Slide 1StatisticsDescriptive StatisticsStatistical Argument FormsParts of a Statistical ArgumentAn ExampleThe PartsStandard FormStatistical vs. Analogical ArgumentsStatistical vs. Analogical ArgumentsAn ExampleStandardizationEvaluating Statistical ArgumentsTrue Premises TestProper Form TestRepresentative SamplesGuideline 1: SizeGuideline 2: VarietySampling TechniquesSimple Random SampleStratified Random SampleSystematic SampleVoluntary Response SampleHaphazard SampleConvenience SamplePurposive SampleCensusA Brain-TeaserPracticeArgument Type (and Parts)StandardizationTrue Premises TestProper Form TestOverall AssessmentP H I L 1 0 1 0B L A K E N E S P I C AC H . 8 : S TAT I S T I C A L A R G U M E N T SCRITICAL THINKINGStatisticsStatistics is the a set of scientific and mathematical procedures for collecting, analyzing, and reporting data.Descriptive Statistics report and analyze data about things people have observed.Argumentative Statistics draw generalizations about things that have NOT been observed based on a sample of things that have been observed.Descriptive Statistics“Of the 1,086 full-time instructional faculty holding rank in academic departments at Georgia State University in 2007, women comprised 484 (or 44.6%) of those positions” (AOW Annual Report 2008).Descriptive:Makes observation of faculty at GSUOf total observed, reports how many are womenNo attempt to convinceNo conclusion about unobserved members of a groupStatistical Argument FormsGeneral:(1) P% of the N observed things in G have F.Therefore,(2) P% of all the things in G have F.Particular:(1) P% of the N observed things in G have F.Therefore,(2) P% of all the things in G have F.(3) X is a thing in G.Therefore,(4) There is a P% chance that X has F.Here, “P” and “N” refer to some number, while “G” refers to a group and “F” refers to a feature.Parts of a Statistical ArgumentThe sample is all the observed things in G.N is the number of things in the sample.The relevant property, F, is the feature or features P% of things in the sample have.The target is all of the things in G. P is the percentage of the things that (are shown to) have F.In a General Statistical Argument, the target is the thing about which we’re attempting to draw a conclusion.Note: N and P may not always be expressed with a number: e.g., “all,” “most,” “many,” “some.”An Example“In a survey of 1,000 students at Georgia State University, researchers found that almost 70% of them played console videogames regularly. The percentage who played videogames regularly increased to 80% when considering PC and cell phone games. The researchers conclude that 80% of college students play some form of videogames regularly” (Made Up Study, 2013). H/t: Zack HopperThe PartsSample: Students at GSUN: 1,000.Relevant property: Playing video games regularly.Target: All college students.P: 80%Argumentative Statistic: Reasons from observation of 1,000 observed GSU students to a conclusion about all college students.Standard Form(1) 80% (P) of the 1,000 (N) college students surveyed (sample) play videogames regularly (F).Therefore,(2) 80% of all college students (target) play videogames regularly. (3) Argle is a college student.Therefore,(4) There is an 80% chance that Argle plays videogames regularly.Statistical vs. Analogical ArgumentsIn a statistical argument, one group (the sample) is being compared to another group (the target), where the first group is a subgroup of the second.In an analogical argument, one group is being compared to another group, but neither is a subgroup of the other.Statistical vs. Analogical ArgumentsOften, however, statistical and analogical arguments are combined.Scientists often attempt to reach conclusions about humans by conducting tests on animals.They rely on a statistical argument that the results observed in the sample generalize to the entire animal species.They also rely on an analogical argument that the animal species is sufficiently similar to humans in relevant ways to permit the conclusion of the statistical argument to be extended to humans.An ExampleA new chemotherapy drug, Tum-away was administered to 800 rhesus macaques (monkeys) with virally induced orbital lymphoma. 75% of the monkeys went into full remission. Because rhesus and human eyes are similar in structure, tissue composition, and photoreceptor distribution, it is likely that this new drug could prove extremely beneficial to roughly ¾ of humans diagnosed with orbital lymphoma.Standardization(1) 75% of the 800 rhesus macaques with orbital lymphoma in the study went into remission after treatment with Tum-away.Therefore,[2] 75% of all rhesus macaques with orbital lymphoma will go into remission after treatment with Tum-away.(3) Rhesus macaques have eye structure x, tissue composition y, and photoreceptor distribution z.(4) Humans have eye structure x, tissue composition y, and photoreceptor distribution z.Therefore,(5) 75% of humans with orbital lymphoma will probably go into remission after treatment with Tum-away.Evaluating Statistical ArgumentsLike all argument forms we’ll survey in this course, statistical arguments are evaluated according to:(1) The True Premises Test.(2) The Proper Form Test. “There are three kinds of lies: lies, damned lies, and statistics.”True Premises TestPremises should be evaluated according to what kinds of statements they are (see Ch. 3 for a refresher). The general form of a statistical argument has only one premise. Usually, it will be a testimonial statement and/or an expert statement (e.g., a report by a scientist on his or her findings, or a secondary report by a journalist or other writer).Proper Form TestA statistical argument passes the Proper Form Test when:(1) It can be put into the General or Particular standard form.(2) The sample used in the argument is sufficiently representative. Remember: because statistical arguments are inductive, they may pass the Proper Form Test to a greater or lesser degree.Representative SamplesA sample is representative when the proportions of every subgroup in the target are exactly matched by the proportions of the subgroups in the sample. A sample that fails to meet this criterion is biased.Two helpful guidelines:(1) Size(2) VarietyGuideline 1: