Statistical significance testing centered on p-values is commonly used to compare NLP system performance, but p-values alone are insufficient because statistical significance differs from practical significance. The latter can be measured by estimating effect size. In this pa-per, we propose a three-stage procedure for comparing NLP system performance and provide a toolkit, NLPStatTest, that automates the process. Users can upload NLP system evaluation scores and the toolkit will analyze these scores, run appropriate significance tests, estimate effect size, and conduct power analysis to estimate Type II error. The toolkit provides a convenient and systematic way to compare NLP system performance that goes beyond statistical significance testing.

Natural language numbers are an example of compositional structures, where larger numbers are composed of operations on smaller numbers. Given that compositional reasoning is a key to natural language understanding, we propose novel multilingual probing tasks tested on DistilBERT, XLM, and BERT to investigate for evidence of compositional reasoning over numerical data in various natural language number systems. By using both grammaticality judgment and value comparison classification tasks in English, Japanese, Danish, and French, we find evidence that the information encoded in these pretrained models’ embeddings is sufficient for grammaticality judgments but generally not for value comparisons. We analyze possible reasons for this and discuss how our tasks could be extended in further studies.