,  name = "QA_mani_hands", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_man_hands %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_mani_hands
AIC	330.649
n_obs	204
lrt_pval	0.251
lrt_chisq	1.32
n_factors	2
est_conditionF	-0.919
est_probabitily_conditionF	0.285
lowerCI_conditionF	-1.319
higherCI_conditionF	-0.52
pval_conditionF	0
zval_conditionF	-4.51
est_conditionM	-0.617
est_probabitily_conditionM	0.35
lowerCI_conditionM	-0.96
higherCI_conditionM	-0.274
pval_conditionM	0
zval_conditionM	-3.523

## Getting chosen

# exclude cases where the host could not choose
data_analysis_tr_chosen <- subset(data_analysis_tr, hands_prop_women > 0 & hands_prop_women < 1) 

nrow(data_analysis_tr_chosen) #49

[1] 49

man_chosen_null <- glmer(gender_questioner_female ~ (1|session_id/talk_id), data_analysis_tr_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

man_chosen <- glmer(gender_questioner_female ~ -1 + condition + (1|session_id/talk_id), data_analysis_tr_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

summary(man_chosen)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + condition + (1 | session_id/talk_id)
   Data: data_analysis_tr_chosen
 Offset: boot::logit(hands_prop_women)

     AIC      BIC   logLik deviance df.resid 
    72.2     79.8    -32.1     64.2       45 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.3525 -1.3582  0.7113  0.7362  1.0412 

Random effects:
 Groups             Name        Variance  Std.Dev. 
 talk_id:session_id (Intercept) 2.434e-15 4.934e-08
 session_id         (Intercept) 0.000e+00 0.000e+00
Number of obs: 49, groups:  talk_id:session_id, 32; session_id, 20

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)
conditionF   0.6124     0.4481   1.366    0.172
conditionM   0.6815     0.4181   1.630    0.103

Correlation of Fixed Effects:
           cndtnF
conditionM 0.000 
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_man_chosen <- collect_out(model = man_chosen, null = man_chosen_null,  name = "QA_mani_chosen", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_man_chosen %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_mani_chosen
AIC	72.233
n_obs	49
lrt_pval	0.91
lrt_chisq	0.013
n_factors	2
est_conditionF	0.612
est_probabitily_conditionF	0.648
lowerCI_conditionF	-0.266
higherCI_conditionF	1.491
pval_conditionF	0.172
zval_conditionF	1.366
est_conditionM	0.681
est_probabitily_conditionM	0.664
lowerCI_conditionM	-0.138
higherCI_conditionM	1.501
pval_conditionM	0.103
zval_conditionM	1.63

6.1.1 Manipulated data only second question

Additionally, we address the same three questions as above but only focus on the probability that a woman asks the second question as opposed to the entire rest of the Q&A.

# select only the second question

data_analysis_tr2 <- subset(data_analysis_tr, question_nr == 2)

data_analysis_tr2_hands <- subset(data_analysis_tr_hands, question_nr == 2)

data_analysis_tr2_chosen <- subset(data_analysis_tr_chosen, question_nr == 2)

### Asking questions
man_ask_q2_null <- glmer(gender_questioner_female ~ -1  + (1|session_id/talk_id), data = data_analysis_tr2, family = binomial, offset = boot::logit(audience_women_prop))

man_ask_q2 <- glmer(gender_questioner_female ~ -1 + condition + (1|session_id/talk_id), data = data_analysis_tr2, family = binomial, offset = boot::logit(audience_women_prop))

summary(man_ask_q2) 

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + condition + (1 | session_id/talk_id)
   Data: data_analysis_tr2
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   101.7    111.0    -46.9     93.7       71 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.2089 -0.8164  0.4417  0.7247  1.2677 

Random effects:
 Groups             Name        Variance  Std.Dev.
 talk_id:session_id (Intercept) 4.303e-07 0.000656
 session_id         (Intercept) 5.447e-01 0.738062
Number of obs: 75, groups:  talk_id:session_id, 75; session_id, 36

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)  
conditionF  -0.8545     0.3959  -2.158   0.0309 *
conditionM   0.5663     0.4733   1.197   0.2315  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
           cndtnF
conditionM -0.041

m_qa_man_ask_q2 <- collect_out(model = man_ask_q2, null = man_ask_q2_null,  name = "QA_mani_asking_Q2", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_man_ask_q2 %>% t() %>% kbl() %>%
  kable_classic_2() #same conclusion as above

model_name	QA_mani_asking_Q2
AIC	101.746
n_obs	75
lrt_pval	0.028
lrt_chisq	7.162
n_factors	2
est_conditionF	-0.855
est_probabitily_conditionF	0.298
lowerCI_conditionF	-1.631
higherCI_conditionF	-0.079
pval_conditionF	0.031
zval_conditionF	-2.158
est_conditionM	0.566
est_probabitily_conditionM	0.638
lowerCI_conditionM	-0.361
higherCI_conditionM	1.494
pval_conditionM	0.231
zval_conditionM	1.197

## Raising hands

man_hands_q2_null <- glmer(cbind(hands_women, hands_men) ~ (1|session_id/talk_id), data = data_analysis_tr2_hands, family = binomial, offset = boot::logit(audience_women_prop))

man_hands_q2 <- glmer(cbind(hands_women, hands_men) ~ -1 + condition + (1|session_id/talk_id), data = data_analysis_tr2_hands, family = binomial, offset = boot::logit(audience_women_prop))

summary(man_hands_q2) 

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: 
cbind(hands_women, hands_men) ~ -1 + condition + (1 | session_id/talk_id)
   Data: data_analysis_tr2_hands
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   127.0    136.1    -59.5    119.0       67 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.92315 -0.74876  0.07772  0.88962  1.55521 

Random effects:
 Groups             Name        Variance  Std.Dev.
 talk_id:session_id (Intercept) 1.001e-10 0.00001 
 session_id         (Intercept) 1.476e-01 0.38423 
Number of obs: 71, groups:  talk_id:session_id, 71; session_id, 36

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)   
conditionF  -0.9311     0.3103  -3.001  0.00269 **
conditionM  -0.3193     0.2936  -1.088  0.27667   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
           cndtnF
conditionM -0.044
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_man_hands_q2 <- collect_out(model = man_hands_q2, null = man_hands_q2_null,  name = "QA_mani_hands_Q2", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_man_hands_q2 %>% t() %>% kbl() %>%
  kable_classic_2() #same conclusion as above

model_name	QA_mani_hands_Q2
AIC	127.042
n_obs	71
lrt_pval	0.137
lrt_chisq	2.214
n_factors	2
est_conditionF	-0.931
est_probabitily_conditionF	0.283
lowerCI_conditionF	-1.539
higherCI_conditionF	-0.323
pval_conditionF	0.003
zval_conditionF	-3.001
est_conditionM	-0.319
est_probabitily_conditionM	0.421
lowerCI_conditionM	-0.895
higherCI_conditionM	0.256
pval_conditionM	0.277
zval_conditionM	-1.088

## Raising hands

nrow(data_analysis_tr2_chosen) #20

[1] 20

man_chosen_q2_null <- glmer(gender_questioner_female ~ (1|session_id/talk_id), data_analysis_tr2_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

man_chosen_q2 <- glmer(gender_questioner_female ~ -1 + condition + (1|session_id/talk_id), data_analysis_tr2_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

summary(man_chosen_q2)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + condition + (1 | session_id/talk_id)
   Data: data_analysis_tr2_chosen
 Offset: boot::logit(hands_prop_women)

     AIC      BIC   logLik deviance df.resid 
    32.0     35.9    -12.0     24.0       16 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.0187 -0.9544  0.4348  0.6058  1.2771 

Random effects:
 Groups             Name        Variance  Std.Dev. 
 talk_id:session_id (Intercept) 2.711e-01 5.207e-01
 session_id         (Intercept) 9.488e-09 9.741e-05
Number of obs: 20, groups:  talk_id:session_id, 20; session_id, 13

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)
conditionF  0.03595    0.68784   0.052    0.958
conditionM  1.62264    1.05474   1.538    0.124

