{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5WEJ5RHGRWXQ5GVKRFE4IXJGXC","short_pith_number":"pith:5WEJ5RHG","schema_version":"1.0","canonical_sha256":"ed889ec4e68daf0e9aaa8949c45d26b882b9103dd98e84d36a75d4713fa19d2c","source":{"kind":"arxiv","id":"1906.08726","version":1},"attestation_state":"computed","paper":{"title":"On the probability of a causal inference is robust for internal validity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","stat.ME","stat.OT"],"primary_cat":"stat.AP","authors_text":"Kenneth A. Frank, Tenglong Li","submitted_at":"2019-06-20T16:13:03Z","abstract_excerpt":"The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a causal inference is robust for internal validity, i.e., the PIV, as a robustness index of causal inference. Formally, the PIV is the probability of rejecting the null hypothesis again based on both the observed sample and the counterfactuals, provided the same null hypothesis has already been rejected based on the observed sample."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.08726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2019-06-20T16:13:03Z","cross_cats_sorted":["econ.EM","stat.ME","stat.OT"],"title_canon_sha256":"53aba1711634a5031eef522e44b7cd8fda87e1983c72f442cc1c290e6112647b","abstract_canon_sha256":"85312f47d48615b4416dbffd4428f979ef31d309d9bfbd4f4feb1ab82d5cba71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:49.465382Z","signature_b64":"WvJDMO1T0EoP/1HsjbYe5ymH5mYTV8q3Fa+ffGiLtHxoGSUwxvIGaCkLdx6vOfcdaKrRHKqwRRkeJM9j2xMmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed889ec4e68daf0e9aaa8949c45d26b882b9103dd98e84d36a75d4713fa19d2c","last_reissued_at":"2026-05-17T23:42:49.464922Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:49.464922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the probability of a causal inference is robust for internal validity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","stat.ME","stat.OT"],"primary_cat":"stat.AP","authors_text":"Kenneth A. Frank, Tenglong Li","submitted_at":"2019-06-20T16:13:03Z","abstract_excerpt":"The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a causal inference is robust for internal validity, i.e., the PIV, as a robustness index of causal inference. Formally, the PIV is the probability of rejecting the null hypothesis again based on both the observed sample and the counterfactuals, provided the same null hypothesis has already been rejected based on the observed sample."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08726","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.08726","created_at":"2026-05-17T23:42:49.464995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.08726v1","created_at":"2026-05-17T23:42:49.464995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08726","created_at":"2026-05-17T23:42:49.464995+00:00"},{"alias_kind":"pith_short_12","alias_value":"5WEJ5RHGRWXQ","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5WEJ5RHGRWXQ5GVK","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5WEJ5RHG","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC","json":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC.json","graph_json":"https://pith.science/api/pith-number/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/graph.json","events_json":"https://pith.science/api/pith-number/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/events.json","paper":"https://pith.science/paper/5WEJ5RHG"},"agent_actions":{"view_html":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC","download_json":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC.json","view_paper":"https://pith.science/paper/5WEJ5RHG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.08726&json=true","fetch_graph":"https://pith.science/api/pith-number/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/graph.json","fetch_events":"https://pith.science/api/pith-number/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/action/storage_attestation","attest_author":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/action/author_attestation","sign_citation":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/action/citation_signature","submit_replication":"https://pith.science/pith/5WEJ5RHGRWXQ5GVKRFE4IXJGXC/action/replication_record"}},"created_at":"2026-05-17T23:42:49.464995+00:00","updated_at":"2026-05-17T23:42:49.464995+00:00"}