1Sociology 357Methods of Sociological InquiryLectures Notes #2Basic ConceptsUnits of Analysis• The objects we study• People• Families• Cities• Newspaper articles• Classes (in school)Variables• Dimensions or aspects of units of analysis which vary. Variables MUST vary.• Formal definition of a variable is a set of exhaustive and mutually exclusivecategories. – Every unit of analysis must fall into exactly one category of a variable.• Variables are defined by researchers2Examples of VariablesMean to nearest dollarAverage incomeCensus tractpercentage to nearest whole percent, or categorize:<20% female20-50% female51-80% female>80% femalesex composition (% female)organizationblue, brown, green, hazel, etceye colorindividualexact income to nearest dollar or categories, e.g.< $10,000$10,000 - $24,999$25,000 - $34,999 incomeindividualCATEGORIES OF VARIABLEVARIABLEUNIT OF ANALYSISLevel of Measurement• Nominal. Exhaustive & mutually exclusive categories. E.g. Eye color, major, sex/gender.• Ordinal. Nominal + ranks. Course grade (A, AB, B etc.); course level (E, I, A)• Interval. Ordinal plus meaningful metric so distance between 1 & 2 = distance between 23 & 24. Few examples: temperature scales.• Ratio. Interval + true zero. Height in inches, income in dollars, number people enrolled in a class.Qualitative/ Quantitative• Qualitative = Nominal + ordinal = qualitative. Can do frequencies, percentages, proportions, mode. • Quantitative = Interval + ratio Can do qualitative + means, standard deviations, correlations, all other statistics. • Very few statistics especially for ordinal. Ordinal variables with 5+ categories can usually be assigned numbers and treated as interval.3Propositions•A proposition is a statement about variables.•Aunivariateproposition is a statement about one variable at a time. "Most UW students drink beer at least once a week." Variable: frequency of beer drinking. UOA: individual, UW students. Statement: "most" drink once a week or more.Bivariate Proposition•A proposition is a statement about variables.•A bivariateproposition is a statement about the relation between two variables. "Males drink beer more often than females." Variables: 1) sex, 2) frequency of beer drinking. Statement: gives relation between them.Multivariate Proposition•A proposition is a statement about variables.•A multivariateproposition states a complex relation among three or more variables. "Among non-depressed students, males drink beer more often than females, but among clinically depressed students, males and females drink beer equally often." Variables: 1) sex, 2) frequency of beer drinking, 3) whether clinically depressed or not.4Hypothesis•A hypothesis is a type of proposition.• Some use proposition and hypothesis as synonyms. • I use hypothesis to mean the proposition being tested in a particular research project. This is the most common usage.• Some use hypothesis to mean a proposition whose truth is uncertain.• (Stern uses hypothesis for the bivariatefinding of a project, even if it is an after-the-fact result.)General Form of a Hypothesis• Conceptual: For population P in condition C, independent variable X causes dependent variable Y.• Operational: For sample p in condition c, independent variable x has a statistical association with dependent variable y.Qualitative Relations• Used with qualitative variables. • Need to be stated in words, listing which categories of one variable have more or fewer units of analysis in each category of the other variable. • Ex: Blacks are more likely to be Democrats than whites are. Variables: race, party choice.• Percentages5Quantitative Relationships -1• Between quantitative variables• Positive = when variable one is greater, the other tends to be too. Height is positively correlated with weight. On the average, taller people weigh moreHeightWeightQuantitative Relationships - 2• Negative = when one variable is greater, the other tends to be smaller. The speed of performing a task is negatively related to accuracy. On the average, the faster you work, the more mistakes you make.Time to complete taskNumber of errorsQuantitative Relations - 3•A curvilinear relation can be any non-linear relation, but is especially a relationship that is first positive then negative, or vice versa. AgeEducationThere is a curvilinear relation between age and education in the US: education rises with age but, because of historical increases in education rates, older adults have less education than younger adults.6• To operationalize a variable is to say how you will measure it• To measure a variable is to use specific observational or operational procedures• The operationalization of a concept is the same thing as its measure or measurement• This has two partsOperationalization=MeasurementOperationalization Part I• First, the procedures for collecting data (e.g. observe, ask questions)• Question: “How often have you smoked marijuana?” vs “Have you every smoked marijuana?”• Observation of fidgets: Take motion picture, count frames in which position changes vs. observe face to face, count number of times hands touch head.Operationalization Part II• Exact distinctions among categories of variables within a procedure• If counting, how you tell the beginning and end of countable things• If distinguishing among types of actions or characteristics, must develop rules for an exhaustive and mutually exclusive set of different types7Operational Variables are Created by Researchers• No measured variable is “natural.” All have to be created by the decisions of the researcher. (But some are easier to operationalize than others.)• Researcher makes sure the categories are exhaustive and mutually exclusive• Researcher decides how precise to bePrecision vs. Accuracy• A more precise variable makes finer distinctions. – Height in inches instead of feet. – Shadings of eye color grey-blue, sky blue, deep blue, violet-blue, blue-green, pure green, yellow-green, light brown, dark brown etc. instead of broad groups blue, brown, hazel• Accuracy is correct classification into the category.• Tradeoff between precision and accuracy. Harder to be accurate with finer distinctions.Range• Categories must be exhaustive, so must encompass the full range the subjects exhibit• “Other, ” “over $100,000,” and “not applicable” are ways to
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