Correlation of Fixed Effects:
           cndtnF
conditionM 0.003 
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_man_chosen_q2 <- collect_out(model = man_chosen_q2, null = man_chosen_q2_null,  name = "QA_mani_chosen_Q2", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_man_chosen_q2 %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_mani_chosen_Q2
AIC	31.963
n_obs	20
lrt_pval	0.127
lrt_chisq	2.327
n_factors	2
est_conditionF	0.036
est_probabitily_conditionF	0.509
lowerCI_conditionF	-1.312
higherCI_conditionF	1.384
pval_conditionF	0.958
zval_conditionF	0.052
est_conditionM	1.623
est_probabitily_conditionM	0.835
lowerCI_conditionM	-0.445
higherCI_conditionM	3.69
pval_conditionM	0.124
zval_conditionM	1.538

6.2 Unmanipulated data

We ask the same question but using the unmanipulated data only, where session hosts were not given any instructions.

### Asking questions

unman_ask_null <- glmer(gender_questioner_female ~ (1|session_id/talk_id), data = data_analysis_c, family = binomial, offset = boot::logit(audience_women_prop))

unman_ask <- glmer(gender_questioner_female ~ -1 + FIRST_questioner_gender + (1|session_id/talk_id), data = data_analysis_c, family = binomial, offset = boot::logit(audience_women_prop))

# LRT
drop1(test="Chisq",unman_ask) 

Single term deletions

Model:
gender_questioner_female ~ -1 + FIRST_questioner_gender + (1 | 
    session_id/talk_id)
                        npar    AIC    LRT Pr(Chi)  
<none>                       288.13                 
FIRST_questioner_gender    1 292.47 6.3415 0.01179 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(unman_ask)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + FIRST_questioner_gender + (1 |  
    session_id/talk_id)
   Data: data_analysis_c
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   288.1    301.6   -140.1    280.1      208 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.5886 -0.8727 -0.6687  1.0096  1.7396 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0        0       
 session_id         (Intercept) 0        0       
Number of obs: 212, groups:  talk_id:session_id, 96; session_id, 24

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)    
FIRST_questioner_genderF  -1.0367     0.1926  -5.384  7.3e-08 ***
FIRST_questioner_genderM  -0.3270     0.2078  -1.574    0.116    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            FIRST__F
FIRST_qst_M 0.000   
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_unman_ask <- collect_out(model = unman_ask, null = unman_ask_null,  name = "QA_unmani_asking", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_unman_ask %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_unmani_asking
AIC	288.129
n_obs	212
lrt_pval	0.012
lrt_chisq	6.341
n_factors	2
est_FIRST_questioner_genderF	-1.037
est_probabitily_FIRST_questioner_genderF	0.262
lowerCI_FIRST_questioner_genderF	-1.414
higherCI_FIRST_questioner_genderF	-0.659
pval_FIRST_questioner_genderF	0
zval_FIRST_questioner_genderF	-5.384
est_FIRST_questioner_genderM	-0.327
est_probabitily_FIRST_questioner_genderM	0.419
lowerCI_FIRST_questioner_genderM	-0.734
higherCI_FIRST_questioner_genderM	0.08
pval_FIRST_questioner_genderM	0.116
zval_FIRST_questioner_genderM	-1.574

### Raising hands

# remove when no hands when were raised, only men or only women
data_analysis_c_hands <- subset(data_analysis_c, hands_total > 0 & !is.na(hands_women) & !is.na(hands_men) & 
  !is.na(hands_total))

unman_hands_null <- glmer(cbind(hands_women, hands_men) ~  (1|session_id/talk_id), data = data_analysis_c_hands, family = binomial, offset = boot::logit(audience_women_prop))

unman_hands <- glmer(cbind(hands_women, hands_men) ~ -1 + FIRST_questioner_gender + (1|session_id/talk_id), data = data_analysis_c_hands, family = binomial, offset = boot::logit(audience_women_prop))

summary(unman_hands)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: cbind(hands_women, hands_men) ~ -1 + FIRST_questioner_gender +  
    (1 | session_id/talk_id)
   Data: data_analysis_c_hands
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   359.7    373.0   -175.8    351.7      202 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.57510 -0.86492 -0.03985  0.80123  1.89468 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0.1891   0.4349  
 session_id         (Intercept) 0.1578   0.3972  
Number of obs: 206, groups:  talk_id:session_id, 96; session_id, 24

