×

# zbMATH — the first resource for mathematics

On the coset pattern matrices and minimum $$M$$-aberration of $${2^{n-p}}$$ designs. (English) Zbl 1086.62086
Summary: The coset pattern matrix (CPM) is formally defined as an elaborate characterization of the aliasing patterns of a fractional factorial design. The possibility of using CPM to check design isomorphism is investigated. Despite containing much information about effect aliasing, the CPM fails to determine a design uniquely. We report and discuss small nonisomorphic designs that have equivalent coset pattern matrices. These examples imply that the aliasing property and the combinatorial structure of a design depend on each other in a complex manner. Based on CPM, a new optimality criterion, called the minimum $$M$$-aberration criterion, is proposed to rank-order designs. Its connections with other existing optimality criteria are discussed.

##### MSC:
 62K15 Factorial statistical designs 62K05 Optimal statistical designs
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.659279465675354, "perplexity": 3273.815743333007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057083.64/warc/CC-MAIN-20210920161518-20210920191518-00286.warc.gz"}