Statistics Ch. 10-12

random

random

when we know the possible values an outcome can have but not the particular value, free of human influence

simulation

models real-world situation by using random-digit outcomes to mimic the uncertainty of a response variable of interest

trial

sequence of several components representing events that we are pretending will take place

simulation component

uses equally likely random digits to model simple random occurrences whose outcomes may not be equally likely

response variable

values record the results of each trial with respect to what we were interested in

population

the entire group of individuals or items that we want to study or draw conclusions about

sample

a subset of individuals selected from a larger population, used to estimate characteristics of the whole population

sample survey

a method of collecting data by asking a subset of individuals from a population in order to infer insights about the entire group

bias

any systematic failure of a sampling method to represent its population (voluntary response, undercoverage, response bias, or nonresponse bias)

randomization

best defense against bias, all individuals given fair and random chance at selection

sample size

The number of individuals in a sample, determines how well the sample represents the population, not the fraction of the population sampled

census

a complete count of a population, typically conducted at regular intervals, to gather demographic and statistical information

population parameter

a value that summarizes a characteristic of the entire population, such as a mean or proportion, hope to estimate it from sampled data

statistic/sample statistic

a numerical value calculated from a sample, used to estimate a population parameter

representative

what a sample is said to be if the statistics computed from it accurately reflect the corresponding population parameters

simple random sample

sample in which each set of n elements in the population has an equal chance of selection

sampling frame

a list of individuals from whom the sample is drawn, individuals not in it cannot be in any sample

sampling variability

the natural tendency of randomly drawn samples to differ from one another, sometimes called sampling error though it is not an error

stratified random sample

a sampling design in which the population is divided into several subpopulations, random individuals are then drawn from each group, groups should be homogenous to reduce variability

cluster sample

entire groups chosen at random, a random sample of these heterogenous groups should be representative of the population, usually selected for convenience/cost

multistage sample

sampling schemes that combine several sampling methods

systematic sample

a sample drawn by selecting individuals with consistent variations from a sampling frame, when there is no relationship between the order of the sampling frame and the variables of interest, this can be representative

pilot survey

a small trial run of a survey to check whether questions are clear

voluntary response bias

bias introduced to a sample when individuals can choose on their own whether to participate in the sample

convenience sample

consists of the individuals who are readily available, often fail to be representative because every individual in the population is not equally easy to sample

undercoverage

a sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population

nonresponse bias

bias introduced when a large fraction of those sampled fails to respond, those who do respond are likely to not represent the entire population, voluntary response bias is a form of this

response bias

anything in a survey design that influences responses, one typical source arises from the wording of questions, which may suggest a favored response

observational study

a study based on data in which no manipulation of factors has been employed

retrospective study

an observational study in which subjects are selected and then their previous conditions or behaviors are determined

prospective study

an observational study in which subjects are followed to observe future outcomes, not an experiment because no treatments are applied, typically focus on estimating differences among groups that might appear as the groups are followed during the course of the study

experiment

manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels

random assignment

to be valid, an experiment must assign experimental units to treatment groups at random

factor

a variable whose levels are manipulated by the experimenter, experiments attempt to discover the effects that differences in these levels may have on the responses of the experimental units

response variable

a variable whose values are compared across different treatments

experimental units

individuals on whom an experiment is performed, usually called subjects or participants when they are human

level

the specific values that the experimenter chooses for a factor

treatment

the process, intervention, or other controlled circumstance applied to randomly assigned experimental units, the different levels of a single factor or the make up of combinations of levels of two or more factors (level → factor → ___)

principals of experimental design

control, randomize, replicate, block

completely randomized design

all experimental units have an equal chance of receiving any treatment

statistically significant

when an observed difference is too large for us to believe that it is likely to have occurred by chance

control group

the experimental units assigned to a baseline treatment level, typically either the default treatment, which is well understood, or a null, placebo treatment, provides basis for comparison

blinding

any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups

single blind

when every individual in either of these classes (influencing results or evaluating results) is blinded

double blind

when everyone in both classes (influencing results and evaluating results) is blinded

placebo

a treatment known to have no effect, administered to one group so that all groups experience the same conditions

placebo effect

the tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo

blocking

When subgroups of the experimental units differ in ways that may affect their responses to treatments, isolate the variability attributable to the differences between the groups so that we can see the differences caused by the treatments more clearly

randomized block design

the subjects are randomly assigned to treatments only within blocks

matching

in a retrospective or prospective study, subjects who are similar in ways not under study may be paired and compared with each other on the variables of interest, reduced unwanted variation similar to blocking

confounding

when the levels of one factor are associated with the levels of another factor in such a way that their effects cannot be separated