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)    
FIRST_questioner_genderF  -0.9023     0.1951  -4.625 3.75e-06 ***
FIRST_questioner_genderM  -0.3108     0.2195  -1.416    0.157    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            FIRST__F
FIRST_qst_M 0.163   

m_qa_unman_hands <- collect_out(model = unman_hands, null = unman_hands_null,  name = "QA_unmani_hands", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_unman_hands %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_unmani_hands
AIC	359.675
n_obs	206
lrt_pval	0.027
lrt_chisq	4.902
n_factors	2
est_FIRST_questioner_genderF	-0.902
est_probabitily_FIRST_questioner_genderF	0.289
lowerCI_FIRST_questioner_genderF	-1.285
higherCI_FIRST_questioner_genderF	-0.52
pval_FIRST_questioner_genderF	0
zval_FIRST_questioner_genderF	-4.625
est_FIRST_questioner_genderM	-0.311
est_probabitily_FIRST_questioner_genderM	0.423
lowerCI_FIRST_questioner_genderM	-0.741
higherCI_FIRST_questioner_genderM	0.12
pval_FIRST_questioner_genderM	0.157
zval_FIRST_questioner_genderM	-1.416

## Getting chosen

# exclude cases where the host could not choose
data_analysis_c_chosen <- subset(data_analysis_c, hands_prop_women > 0 & hands_prop_women < 1) 

nrow(data_analysis_c_chosen) #51

[1] 51

unman_chosen_null <- glmer(gender_questioner_female ~ (1|session_id/talk_id), data_analysis_c_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

unman_chosen <- glmer(gender_questioner_female ~ -1 + FIRST_questioner_gender + (1|session_id/talk_id), data_analysis_c_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

summary(unman_chosen)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + FIRST_questioner_gender + (1 |  
    session_id/talk_id)
   Data: data_analysis_c_chosen
 Offset: boot::logit(hands_prop_women)

     AIC      BIC   logLik deviance df.resid 
    76.4     84.2    -34.2     68.4       47 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.6208 -0.9358 -0.5403  1.0686  1.5113 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0.0e+00  0e+00   
 session_id         (Intercept) 2.5e-15  5e-08   
Number of obs: 51, groups:  talk_id:session_id, 37; session_id, 21

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)
FIRST_questioner_genderF  -0.1327     0.3641  -0.365    0.715
FIRST_questioner_genderM  -0.3320     0.4707  -0.705    0.481

Correlation of Fixed Effects:
            FIRST__F
FIRST_qst_M 0.000   
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_unman_chosen <- collect_out(model = unman_chosen, null = unman_chosen_null,  name = "QA_unmani_chosen", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_unman_chosen %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_unmani_chosen
AIC	76.428
n_obs	51
lrt_pval	0.738
lrt_chisq	0.112
n_factors	2
est_FIRST_questioner_genderF	-0.133
est_probabitily_FIRST_questioner_genderF	0.467
lowerCI_FIRST_questioner_genderF	-0.846
higherCI_FIRST_questioner_genderF	0.581
pval_FIRST_questioner_genderF	0.715
zval_FIRST_questioner_genderF	-0.365
est_FIRST_questioner_genderM	-0.332
est_probabitily_FIRST_questioner_genderM	0.418
lowerCI_FIRST_questioner_genderM	-1.254
higherCI_FIRST_questioner_genderM	0.59
pval_FIRST_questioner_genderM	0.481
zval_FIRST_questioner_genderM	-0.705

6.2.1 Unmanipulated data only second question

Additionally, we address the same three questions as above but only focus on the probability that a woman asks the second question as opposed to the entire rest of the Q&A.

