Ch. 1: The Nature of Probability and Statistics

Biostats / D'Agostino

variable

a characteristic or attribute that can assume different values

population

consists of all subjects (human or otherwise) that are being studied

sample

a group of subjects selected from a population

descriptive statistics

consists of the collection, organization, summarization, and presentation of data

inferential statistics

consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions

qualitative variables

variables that have distinct categories according to some characteristics or attribute (non-number variables)

quantitative variables

variables that can be counted or measured (numbers)

discrete variables

values that can be counted (things you can’t count parts of ex: people)

continuous variables

variables that can be assumed an infinite number of values between any two specific values (fractions and decimals)

nominal level of measurement

classifies data into mutually exclusive (nonoverlapping) categories in which no order or ranking can be imposed on the data

ex: telephone numbers, zip code

ordinal level of measurement

classifies data into categories that can be ranked; however, precise differences between the ranks do not exist

ex: pizza size, restaurant ratings

interval level of measurement

ranks data, and precise differences between units of measure do exist however, there is no significant zero

ex: SAT scores, IQ tests, temperature

ratio level of measurement

possesses all the characteristics of interval measurement, and there exists a true zero. ratios also exist between the measurements (twice as much or half as much)

ex: weight, height, area, number of phone calls received,

random sample

a sample in which all members of the population have an equal chance of being selected

systematic sample

sample obtained by selecting every kth member of the population where k is a counting number

stratified sample

sample obtained by dividing the population into subgroups (strata) according to some characteristic relevant to the study—subjects selected at random from each subgroup

cluster sample

sample obtained by dividing the population into sections or clusters and then selecting one or more clusters at random and using all members in the cluster(s) as members of the sample

convenience sample

samples obtained by immediate availability and easy accessibility

ex: subjects chosen from same classroom, or outside of the mall

sampling error

difference between the results obtained from a sample and the results obtained from the whole population

nonsampling error

occurs when the data are obtained erroneously or the sample is biased

ex: equipment failure, biased questions

observational study

researcher observes what is happening or what has happened in the past and tries to draw conclusions based on these observations

pros and cons of observational studies

pros: natural setting, could be cheaper, useful for unethical or impossible situations

cons: no control over variables and outside factors, chances of bias or confounding variables, cant prove only correlate

experimental study

researcher manipulates one of the variables and tries to determine how the manipulation influences other variables (experimentation)

pros and cons of experimental studies

pros: control over variables,

cons: hawthorne (awareness of being in a study) and placebo (belief of having treatment) effect, confounding variables

independent/explanatory variable

in an experimental study; the variable that is being manipulated by the researcher

dependent/outcome variable

in an experimental study; the variable that is being studied for changes due to the changes of the independent variable (studied outcome)

confounding variable

a variable that influences the dependent/outcome variable but was not separated from the independent variable

ex: studying health effects on exercise but things like diet are not being taken into account

ways to minimize placebo effect:

double blinding and blocking

double blinding

subjects and researchers are not told which groups are given the placebos

blocking

dividing participants into groups (blocks) based on a characteristic

ex: separating genders for a medical study

suspect samples

very small samples → not representative of population

ambiguous averages

choosing between the mean, mode, median, midrange to best fit your conclusion (misleading)

changing the subject

using different values to represent how info is perceived

ex: 0.1% of GDP → $20 billion; one could look really small while the other looks really big (misleading)

detached statistics

stats without comparison

ex: 20% less fat (does not specify what it is being compared to → misleading)

implied connections

claims made on products that are not actually proven true

ex: “It may help with heart disease!” → was not even proven for the product (misleading)

faulty survey questions

questions that are too vague, biased, or encourage a type of response

ex: a question presents a negative view of somebody then asks the subject what they think of that person (misleading due to bias)