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**preview**shows half of the first page. to view the full**1 pages of the document.**CH1 – THE STATISTICAL IMAGINATION

FIELD OF STATISTICS – set of procedures for gathers, measuring,

classifying, coding, computing, analyzing and summarizing systematically

acquired numerical information

o Goal: balanced perspective w/ precision in gathering/presenting info

Counters perceptions of reality distorted by subjective feelings,

biases, prejudices

Linking the Statistical Imagination to the Sociological Imagination

Sociological Imagination – An awareness of relationships of the individual

to the wider society and to history

o Recognize individual behavior is conducted in relationship to larger

social structures

o i.e. see isolated detail as part of larger picture

STATISTICAL IMAGINATION – Appreciate how usual/usual an event,

circumstance, or behavior is in relation to a larger set of similar events and

an appreciation of an event’s causes and consequences

o Involve prediction, inference, probabilistic thinking,

o Req. keep track of details minimize error

o Understand most events are predictable

Occurrence probability based on long-term trends/circumstances

o Understand broader picture of reality, to overcome

misunderstandings, prejudices, narrow-mindedness

Statistical interpretation must take into account circumstances of a

phenomenon, incl. social values of society or groups w/i it

o Social values may limit/enlarge human response to a statistic

o Normative Statistic – culturally bound, its interpretation depends on

the place, time and culture in which it is observed

o Social Norm – a shared idea of the behavior that is appropriate or

inappropriate in a given situation in a given culture

Statistical Norm – a phenomenon’s average rate of occurrence

o Differ btwn societies, groups b/c influenced by social norm

o An existent average

o Ex. US IMRs high amongst MEDCs, low amongst all nations

Statistical Ideal – a phenomenon’s socially desired rate of occurrence

o Influence by Social Values – Shared ideas among the members of a

society about the way things ought to be

Ex. States: freedom, equality, material comfort

o Often substitute statistical norms

o Statistical ideal debates may reveal underlying conflicts/opinions on

social values

Statistics and Sciences: Tools for Proportional Thinking

STATISTICS – observing & organizing systematically acquired numerical info

o Statistics gathering follow carefully controlled procedures

Need sample proportional to entire study population

Data – systematically acquired information that is organized by following

procedures of science and statistics

Statistical analysis vital to scientific method

o Follow procedures, make precise measurements of & accurate

prediction on events

o Always incl. knowing limitations of reasoning & mathematical

procedures influence on predictions

Statistics results w/ range of error, degree of confidence

o STATISTICAL ERROR – know degrees of imprecision in the procedures

used to gather and process information

Descriptive Statistics – how many observations were recorded & how

frequently each score or category of observation occurred in the data

Inferential Statistics – show cause-and-effect relationships and to test

hypotheses and scientific theories

draw conclusions on something

o Computed descriptive statistics

Science – a systematic method of explaining empirical phenomena

o Empirical – observable and measurable

o Social science use w/ indirect measurements b/c intangible focuses

Ex. survey questionnaires to measure opinions, knowledge,

attitudes, behavior

o Scientific Theory – a set of interrelated, logically organized statements

that explain a phenomenon of special interest and that have been

corroborated through observation and analysis

Theories describes situations, organized explanation of facts

Ideas constituting a theory is tested vs. observable facts

Corroborated theory = its ideas successfully predict

observable facts

Adequate scientific theory accomplishes:

1. Provide understanding of phenomenon: how, when,

why, occurs under what conditions

2. Allows make empirical predictions, w/ similar cases

o Scientists also skeptics: req. critical & doubting attitude

Tolerate uncertainty & not draw quick conclusions

Informed Common Sense – used in science, that which is

weighed and double check against carefully gather data

VARIABLES – measurable phenomena that vary (changes) over time or that

differs btwn places & individuals

o Represented by capital English letters –ex. X = gender

o Subjects’ feature, where subject = people or objects

o Variation – how much the measurement of a variable differ among

study subjects

o Constants – characteristic of study subjects that do not vary

Could be intentional as control variables, isolate effects

o Dependent Variable – want to explain this variable’s variation

o Independent Variable – predictor variables that are related to/predict

variation in the DV

o HYPOTHESIS – a predication about the relationship of two variables,

asserting that differences among the measurements of an IV will

correspond to differences among the measurements of a DV

Myth – widely held beliefs that are false

Research Process

o 1. Specify the Research Question

o 2. Review the Scientific Literature

Check propose research is not redundant/overlap

o 3. Propose a theory and state hypotheses

Hypotheses generated by theory, establish facts in scientific lit.

If research outcomes match theory direct data expectations, then

theory corroborated

Exploratory Studies – solve immediate practical problem, explore

new phenomena that’s unknown w/ no theoretical basis

Use loose organize ideas/question, doesn’t employ theory

o 4. Select a Research Design

o 5. Collect Data

o 6. Analyze the data and draw conclusions our concern

o 7. Disseminate the results, to public & scientific community

Publication process incl. strenuous peer review w/ checks &

balances, ensure accurate/un-bias

Proportional Thinking: Calculating Proportions, Percentages, Rates

Proportional Thinking – weighing the part against the whole, calculating

the likelihood of the phenomenon occurring over the long run

Mathematical Proportions – division problems that weight a part (the

numerator) against a whole (the denominator)

o FRACTION – a way of expressing what part of the whole (or total

number) a category of observations constitutes

PROPORTION (p) – part of the total amount or number of observation,

expressed in decimal form; denominator out of 1

o PERCENTAGE (%) – a proportion multiply by 100; denominator of 100

RATE OF OCCURRENCE – the frequency of occurrences of a pheromone in

relation to some specified, useful “base” number of subjects in a population

p = proportion of total group in a category

o ex. p = 0.00000018, then:

p(10 million) = 1.8 per 10million

The Problem of Small Denominators

Percentage change

o If initial sample small, small changes would appear large

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