Exam 1 Definitions

Chapters 1 and 2

Definition of Statistics

The science of collecting, organizing, and analyzing and interpreting data to make decisions

What does data consist of?

Data consists of information coming from observations, counts, measurements, or responses

What are the two types of data sets?

Population and Sample

Definition of Population

The collection of all outcomes, responses, measurements, or counts that are of interest

Definition of Sample

A subset, or part, of the population

Why is a sample used?

To gain information about a population

Definition and example of a parameter

A numerical description of a population  characteristic.

Average age of all people in the United States

Definition and example of a statistic

A numerical description of a sample characteristic.

Average age of people from a sample of three states

What are the steps to designing a statistical study?

1. Identify the variable(s) of interest (the focus) and the population of the study.

2. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population.

3. Collect the data.

4. Describe the data using descriptive statistics techniques.

5. Interpret the data and make decisions about the population using inferential statistics.

6. Identify any possible errors.

What happens in an observational study?

• A researcher observes and measures characteristics of interest of part of a population.

• Researchers measured the amount of time people spent doing various activities without influencing the responses

What happens in an experiment?

A treatment is applied to part of a population, called a treatment group, and responses are observed.

What is the control group?

A group in which no treatment is given

What are subjects in an experiment called?

Experimental units

Definition of placebo

A harmless, fake treatment that is made to look like the real treatment

Types of data collection

Simulation

Survey

What happens in a simulation experiment?

• Uses a mathematical or physical model to reproduce the conditions of a situation or process.

• Often involves the use of computers.

• Allow you to study situations that are impractical or even dangerous to create in real life.

What happens in a survey?

• An investigation of one or more characteristics of a population.

• Surveys are carried out on people by asking them questions.

• Commonly done by interview, Internet, phone, or mail.

• In designing a survey, it is important to word the questions so that they do not lead to biased results, which are not representative of a population.

What are three key elements of a well-designed experiment?

Control, randomization, and replication

What is a confounding variable(s)?

• Occurs when an experimenter cannot tell the difference between the effects of different factors on a variable.

What is the placebo effect? What can be done to minimize the placebo effect?

• occurs when a subject reacts favorably to a placebo when in fact the subject has been given a fake treatment.

• To help control or minimize the placebo effect, a technique called blinding can be used

What is blinding?

• Blinding is a technique in which the subjects do not know whether they are receiving a treatment or a placebo

What is a double-blind experiment?

• Double-blind experiment neither the subject nor the experimenter knows if the subject is receiving a treatment or a placebo.

Definition of randomization

• A process of randomly assigning subjects to different treatment groups.

What is a completely randomized design?

• Subjects are assigned to different treatment groups through random selection.

What is randomized block design?

• Divide subjects with similar characteristics into blocks, and then within each block, randomly assign subjects to treatment groups.

What is matched-pairs design?

Subjects are paired up according to a similarity.

One subject in the pair is randomly selected to receive one treatment while the other subject receives a different treatment

Sample size definition

Number of subjects in a study

What is replication?

• The repetition of an experiment using a large group of subjects.

Census definition

Count or measure of an entire population

Sampling definition

A count or measure of part of a population and is more commonly used in statistical studies

Sampling error definition

The difference between the results of a sample and those of the population

Random sample definition

Every member of the population has an equal chance of being selected.

Simple random sample definition

Every possible sample of the same size has the same chance of being selected.

How can random numbers be generated?

By a random number table, a software program, or a calculator

Explain how to use stratified sampling

• Divide a population into groups (strata) and select a random sample from each group.

Explain how to use cluster sampling

• Divide the population into groups (clusters) and select all of the members in one or more, but not all, of the clusters.

Explain how to use systematic sampling

• Choose a starting value at random. Then choose every k^th member of the population.

What is convenience sampling?

Choosing only members of a population that are easy to get

What is a problem with convenience sampling?

Often leads to biased studies

What is a frequency distribution?

It is a table that shows classes of data entries with a count of the number of entries in each class

What is a class in statistics?

An interval of data

What is the frequency(f) of a class?

The number of data entries in the class

What is the lower limit of a class?

The least number that can belong to the class

What is an upper limit of a class

The greatest number that can belong to the class

What is the class width?

The distance between lower(or upper) limits of consecutive classes

What is the range(definition)?

The difference between the maximum and minimum data entries

Do classes over lap in frequency distribution?

No, classes do not overlap

What is the usual number of classes? Why?

Between 5 and 20, otherwise it may be difficult to detect any patterns

How to find the class width?

Determine the range of data

Divide the range by the number of class

Round up to the next convenient number

Midpoint definition

Sum of the lower and upper limits of the class divided by two

Midpoint formula

(lower class limit + Upper class limit)/2

What is relative frequency?

Relative frequency of a class is the portion, or percentage, of the data that falls in that class

Formula for relative frequency

Class frequency(f)/sample size(n)

Cumulative frequency definition

The sum of the frequencies of that class and all previous classes

What is the cumulative frequency of the last class equal to?

The sample size, n(n= sum of all values)

What is a frequency histogram?

It is a graph of the frequency distribution that is used to represent the frequency distribution of a data set

What are class boundaries?

The numbers that separate classes without forming gaps between them

What is a frequency polygon?

A line graph that emphasize the continuous change in frequencies

What is a relative frequency histogram?

Has the same shape and the same horizontal scale as the corresponding frequency histogram

the vertical scale measures the relative frequencies, not the frequencies

What is another name for a cumulative frequency graph

Ogive

What is an ogive?

A line graph the displays the cumulative frequency of each class at its upper class boundary

What is a cumulative frequency graph used for?

To describe the number of data entries taht are less than or equal to a certain value

What is the measure of central tendency?

A value that represents a typical, or central, entry of a data set

What are the three most commonly used measures of central tendency?

Mean, median, and mode

What is the mean of a data set?

The sum of the data entries divided by the number of entries

What is the median?

The value that lies in the middle of the data when the data set is ordered

Measures the center of an ordered data set by dividing it into two equal parts

How to find the median?

Odd number of entries: median is the middle data entry

Even number of entries: median is the mean of the two middle data entries