Statistics Exam Terms

Experimental Unit

Experimental Unit

An object (person, thing, event, transaction, etc.) upon which we collect data

Population

A set of units (usually people, objects, transactions, or events) that we are interested in studying

Sample

A subset of the units of a population

Parameter

A summary measure (i.e., an average, a proportion, etc.) that reflects the entire population

Statistic

Summary measure is determined using the data collected from the sample

Examples of Populations

All people in the U.S. (each person is an experimental unit)

All U.S. males age 18-35

All sales made by the ND Bookstore last week

Variable

A characteristic or property of an individual unit. Often notated with capital letters such as X or Y.

Examples of Variables

What is your eye color?

How much cash do you have on you?

Do you suffer from diabetes

Qualitative/Categorical

Data collected on non-numerical variables. Can be expressed in words

Quantitative

Data collected on numerical variables, Can be mathematically summarized

Nominal

No “order” exists for the categories

Ordinal

The values can be ordered (arranged from lowest to highest)

Discrete

Can list the possible values and the pattern of values (i.e., integers)

Continuous

The possible values can be any value in a range, with any number of decimal places

Published sources

Includes government agencies such as the U.S. Census and Bureau of Labor Statistics, newspapers, academic journals, universities, and websites

Designed Experiment

The researcher actively imposes a treatment on the sample units.

Observational Studies

The researcher does not actively impose treatment on the experimental units, but records the values of the variable of interest.

Sample Surveys

A researcher can also conduct surveys via mail, telephone, e-mail, or in-person interviews

Simple Random Sample

A sample selected from the population in such a way that every sample of size n has an equal chance of selection

Selection Bias

This results when some subset of the experimental units in the population is excluded so that these units have no chance of being selected in the sample

Nonresponse Bias

This occurs when the researcher conducting the survey or study are unable to obtain data on all experimental units selected for the sample.

Measurement Error

This refers to inaccuracies in the values of the data recorded. Errors may be due to ambiguous or leading questions.

Experiment

A planned operation carried out under controlled conditions

Outcomes

A single result of an experiment

Sample Space

The set of all possible outcomes

Event

One or more of the outcomes

Probability

The predicted chance (or long-term relative frequency) of an event.

Probabilities must be…

values between 0 and 1, inclusive: 0<or equal P(A) < or equal 1

Probabilities of all outcomes must add to

1

Classical

All outcomes are assumed equally likely

Empirical

Probabilities are based on results of a random sample

Subjective

An expert provides the probabilities

Intersection of two events (A and B):

the group of outcomes in both A and B

Union of two events (A or B):

the group of outcomes in A or B (or both)

Complement of an Event, A: A' =

the group of outcomes NOT in A

Conditional Event, A/B:

A occurs given that B i s known to occur

Mutually Exclusive Events:

A and B have no overlap

Independent Events:

Knowing that A has occurred does not affect the probability ofB (and vice-versa).

Mutually Exclusive

Events that cannot occur at the same time.

Contingency Table

Provides a way of portraying data that can facilitate calculating probabilities

Tree Diagram

A special type of graph is used to determine the outcomes of an experiment

Venn Diagram

A picture that represents the outcome of an experiment. Generally consists of a box that represents the sample space S together with circles or ovals

Random Variable

A numerical description of the outcome of an experiment.

Discrete Random Variable

The possible values are distinct, predictable, and can be listed. The number of values can be either finite or infinite. Probabilities can be assigned to each value, but they might not be equal.

Continuous Random Variable

The possible values cannot be listed individually since the variables can take on any value in a range. It is not possible to list every distinct value. The number of values is always infinite and the probability of any specific value is zero.

Probability Distribution

A table, graph, or formula that specifies the probability associated with each possible value that the random variable can assume

Requirements for the Probability Distribution of a Discrete Random Variable X

0< or equal p(x) < or equal 1 , for all x

All x p(x) =1 , where the summation of P(x) is over all possible values of x

Characteristics of a Binomial Random Variable

1. The experment consists of n identical trials

2. There are only 2 possible outcomes on each trial. We denote one outcome by S (or 1) for success, and F (or 0) for failure.

3. The probability of success is constant from trial to trial. This probability is denoted by p, and the probability of failure is

q= 1-p

4. The trials are independent → The binomial random variable x represents number of successes in n trials

Unimodal

only has one peak in the distribution

Bimodal

has two peaks in the distribution

Multi-modal

a multimodal distribution is a probability distribution with more than one mode

frequency

the number of observations in a data set falling in a particular category

relative frequency

frequency divided by the total number of observations in the data set.

n

the number of data observations

percentage frequency

class relative frequency multiplied by 100