# select only the second question

data_analysis_c2 <- subset(data_analysis_c, question_nr == 2)

data_analysis_c2_hands <- subset(data_analysis_c_hands, question_nr == 2)

data_analysis_c2_chosen <- subset(data_analysis_c_chosen, question_nr == 2)

### Asking questions
unman_ask_q2_null <- glmer(gender_questioner_female ~ -1  + (1|session_id/talk_id), data = data_analysis_c2, family = binomial, offset = boot::logit(audience_women_prop))

unman_ask_q2 <- glmer(gender_questioner_female ~ -1 + FIRST_questioner_gender + (1|session_id/talk_id), data = data_analysis_c2, family = binomial, offset = boot::logit(audience_women_prop))

summary(unman_ask_q2) 

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + FIRST_questioner_gender + (1 |  
    session_id/talk_id)
   Data: data_analysis_c2
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   107.1    116.4    -49.5     99.1       72 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.7007 -0.8280 -0.5853  0.8800  1.8124 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0.05513  0.2348  
 session_id         (Intercept) 0.00000  0.0000  
Number of obs: 76, groups:  talk_id:session_id, 76; session_id, 24

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)    
FIRST_questioner_genderF  -1.2957     0.3612  -3.587 0.000335 ***
FIRST_questioner_genderM  -0.1497     0.3505  -0.427 0.669395    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            FIRST__F
FIRST_qst_M -0.056  
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_unman_ask_q2 <- collect_out(model = unman_ask_q2, null = unman_ask_q2_null,  name = "QA_unmani_asking_Q2", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_unman_ask_q2 %>% t() %>% kbl() %>%
  kable_classic_2() #same conclusion as above

model_name	QA_unmani_asking_Q2
AIC	107.051
n_obs	76
lrt_pval	0.001
lrt_chisq	13.323
n_factors	2
est_FIRST_questioner_genderF	-1.296
est_probabitily_FIRST_questioner_genderF	0.215
lowerCI_FIRST_questioner_genderF	-2.004
higherCI_FIRST_questioner_genderF	-0.588
pval_FIRST_questioner_genderF	0
zval_FIRST_questioner_genderF	-3.587
est_FIRST_questioner_genderM	-0.15
est_probabitily_FIRST_questioner_genderM	0.463
lowerCI_FIRST_questioner_genderM	-0.837
higherCI_FIRST_questioner_genderM	0.537
pval_FIRST_questioner_genderM	0.669
zval_FIRST_questioner_genderM	-0.427

## Raising hands

unman_hands_q2_null <- glmer(cbind(hands_women, hands_men) ~ (1|session_id/talk_id), data = data_analysis_c2_hands, family = binomial, offset = boot::logit(audience_women_prop))

unman_hands_q2 <- glmer(cbind(hands_women, hands_men) ~ -1 + FIRST_questioner_gender + (1|session_id/talk_id), data = data_analysis_c2_hands, family = binomial, offset = boot::logit(audience_women_prop))

summary(unman_hands_q2) 

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: cbind(hands_women, hands_men) ~ -1 + FIRST_questioner_gender +  
    (1 | session_id/talk_id)
   Data: data_analysis_c2_hands
 Offset: boot::logit(audience_women_prop)

     AIC      BIC   logLik deviance df.resid 
   137.8    147.1    -64.9    129.8       71 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.7399 -0.9241 -0.0471  0.7580  2.6671 

Random effects:
 Groups             Name        Variance  Std.Dev. 
 talk_id:session_id (Intercept) 1.091e-10 1.044e-05
 session_id         (Intercept) 1.140e-02 1.068e-01
Number of obs: 75, groups:  talk_id:session_id, 75; session_id, 24

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)    
FIRST_questioner_genderF  -1.0803     0.2258  -4.783 1.73e-06 ***
FIRST_questioner_genderM  -0.1449     0.2789  -0.520    0.603    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            FIRST__F
FIRST_qst_M 0.024   
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_unman_hands_q2 <- collect_out(model = unman_hands_q2, null = unman_hands_q2_null,  name = "QA_unmani_hands_Q2", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_unman_hands_q2 %>% t() %>% kbl() %>%
  kable_classic_2() #same conclusion as above

model_name	QA_unmani_hands_Q2
AIC	137.786
n_obs	75
lrt_pval	0.008
lrt_chisq	7.012
n_factors	2
est_FIRST_questioner_genderF	-1.08
est_probabitily_FIRST_questioner_genderF	0.253
lowerCI_FIRST_questioner_genderF	-1.523
higherCI_FIRST_questioner_genderF	-0.638
pval_FIRST_questioner_genderF	0
zval_FIRST_questioner_genderF	-4.783
est_FIRST_questioner_genderM	-0.145
est_probabitily_FIRST_questioner_genderM	0.464
lowerCI_FIRST_questioner_genderM	-0.692
higherCI_FIRST_questioner_genderM	0.402
pval_FIRST_questioner_genderM	0.603
zval_FIRST_questioner_genderM	-0.52

