• ordinary random variation.
• statistical significance
When the difference between the results for the two
treatments is so large that it would be rare to see such a
difference by ordinary random variation, we say that the
results are statistically significant.
Other Random Sampling Designs (other than Simple Random
• Cluster Random Sampling
• Stratified Random Sampling
Retrospective Observational Studies (backward looking)
Prospective Observational Studies (forward looking)
Multifactor Experiments
Matched Pairs Designs
Blocking Designs
• Law of Large Numbers
As the number of trials increases, the proportion of
occurrences of any given outcome approaches a particular
number “in the long run”.
(We need to assume that the outcome of any one trial does
not depend on the outcome of any other trial.)
• Probability
With a randomized experiment or a random sample or other
random phenomenon (such as a simulation), the probability
of a particular outcome is the proportion of times that the
outcome would occur in a long run of observations.
• Independent Trials
Different trials of a random phenomenon are independent if
the outcome of any one trial is not affected by the outcome of
any other trial.
How to Find Probabilities?
• In practice, the sample proportion estimates the actual
• Sample Space
For a random phenomenon, the sample space is the set of all
possible outcomes.
• Event
An event is a subset of the sample space.
Probabilities for a Sample Space
• The probability of each individual outcome is between 0 and 1.
• The total of all the indicidual probabilities equals 1.
Probability of an Event
• The probability of an event A, denoted by P(A), is obtained
by adding the probabilities of the individual outcomes in the
• When all the possible outcomes are equally likely,
P(A) =
number of outcomes in event A
number of outcomes in the sample space
In practice, equally likely outcomes are unusual.