{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:U75KTWO2HIZ2VAV2R5TSSR5676","short_pith_number":"pith:U75KTWO2","canonical_record":{"source":{"id":"2102.06770","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-02-12T20:56:12Z","cross_cats_sorted":["econ.EM"],"title_canon_sha256":"edc5a6444654c5e9c14dc5502c6c77020d1dd6b0dd68e0dd5b23a6b7af6f5940","abstract_canon_sha256":"cf9b8699b2077647de881d0835080adebae2a351ca6953183da123d0110b8b25"},"schema_version":"1.0"},"canonical_sha256":"a7faa9d9da3a33aa82ba8f672947beffb9a63de21cbde6a94da6b56f3cfdd99a","source":{"kind":"arxiv","id":"2102.06770","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06770","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06770v2","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06770","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"U75KTWO2HIZ2","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"pith_short_16","alias_value":"U75KTWO2HIZ2VAV2","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"pith_short_8","alias_value":"U75KTWO2","created_at":"2026-07-05T03:22:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:U75KTWO2HIZ2VAV2R5TSSR5676","target":"record","payload":{"canonical_record":{"source":{"id":"2102.06770","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-02-12T20:56:12Z","cross_cats_sorted":["econ.EM"],"title_canon_sha256":"edc5a6444654c5e9c14dc5502c6c77020d1dd6b0dd68e0dd5b23a6b7af6f5940","abstract_canon_sha256":"cf9b8699b2077647de881d0835080adebae2a351ca6953183da123d0110b8b25"},"schema_version":"1.0"},"canonical_sha256":"a7faa9d9da3a33aa82ba8f672947beffb9a63de21cbde6a94da6b56f3cfdd99a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:22:45.197974Z","signature_b64":"UTdQygpG5j21DKTrYjpLw5pourRg0lmyYwn5G1lxnEM0i00DlFw+cJ/tacBjnLn54k46u2VV6rMk5kmJ7yCXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7faa9d9da3a33aa82ba8f672947beffb9a63de21cbde6a94da6b56f3cfdd99a","last_reissued_at":"2026-07-05T03:22:45.197494Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:22:45.197494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.06770","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPjEG5sgqn4foqiXN9zI9m+4KaHjLjFcbp/oKEaf9WKoQMkX7UsV33RLk0afV9kcBgscyozMyrr9QGNoFJ9lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T12:44:44.753218Z"},"content_sha256":"8b0d9a14fe6e34fcc775397488207563156b37461f1595187781ea8d082f22bf","schema_version":"1.0","event_id":"sha256:8b0d9a14fe6e34fcc775397488207563156b37461f1595187781ea8d082f22bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:U75KTWO2HIZ2VAV2R5TSSR5676","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Power for Estimating Treatment Effects Using Difference-in-Differences and Comparative Interrupted Time Series Designs with Variation in Treatment Timing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["econ.EM"],"primary_cat":"stat.ME","authors_text":"Peter Z. Schochet","submitted_at":"2021-02-12T20:56:12Z","abstract_excerpt":"This article develops new closed-form variance expressions for power analyses for commonly used difference-in-differences (DID) and comparative interrupted time series (CITS) panel data estimators. The main contribution is to incorporate variation in treatment timing into the analysis. The power formulas also account for other key design features that arise in practice: autocorrelated errors, unequal measurement intervals, and clustering due to the unit of treatment assignment. We consider power formulas for both cross-sectional and longitudinal models and allow for covariates. An illustrative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06770","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.06770/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qtp8J7A0f28M55BZGbcU0aDK1XERJic98irh4uD3MW8P6+z/wqEO/858bK+qM0kAhzhy2ufI/a4PHF7r1/5YBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T12:44:44.753621Z"},"content_sha256":"71bb046f3fee44d164c20c42dd965b1375380dbf7cdcdbc0c225cbdee84a8317","schema_version":"1.0","event_id":"sha256:71bb046f3fee44d164c20c42dd965b1375380dbf7cdcdbc0c225cbdee84a8317"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U75KTWO2HIZ2VAV2R5TSSR5676/bundle.json","state_url":"https://pith.science/pith/U75KTWO2HIZ2VAV2R5TSSR5676/