Chapter 1 - Collecting Data

Statistics

the science and art of collecting, analyzing, and drawing conclusions from data.

Plausible

believable

The statistical problem-solving process

consists of four steps:
1. Ask questions
2. Collect/consider Data
3. Analyze Data
4. Interpret Results

an individual

a person, animal, or thing described in a set of data.

a variable

any attribute that can take different values for different individuals.

categorical variable

takes values that are labels, which place each individual into a particular group, called a category.

quantitative variable

takes number values that are quantities—counts or measurements

population

in a statistical study is the entire group of individuals we want information about

census

collects data from every individual in the population

sample

a subset of individuals in the population from which we collect data

observational study

observes individuals and measures variables of interest, but does not attempt to influence the responses

experiment

deliberately imposes treatments (conditions) on individuals to measure their responses.

convenience sample

consists of individuals from the population which are easy to reach

bias

shown by the design of a statistical study if it is very likely to under or overestimate the value you want to know

voluntary response sample

a sample that consists of people who choose to be in the sample by responding to a general invitation

random sample

consists of individuals from the population who are selected for the sample using a chance process

Nonresponse

occurs when an individual chosen for the sample can’t be contacted or refuses to participate

Response bias

occurs when there is a consistent pattern of inaccurate responses to a survey question.

Sampling Variability

the cause for random samples of the same size from the same population producing different estimates

What are the steps to SRS?

1. Label each individual based on population size from 1 to n

2. Use a random number generator to obtain x amount of integers.

3. Select each individual according to each corresponding integer that was randomly selected.

inference

the process of drawing conclusions about a population on the basis of sample data.

stratified random sampling

selects a sample by choosing an SRS from each stratum and combining the SRSs into one overall sample

strata

a group of individuals in a population that share characteristics thought to be associated with the variables being measured in a study

cluster random sampling

selects a sample by randomly choosing clusters and including each member of the selected clusters in the sample

cluster

a group of individuals in the population that are located near each other

Systematic random sampling

response variable

measures the outcome of a study

explanatory variable

can help explain or predict changes in a response variable

treatment

a specific condition applied to the individuals in an experiment

experimental unit

the object to which a treatment is randomly assigned, for example, humans are typically referred to as subjects

placebo

a treatment that has no active ingredient but is otherwise like other treatments

control group

a group used to provide a baseline for comparing the effects of other treatments.

placebo effect

describes the fact that subjects will respond favorable to any treatment, even an inactive treatment

double blind experiment

an experiment where neither the subjects nor those who interact with them and measure the response variable know which treatment a subject is receiving. (both don’t know)

single blind experiment

an experiment where either the subjects or the people who interact with them and measure the response variable don’t know which treatment a subject is receiving (one knows, the other doesn’t)

random assignment

means that treatments are assigned to experimental units using a chance process

completely randomized design

an experiment where the experimental units are assigned to the treatments completely at random.

statistically significant

describes an observed difference between groups in an experiment so large that is unlikely to be explained by chance variation in random assignment.

block

a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to treatments

experimentation with blocks

1. Form Blocks

2. Randomly assign treatments to experimental units within blocks

3. Record and compare results

matched pairs design

a common experimental design that uses blocks of size 2.

replication

the idea that we should use enough subjects to create roughly equivalent groups in an experiment