1 Statistics A new language Specific notations that differ across disciplines Statistics and math are very different

BASIC ALGEGRA CONCEPTS AND NOTATIONS Definition of Subtraction: a - b = a + (-b) Multiplicative Inverse: a * (1/a) = 1 (a≠0) Multiplication times 0: a * 0 = 0 Associative of Multiplication: (a * b) * c = a * (b * c) Commutative of Multiplication: a * b = b * a Distributive Law: a(b + c) = ab + ac Definition of Division: a / b = a(1/b) 2

Polynomial Identities (a+b) 2 = a 2 + 2ab + b 2 (a+b)(c+d) = ac + ad + bc + bd a 2 - b 2 = (a+b)(a-b) (Difference of squares) (x + a)(x + b) = x 2 + ax + bx + ab ax 2 + bx + c = 0 (Quadratic Formula) 3

Powers x a x b = x (a + b) x a y a = (xy) a (x a ) b = x (ab) x (a/b) = bth root of (x a ): Example X (1/2) = √X x (-a) = 1 / x a x (a - b) = x a / x b 4

5 where does the term statistics come from? 17th century European studies (England and France) that attempted to calculate population size and life expectancy. Analysts tried to count births, deaths and marriages because they believed that the growing population was evidence of a healthy state.

6 Those who conducted such numeric studies- as well as other, nonquantitative analyses of social and political prosperity-came to be called statists. over time, the statists social research led to the new term for quantitative evidence; statistics.

7 Why the boom in statistics by both professionals and laymen? –numbers offered a kind of precision. –an authoritative way to describe social problems –the media find numbers useful to make stories interesting, seem important "sound bite' –Statistics can appear to be factual/unbiased

Garbage in Garbage Out Statistics requires good data What do we mean by that? Sample is representative –Randomly selected –Response rate is unbiased –Questions are not leading Measures are clearly connected to concepts Measures are reliable and valid 8

9 Developing Measures Conceptualization Nominal Definition Operational Definition Measurement in the Real World

10 Conceptualization Process of specifying what we mean when we use particular terms. Produces an agreed upon meaning for a concept for the purposes of research. Describes the indicators we'll use to measure the concept and the different aspects of the concept.

11 Babbie’s Example Anomie What does this mean? Societal condition of normlessness; social instability How do we define this concept? Durkheim uses it to describe societies Others use it to describe individuals –Some experience anomie

12 Anomie How do we measure anomie? Ask respondents if they agree with a set of statements See page 142 (Chapter 5) in Babbie –The lot of the average man is getting worse –Not fair to bring children into world the way things look for the future –Don’t know who you can count on –Public officials not interested in problems of average man

13 Political Science Example Political Apathy What does this mean? How are we going to measure this concept

14 Concepts A concept may have multiple dimensions –Religiosity examples –A belief dimension –A ritual dimension –A knowledge dimension Indicators –How do we observe religiosity? –Attending religious services Complex concepts are likely to have multiple dimensions and require multiple indicators

15 Reliability GENERAL DEFINITION: - Accuracy or precision of a measuring instrument. - Consistency - Similar results: stability, dependability predictability

16 Tests for Checking Reliability Test-retest method - take the same measurement more than once. Equivalence: use "essentially the same" measurement items on the same instrument or on different instruments and compare the answers (same time period). Split-half, Random half, alternate forms. Use established measures.

17 Internal Validity DEFINITION: the ability of the measuring instrument to measure one's theoretical concepts. METHODS OF ASSESSING VALIDITY: CRITERIAL-RELATED VALIDITY (predictive): predict to an outside criterion and compare the outcome to the outside criterion a. Concurrent: comparison to an existing or current outside criterion b. Predictive: comparison to a future outside criterion

18 Validity (cont.) CONTENT VALIDITY: representativeness of what is being measured to the intended concepts. Does it cover the range of meanings. FACE VALIDITY: obvious and self-evident content CONSTRUCT VALIDITY: degree to which a measure is related to other variables as expected within a system of theoretical relationships. A measure of martial satisfaction should be associated with a measure of marital fidelity. EXTERNAL -- concerned with the generalizability of the test/method

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