## Raising hands

nrow(data_analysis_c2_chosen) #26

[1] 26

unman_chosen_q2_null <- glmer(gender_questioner_female ~ (1|session_id/talk_id), data_analysis_c2_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

unman_chosen_q2 <- glmer(gender_questioner_female ~ -1 + FIRST_questioner_gender + (1|session_id/talk_id), data_analysis_c2_chosen, family = "binomial", offset = boot::logit(hands_prop_women))

summary(unman_chosen)

Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: gender_questioner_female ~ -1 + FIRST_questioner_gender + (1 |  
    session_id/talk_id)
   Data: data_analysis_c_chosen
 Offset: boot::logit(hands_prop_women)

     AIC      BIC   logLik deviance df.resid 
    76.4     84.2    -34.2     68.4       47 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.6208 -0.9358 -0.5403  1.0686  1.5113 

Random effects:
 Groups             Name        Variance Std.Dev.
 talk_id:session_id (Intercept) 0.0e+00  0e+00   
 session_id         (Intercept) 2.5e-15  5e-08   
Number of obs: 51, groups:  talk_id:session_id, 37; session_id, 21

Fixed effects:
                         Estimate Std. Error z value Pr(>|z|)
FIRST_questioner_genderF  -0.1327     0.3641  -0.365    0.715
FIRST_questioner_genderM  -0.3320     0.4707  -0.705    0.481

Correlation of Fixed Effects:
            FIRST__F
FIRST_qst_M 0.000   
optimizer (Nelder_Mead) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

m_qa_unman_chosen_q2 <- collect_out(model = unman_chosen_q2, null = unman_chosen_q2_null,  name = "QA_unmani_chosen_Q2", n_factors = 2, type = "exp", save="yes", dir="../results/question-asking/")

m_qa_unman_chosen_q2 %>% t() %>% kbl() %>%
  kable_classic_2()

model_name	QA_unmani_chosen_Q2
AIC	42.294
n_obs	26
lrt_pval	0.898
lrt_chisq	0.016
n_factors	2
est_FIRST_questioner_genderF	-0.256
est_probabitily_FIRST_questioner_genderF	0.436
lowerCI_FIRST_questioner_genderF	-1.357
higherCI_FIRST_questioner_genderF	0.846
pval_FIRST_questioner_genderF	0.649
zval_FIRST_questioner_genderF	-0.455
est_FIRST_questioner_genderM	-0.364
est_probabitily_FIRST_questioner_genderM	0.41
lowerCI_FIRST_questioner_genderM	-1.651
higherCI_FIRST_questioner_genderM	0.922
pval_FIRST_questioner_genderM	0.579
zval_FIRST_questioner_genderM	-0.555

6.3 Plots

Let’s try to play around with ways of showing the raw data of the effect of the gender of the first questioner on the probability that a woman asks a question in the rest of the session.

