`alternative_statistics.Rmd`

This time we’ll use the simple bootstrapping techniques in `weat_boot`

and `wefat_boot`

.

First we load up the package and arrange the graphics

```
library(cbn)
library(ggplot2)
theme_set(theme_minimal())
```

Are flowers more pleasant than insects?

Grab the items from the first WEAT study and the vectors corresponding to those words

```
its <- cbn_get_items("WEAT", 1)
head(its)
#> Study Condition Word Role
#> 1 WEAT1 Flowers aster target
#> 2 WEAT1 Flowers clover target
#> 3 WEAT1 Flowers hyacinth target
#> 4 WEAT1 Flowers marigold target
#> 5 WEAT1 Flowers poppy target
#> 6 WEAT1 Flowers azalea target
its_vecs <- cbn_get_item_vectors("WEAT", 1)
dim(its_vecs)
#> [1] 100 300
```

Now get a bootstrapped difference of differences of cosines

```
res <- weat_boot(its, its_vecs,
x_name = "Flowers", y_name = "Insects",
a_name = "Pleasant", b_name = "Unpleasant",
se.calc = "quantile")
res
#> diff lwr upr median
#> 1 0.1547512 0.09589897 0.2052987 0.1499265
```

Apparently flowers are more pleasant than insects.

Same as before to get items and vectors

```
its <- cbn_get_items("WEFAT", 1)
its_vecs <- cbn_get_item_vectors("WEFAT", 1)
```

Now to get bootstrapped differences of cosines. Note that there is no `y_name`

this time and we will get a statistic for each `x_name`

.

```
res <- wefat_boot(its, its_vecs, x_name = "Careers",
a_name = "MaleAttributes", b_name = "FemaleAttributes",
se.calc = "quantile")
head(res)
#> Careers diff lwr upr median
#> 1 nurse -0.1766406 -0.2265163 -0.10965455 -0.1706386
#> 2 receptionist -0.1369632 -0.1814540 -0.07422269 -0.1322328
#> 3 hygienist -0.1182356 -0.1540728 -0.06979447 -0.1154005
#> 4 librarian -0.1158335 -0.1433721 -0.07780748 -0.1124864
#> 5 nutritionist -0.1115838 -0.1574553 -0.05085981 -0.1086956
#> 6 therapist -0.1042064 -0.1499876 -0.04410492 -0.1017079
```

This is a bit hard to interpret, so we’ll make a picture

```
ggplot(res, aes(x = median, y = 1:nrow(res))) +
geom_point(col = "grey") +
geom_point(aes(x = diff)) +
geom_errorbarh(aes(xmin = lwr, xmax = upr), height = 0) +
geom_text(aes(x = upr, label = Careers), hjust = "left", nudge_x = 0.005) +
xlim(-0.25, 0.25) +
ylab("Careers") +
xlab("Cosine difference (male - female)")
```

This will work quite generally for WEFATs, but remember to mention the right condition name in `geom_text`

.

I don’t have the male / female proportions for different jobs, so we can’t compare them right now.

First we get the vector differences

```
its <- cbn_get_items("WEFAT", 2)
its_vecs <- cbn_get_item_vectors("WEFAT", 2)
res <- wefat_boot(its, its_vecs, x_name = "AndrogynousNames",
a_name = "MaleAttributes", b_name = "FemaleAttributes",
se.calc = "quantile")
```

Then we find the gender proportions for each name from the census.

This is most easily done using the `gender`

package, which queries the US Social Security Administration to get the proportion of stated males and females with any particular first name.

This data is bundled with the package, so we’ll join this to `res`

```
data(cbn_gender_name_stats)
head(cbn_gender_name_stats)
#> name proportion_male proportion_female gender year_min year_max
#> 1 Adam 0.9959 0.0041 male 1932 2012
#> 2 Adrian 0.9268 0.0732 male 1932 2012
#> 3 Agnes 0.0023 0.9977 female 1932 2012
#> 4 Aisha 0.0014 0.9986 female 1932 2012
#> 5 Aisha 0.0014 0.9986 female 1932 2012
#> 6 Alan 0.9968 0.0032 male 1932 2012
res <- merge(res, cbn_gender_name_stats,
by.x = "AndrogynousNames", by.y = "name")
```

If you want to do it yourself, e.g. to look at gender over different time periods, or use a different gender source, then

```
library(gender)
names <- c("Hugh", "Pugh", "Barney")
gender_name_stats <- gender(names)
```

and replace `cbn_gender_name_stats`

with `gender_name_stats`

.

To see how they relate, we’ll plot proportion male with the `diff`

column of `res`

```
ggplot(res, aes(x = proportion_male, y = diff)) +
geom_hline(yintercept = 0, alpha = 0.5, color = "grey") +
geom_point() +
geom_text(aes(label = AndrogynousNames), hjust = "left", nudge_x = 0.005) +
xlim(0, 1) +
xlab("Population proportion male") +
ylab("Cosine difference (male - female)")
```

The correlation is

```
cor.test(res$diff,res$proportion_male)
#>
#> Pearson's product-moment correlation
#>
#> data: res$diff and res$proportion_male
#> t = 11.421, df = 50, p-value = 1.526e-15
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#> 0.7517686 0.9116148
#> sample estimates:
#> cor
#> 0.8502362
```