Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, an unreplicated $k$ factorial experiment would be the least costly. In an unreplicated experiment, the researcher cannot use analysis of variance to analyze the data. We propose a method that analyzes the data using normal probability plot of estimated contrast of the main effects and interactions. This method is applied to data and compared with Tukey's method that test for non-additivity. Our method is also discussed for use when the response is a multivariate set of measurements.
","abstract_html":"<p>Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, an unreplicated $k$ factorial experiment would be the least costly. In an unreplicated experiment, the researcher cannot use analysis of variance to analyze the data. We propose a method that analyzes the data using normal probability plot of estimated contrast of the main effects and interactions. This method is applied to data and compared with Tukey's method that test for non-additivity. Our method is also discussed for use when the response is a multivariate set of measurements.</p>","abstract_has_math":true,"creators":["Yang, Meixi"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Broderick Oluyede","Lili Yu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:00Z","subjects":["ETD","Contrast","normal probability plot","factorial design","Tukey","Design of Experiments and Sample Surveys"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1147","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Broderick Oluyede","Lili Yu"]},{"key":"dc:creator","label":"Author","values":["Yang, Meixi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Contrast","normal probability plot","factorial design","Tukey","Design of Experiments and Sample Surveys"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1147"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, an unreplicated $k$ factorial experiment would be the least costly. In an unreplicated experiment, the researcher cannot use analysis of variance to analyze the data. We propose a method that analyzes the data using normal probability plot of estimated contrast of the main effects and interactions. This method is applied to data and compared with Tukey's method that test for non-additivity. Our method is also discussed for use when the response is a multivariate set of measurements.
"]},{"key":"dc:title","label":"Title","values":["Statistical Analysis of Unreplicated Factorial Designs Using Contrasts"]}]}],"canonical_facts":{"dc:contributor":["Broderick Oluyede","Lili Yu"],"dc:creator":["Yang, Meixi"],"dc:date.available":["2014-07-01T07:00:00Z"],"dc:description.abstract":["Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, an unreplicated $k$ factorial experiment would be the least costly. In an unreplicated experiment, the researcher cannot use analysis of variance to analyze the data. We propose a method that analyzes the data using normal probability plot of estimated contrast of the main effects and interactions. This method is applied to data and compared with Tukey's method that test for non-additivity. Our method is also discussed for use when the response is a multivariate set of measurements.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1147"],"dc:subject":["ETD","Contrast","normal probability plot","factorial design","Tukey","Design of Experiments and Sample Surveys"],"dc:title":["Statistical Analysis of Unreplicated Factorial Designs Using Contrasts"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:28:00Z"}