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U75KTWO2HIZ2VAV2R5TSSR5676/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-08T12:44:44Z","links":{"resolver":"https://pith.science/pith/U75KTWO2HIZ2VAV2R5TSSR5676","bundle":"https://pith.science/pith/U75KTWO2HIZ2VAV2R5TSSR5676/bundle.json","state":"https://pith.science/pith/U75KTWO2HIZ2VAV2R5TSSR5676/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U75KTWO2HIZ2VAV2R5TSSR5676/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:U75KTWO2HIZ2VAV2R5TSSR5676","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cf9b8699b2077647de881d0835080adebae2a351ca6953183da123d0110b8b25","cross_cats_sorted":["econ.EM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-02-12T20:56:12Z","title_canon_sha256":"edc5a6444654c5e9c14dc5502c6c77020d1dd6b0dd68e0dd5b23a6b7af6f5940"},"schema_version":"1.0","source":{"id":"2102.06770","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06770","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06770v2","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06770","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"U75KTWO2HIZ2","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"pith_short_16","alias_value":"U75KTWO2HIZ2VAV2","created_at":"2026-07-05T03:22:45Z"},{"alias_kind":"pith_short_8","alias_value":"U75KTWO2","created_at":"2026-07-05T03:22:45Z"}],"graph_snapshots":[{"event_id":"sha256:71bb046f3fee44d164c20c42dd965b1375380dbf7cdcdbc0c225cbdee84a8317","target":"graph","created_at":"2026-07-05T03:22:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.06770/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article develops new closed-form variance expressions for power analyses for commonly used difference-in-differences (DID) and comparative interrupted time series (CITS) panel data estimators. The main contribution is to incorporate variation in treatment timing into the analysis. The power formulas also account for other key design features that arise in practice: autocorrelated errors, unequal measurement intervals, and clustering due to the unit of treatment assignment. We consider power formulas for both cross-sectional and longitudinal models and allow for covariates. An illustrative","authors_text":"Peter Z. Schochet","cross_cats":["econ.EM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-02-12T20:56:12Z","title":"Statistical Power for Estimating Treatment Effects Using Difference-in-Differences and Comparative Interrupted Time Series Designs with Variation in Treatment Timing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06770","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8b0d9a14fe6e34fcc775397488207563156b37461f1595187781ea8d082f22bf","target":"record","created_at":"2026-07-05T03:22:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cf9b8699b2077647de881d0835080adebae2a351ca6953183da123d0110b8b25","cross_cats_sorted":["econ.EM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2021-02-12T20:56:12Z","title_canon_sha256":"edc5a6444654c5e9c14dc5502c6c77020d1dd6b0dd68e0dd5b23a6b7af6f5940"},"schema_version":"1.0","source":{"id":"2102.06770","kind":"arxiv","version":2}},"canonical_sha256":"a7faa9d9da3a33aa82ba8f672947beffb9a63de21cbde6a94da6b56f3cfdd99a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7faa9d9da3a33aa82ba8f672947beffb9a63de21cbde6a94da6b56f3cfdd99a","first_computed_at":"2026-07-05T03:22:45.197494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:22:45.197494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UTdQygpG5j21DKTrYjpLw5pourRg0lmyYwn5G1lxnEM0i00DlFw+cJ/tacBjnLn54k46u2VV6rMk5kmJ7yCXDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:22:45.197974Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.06770","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b0d9a14fe6e34fcc775397488207563156b37461f1595187781ea8d082f22bf","sha256:71bb046f3fee44d164c20c42dd965b1375380dbf7cdcdbc0c225cbdee84a8317"],"state_sha256":"a96ab619b611853acf248e810231f4fae726e3fce536c8418eb4dcd883c1552f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ml9g0+FOu4qydyCc+B0EOUOklZo84kopdGPpKTH8KTV7x90XmcNVFWmqkujg71yFNZTVP5ApZ5F3oVEQacjiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T12:44:44.755879Z","bundle_sha256":"efbb00e06dda283dfba6ff14c06acc252c96521494f9b524c11f267c6d6e0788"}}