Math 146: Introductory Statistics questions and answers

Multiplication Rule for Independent Events

P(A and B)= P(A) x P(B)

P(A n B)

The probability that A and B BOTH occur.

Can only be used when events are independent.

If events are DISJOINT, P(A n B) = 0.

Addition Rule for Disjoint Events

P(A or B)=P(A)+P(B)

P(AUB)

The probability that A or B or BOTH occur.

Can only be used with DISJOINT events.

For nondisjoint events, see General Addition Rule.

relative frequency

The number of times a specific event occurred out of the total number of repetitions.

# of times A occurred / total number of repetitions

random experiment

An experiment that produces an outcome that cannot be predicted in advance.

sample space (S)

The list of all possible outcomes.

What must the probability of all outcomes in a sample space equal?

1

The Compliment Rule

P(not A)= 1-P(A)

or

P(A)= 1-P(not A)

Where the probability of an event and its complement equal 1.

Disjoint (mutually exclusive) events

Events that CANNOT occur at the same time/together.

e.g. Being both male and female.

Simpson Paradox

A phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.

Hawthorne effect

When people in an experiment behave differently than they would normally behave because they are aware that they are being observed.

observational study

Explanatory (Independent) variable is allowed to occur naturally, not controlled.

Values of the variable of interest are recorded as they naturally occur with NO researched interference.

Hard to establish causation because of lurking variables.

If possible, control for suspected lurking variables by studying groups of similar individuals separately.

experiment

The explanatory variable IS controlled by the researcher. Treatment is imposed.

Randomized assignment to treatments automatically controls for all lurking variables.

Marking researchers blind avoids conscious or subconscious influences on their subjective assessment of responses.

Optimal for establishing causation: Randomized double-blind experiment.

A lack of realism may prevent from generalizing results to real life.

Noncompliance may undermine results. Volunteer sample may help.

factor

The explanatory variable in an experiment

treatments (ttt)

Different imposed values of the explanatory variable.

e.g. Four different possible tobacco quitting methods

control group

In an experiment, the group that is NOT exposed to the treatment.

Contrasts with the experimental group and serves as a comparison for evaluating the effect of the treatment.

subjects

Human participants in an experiment.

confounding variable

A factor other than the independent variable that might produce an effect in an experiment.

"The lurking variable is confounded (tied in) with the explanatory variable's values."

sample survey

A type of observational study in which individuals report variables' values themselves, frequently giving their opinions.

prospective observational study

Seeks information about variables' values to occur in the future.

retrospective observational study

Seeks information about variables' values in the past.

sampling

Choosing a representative sample from the population of interest.

volunteer sampling

A sampling method where individuals self-select themselves to be included in a study.

Usually biased, so quite useless in terms of the population as a whole.

convenience sampling

Using a sample of people who are readily available to participate.

Fairly representative but often subtle bias exists due to specific reasons people may be in a certain location.

sampling frame

A list of all the elements in a population from which the sample is drawn.

e.g.

Population: Students taking Stat 101

Sampling frame: A list of the names of all the students taking Stat 101

systematic sampling

A type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed periodic interval ("sampling interval").

e.g. Every 50th name on a long list.

simple random sampling

Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample.

cluster sampling

Divides the population into even groups (clusters) and randomly selects a simple random sample of clusters for data analysis.

e.g. To sample HS seniors in a certain city, select 3 high schools at random among all HSs in the city, and use ALL HS seniors in each.

This method is only suitable if the groups are going to be heterogeneous (low variance between clusters).

stratified sampling

Used when the population is naturally dividied into subpopulations - "strata/stratum".

A simple random sample will then be chosen FROM each stratum (as opposed to using the entire cluster as in clusters sampling), resulting in a sample that contains all the random samples put together.