{"doi":"10.5951/jresematheduc.8.5.0385","title":"A Forum for Researchers: A Note on the Power of Statistical Tests","abstract":"<jats:p>In the classical decision-making model, the experimenter seeks to demonstrate a difference between the distributions of two or more samples (or a sample and a population) for some parameter. A null hypothesis is stated that there is no “significant” difference between the distributions, and probabilistic models are used to determine the probability that any difference is due to chance. Philosophically, the researcher decides in advance that he is only willing to accept a probability less than a given size for making the error of assuming that the difference is real when it is actually due to chance. The a priori probability of such an error (Type I) is designated α. But the possibility of another error exists: the error of failing to reject a null hypothesis when the difference is real. (The a priori probability of such an error is designated β.) Whereas the probability of a Type I error has been controlled by the choice of a significance criterion, the Type II error (failing to reject a false null hypothesis) has seldom been controlled. However, the use of the technique of power analysis now makes it possible to control the probability of a Type II error with little more difficulty than the technique used to control the probability of a Type I error.</jats:p>","journal":"Journal for Research in Mathematics Education","year":1977,"id":39758,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":194471,"name":"Robert C. Clark","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.0,"endowment":0.0,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W3069995450","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.23221708,"influential_citations":0,"citation_trend":[],"oa_status":"closed","license":null,"oa_locations":[{"url":"https://pubs.nctm.org/view/journals/jrme/8/5/article-p385.xml","host_type":"publisher"},{"url":"https://pubs.nctm.org/downloadpdf/journals/jrme/8/5/article-p385.xml","host_type":"publisher"},{"url":"https://doi.org/10.5951/jresematheduc.8.5.0385","host_type":"journal"}],"fields_of_study":["Bayesian Modeling and Causal Inference","Psychology","Mathematics","Education"],"mesh_terms":[],"keywords":["Type I and type II errors","Null hypothesis","Statistical power","Statistics","Mathematics","A priori and a posteriori","Probabilistic logic","Sample size determination","Statistical hypothesis testing","Null (SQL)","Alternative hypothesis","Population","Econometrics","Computer science","Data mining"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Peace, Justice and strong institutions"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-11T22:17:00.014787Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}