prop_plot <- data.frame(what = rep(c("Asking questions", "Raising hands", "Getting chosen"), times=4),
                        data = rep(c("Manipulated", "Unmanipulated"), each = 6),
                        gender_first = rep(c(rep(c("Woman"), times=3), rep(c("Man"), times=3)), times=2),
                        est = c(m_qa_man_ask$est_conditionF,
                                     m_qa_man_hands$est_conditionF,
                                     m_qa_man_chosen$est_conditionF,
                                     m_qa_man_ask$est_conditionM,
                                     m_qa_man_hands$est_conditionM,
                                     m_qa_man_chosen$est_conditionM,
                                     m_qa_unman_ask$est_FIRST_questioner_genderF,
                                     m_qa_unman_hands$est_FIRST_questioner_genderF,
                                     m_qa_unman_chosen$est_FIRST_questioner_genderF,
                                     m_qa_unman_ask$est_FIRST_questioner_genderM,
                                     m_qa_unman_hands$est_FIRST_questioner_genderM,
                                     m_qa_unman_chosen$est_FIRST_questioner_genderM),
                        lower = c(m_qa_man_ask$lowerCI_conditionF,
                                     m_qa_man_hands$lowerCI_conditionF,
                                     m_qa_man_chosen$lowerCI_conditionF,
                                     m_qa_man_ask$lowerCI_conditionM,
                                     m_qa_man_hands$lowerCI_conditionM,
                                     m_qa_man_chosen$lowerCI_conditionM,
                                m_qa_unman_ask$lowerCI_FIRST_questioner_genderF,
                                     m_qa_unman_hands$lowerCI_FIRST_questioner_genderF,
                                     m_qa_unman_chosen$lowerCI_FIRST_questioner_genderF,
                                     m_qa_unman_ask$lowerCI_FIRST_questioner_genderM,
                                     m_qa_unman_hands$lowerCI_FIRST_questioner_genderM,
                                     m_qa_unman_chosen$lowerCI_FIRST_questioner_genderM),
                        higher = c(m_qa_man_ask$higherCI_conditionF,
                                     m_qa_man_hands$higherCI_conditionF,
                                     m_qa_man_chosen$higherCI_conditionF,
                                     m_qa_man_ask$higherCI_conditionM,
                                     m_qa_man_hands$higherCI_conditionM,
                                     m_qa_man_chosen$higherCI_conditionM,
                                     m_qa_unman_ask$higherCI_FIRST_questioner_genderF,
                                     m_qa_unman_hands$higherCI_FIRST_questioner_genderF,
                                     m_qa_unman_chosen$higherCI_FIRST_questioner_genderF,
                                     m_qa_unman_ask$higherCI_FIRST_questioner_genderM,
                                     m_qa_unman_hands$higherCI_FIRST_questioner_genderM,
                                     m_qa_unman_chosen$higherCI_FIRST_questioner_genderM),
                         pval = c(m_qa_man_ask$pval_conditionF,
                                     m_qa_man_hands$pval_conditionF,
                                     m_qa_man_chosen$pval_conditionF,
                                     m_qa_man_ask$pval_conditionM,
                                     m_qa_man_hands$pval_conditionM,
                                     m_qa_man_chosen$pval_conditionM,
                                     m_qa_unman_ask$pval_FIRST_questioner_genderF,
                                     m_qa_unman_hands$pval_FIRST_questioner_genderF,
                                     m_qa_unman_chosen$pval_FIRST_questioner_genderF,
                                     m_qa_unman_ask$pval_FIRST_questioner_genderM,
                                     m_qa_unman_hands$pval_FIRST_questioner_genderM,
                                     m_qa_unman_chosen$pval_FIRST_questioner_genderM))


col_sig <- clrs[c(10,2)] %>%
  color() %>% 
  set_names(nm = c("sig", "nonsig"))

prop_plot <- prop_plot %>% mutate(est_prob = plogis(est),
                                  lower_prob = plogis(lower),
                                  higher_prob = plogis(higher),
                                  sig = case_when(pval < 0.05 ~ "sig", pval >= 0.05 ~ "nonsig"))


prop_plot$what <- factor(prop_plot$what, levels = c("Asking questions", "Raising hands", "Getting chosen"))
prop_plot$data <- factor(prop_plot$data, levels = c("Unmanipulated", "Manipulated"))

ggplot(prop_plot) +
  geom_point(aes(y = est_prob, x = gender_first, col = sig), size = 6) + 
  geom_segment(aes(y = lower_prob, yend = higher_prob, x = gender_first),
               linewidth=1) +
  geom_hline(yintercept = 0.5, col = "red", linetype = "dotted") +
  
  labs(y = "Probability for women and 95% CI", x = "Perceived gender first questioner") + 
  facet_grid(data~what, scales="free_x")+
  scale_color_manual(values = col_sig) +
  theme(legend.position = "none",
        strip.text = element_text(size = 16),
        panel.border = element_rect(color = "black", fill = NA, size = 1)) -> plot_exp

plot_exp

ggsave(plot_exp, file = "../plots/main/fig4_qa_exp.png", width=10, height=8)