In recent years, word embeddings have been widely used to measure biases in texts. Even if they have proven to be effective in detecting a wide variety of biases, metrics based on word embeddings lack transparency and interpretability. We analyze an alternative PMI-based metric to quantify biases in texts. It can be expressed as a function of conditional probabilities, which provides a simple interpretation in terms of word co-occurrences. We also prove that it can be approximated by an odds ratio, which allows estimating confidence intervals and statistical significance of textual biases. This approach produces similar results to metrics based on word embeddings when capturing gender gaps of the real world embedded in large corpora.

Numerous works use word embedding-based metrics to quantify societal biases and stereotypes in texts. Recent studies have found that word embeddings can capture semantic similarity but may be affected by word frequency. In this work we study the effect of frequency when measuring female vs. male gender bias with word embedding-based bias quantification methods. We find that Skip-gram with negative sampling and GloVe tend to detect male bias in high frequency words, while GloVe tends to return female bias in low frequency words. We show these behaviors still exist when words are randomly shuffled. This proves that the frequency-based effect observed in unshuffled corpora stems from properties of the metric rather than from word associations. The effect is spurious and problematic since bias metrics should depend exclusively on word co-occurrences and not individual word frequencies. Finally, we compare these results with the ones obtained with an alternative metric based on Pointwise Mutual Information. We find that this metric does not show a clear dependence on frequency, even though it is slightly skewed towards male bias across all frequencies.