Normal and half-normal probability plots are often used in analyzing unreplicated two level factorial and fractional factorial designs. Typically no objective method is used with these plots for assessing if a plotted point is associated with a nonzero effect. Firstly, we provide an analysis of the plotting positions used in constructing these plots. Based on the results of our study, we recommend a set of plotting positions to be used with the normal probability plot. We also suggest that these results would apply to half-normal plots and recommend a set of plotting positions to be used with this plot. Secondly, we give a method for selecting critical values so the plot can be used to objectively assess which effects, if any, are nonzero. Some examples are given illustrating the use of our method.
","abstract_html":"<p>Normal and half-normal probability plots are often used in analyzing unreplicated two level factorial and fractional factorial designs. Typically no objective method is used with these plots for assessing if a plotted point is associated with a nonzero effect. Firstly, we provide an analysis of the plotting positions used in constructing these plots. Based on the results of our study, we recommend a set of plotting positions to be used with the normal probability plot. We also suggest that these results would apply to half-normal plots and recommend a set of plotting positions to be used with this plot. Secondly, we give a method for selecting critical values so the plot can be used to objectively assess which effects, if any, are nonzero. Some examples are given illustrating the use of our method.</p>","abstract_has_math":false,"creators":["Vora, Minal A."],"institution":null,"degree_name":"Master of Science in Mathematics","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":["Broderick O. Oluyede","Patricia B. Humphrey"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-01-01T08:00:00Z","date_published":"2004-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:15Z","subjects":["ETD","Critical values","Estimated percentiles","Normal distribution","Order statistics","Probability plot","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd_legacy/38","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Broderick O. Oluyede","Patricia B. Humphrey"]},{"key":"dc:creator","label":"Author","values":["Vora, Minal A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["1970-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Critical values","Estimated percentiles","Normal distribution","Order statistics","Probability plot","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd_legacy/38"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Normal and half-normal probability plots are often used in analyzing unreplicated two level factorial and fractional factorial designs. Typically no objective method is used with these plots for assessing if a plotted point is associated with a nonzero effect. Firstly, we provide an analysis of the plotting positions used in constructing these plots. Based on the results of our study, we recommend a set of plotting positions to be used with the normal probability plot. We also suggest that these results would apply to half-normal plots and recommend a set of plotting positions to be used with this plot. Secondly, we give a method for selecting critical values so the plot can be used to objectively assess which effects, if any, are nonzero. Some examples are given illustrating the use of our method.
"]},{"key":"dc:title","label":"Title","values":["Analyzing Unreplicated Two Level Factorial Designs"]}]}],"canonical_facts":{"dc:contributor":["Broderick O. Oluyede","Patricia B. Humphrey"],"dc:creator":["Vora, Minal A."],"dc:date.available":["1970-01-01T08:00:00Z"],"dc:description.abstract":["Normal and half-normal probability plots are often used in analyzing unreplicated two level factorial and fractional factorial designs. Typically no objective method is used with these plots for assessing if a plotted point is associated with a nonzero effect. Firstly, we provide an analysis of the plotting positions used in constructing these plots. Based on the results of our study, we recommend a set of plotting positions to be used with the normal probability plot. We also suggest that these results would apply to half-normal plots and recommend a set of plotting positions to be used with this plot. Secondly, we give a method for selecting critical values so the plot can be used to objectively assess which effects, if any, are nonzero. Some examples are given illustrating the use of our method.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd_legacy/38"],"dc:subject":["ETD","Critical values","Estimated percentiles","Normal distribution","Order statistics","Probability plot","Mathematics"],"dc:title":["Analyzing Unreplicated Two Level Factorial Designs"],"thesis:degree_discipline":["Department of Mathematics"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics"]},"updated_at":"2026-07-24T02:28:15Z"}