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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?
Label each individual based on population size from 1 to n
Use a random number generator to obtain x amount of integers.
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
Form Blocks
Randomly assign treatments to experimental units within blocks
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
