Download Introduction - Faculty of Health Sciences

Introduction to Statistics
Parameter: measurable characteristic of a population.
Population: all members of a definable group.
For statistical purposes a population must have
definable characteristics even if it is not possible
to measure the variable or even count the
number of members in the population.
Sample: subset or subgroup of a population.
Usually obtained by random sampling of a single
population.
Statistic: measurable characteristic of a sample.
E.g., height, weight, political affiliation, ethnicity,
aerobic capacity, strength, power, ....
Data or Data Set: collection of numerical and/or nonnumerical values (plural of datum).
Datum: single measured value (singular of data).
Statistics
Statistics: 1. plural of statistic, 2. science of conducting
studies to collect, organize, summarize, analyze and draw
conclusions from data.
Descriptive statistics: collection, description,
organization, presentation and analysis of data.
Inferential statistics: generalizing from samples to
populations, testing of hypotheses, determining
relationships among variables and making decisions,
uses probability theory to make decisions.
Hypothesis: “less than a thesis”, a testable
conjecture based on a theory.
Thesis: a dissertation or learned argument which
defends a particular proposition or theory.
Qualitative measurements:
typically non-numerical, subjectively measured,
judgmentally determined, categorical.
E.g., religious affiliation, teacher/professor
evaluations, emotional states, flavour, gender.
Quantitative measurements:
typically numerical, objectively measured, reliability
(repeatability or precision) and validity (accuracy) can be
evaluated against a criterion.
E.g., salary, course grade, foot size, IQ, age, girth.
Types of quantitative measures:
Constants: quantities with fixed characteristics.
Physical constants: G, c, h (Planck’s constant)
Mathematical constants: p, e, i
Variables: quantities whose characteristics vary.
Discrete variables: numerical variables that
have finitely many possibilities (usually
integers), countable many possible values
Examples: value of $ bills or coins, card count
Continuous variables: numerical variables that
have infinitely many possible values within
a range of values (numbers between –1 and
+1) or unbounded (Real numbers, numbers
greater than 0).
Examples: height, duration, angle (only a fixed
number of significant figures are reported).
Significant Figures:
When reporting numerical information, especially when
obtained by a calculator, usually only 3 or 4 digits are
required. The general rule that is accurate to 0.5% holds
that only 4 significant figures are needed if the first
nonzero number is a 1 and 3 when it is not.
Examples:
234 000, 1.234, 2.45, 0.003 45, 0.1234,
8910, and 56 100.
Exceptions are frequencies and counts when all digits are
reported and financial numbers, hich are too nearest
dollar or nearest cent depending on the amount.
Measurement Scales
Nominal: classifies data into mutually exclusive
(nonoverlapping), exhaustive categories in which no
ordering or ranking of the categories is implied.
E.g., colour, flavour, religion, gender, sex,
nationality, county of residence, postal code.
Ordinal: classifies data into categories that can be
ordered or ranked (highest to lowest or vice versa),
precise differences between categories does not exist.
E.g., teaching evaluations, letter grade (A+, A, A–, ...
F), judges scores (0–10), preferences (polls), skill
rankings.
Interval: numerical data with precise differences between
categories but with no true zero (i.e., zero implies absence
of quantity).
E.g., IQ (0 means could not be measured),
temperature (degrees Celsius), z-scores (0 is average
value), acidity (pH, 7 is neutral).
Ratio: interval data with a true zero, true ratios exist
E.g., height, weight, temperature (in Kelvins),
strength, price, age, duration.
Methods of Sampling
Random: subjects are randomly selected from a
population, all subjects have equal probability of being
selected, subjects may not be selected twice.
Systematic: subjects are numbered sequentially and
every nth subject is selected to obtain a sample of N/n
subjects (N is number of people in population).
Stratified: population is divided into identifiable groups
(strata) by some relevant variable (income, gender, age,
education) and each strata is sampled randomly in
proportion to the strata’s relative size in the population.
Cluster: subjects are randomly sampled from
representative clusters or regions of the population.
Economical method if subjects are widely dispersed
geographically.
Convenience: typically used in student projects and by
journalists, uses subjects that can be conveniently polled
or tested. Not suitable for pollsters or medical research.