Chapter 1 Statistics

Front 1

Deterministic system

Back 1

A system in which no randomness is involved in the development of future states of the system. A deterministic model will always produce the same output from a given starting condition or initial state.

Front 2

Probabilistic system

Back 2

A system where events and occurrences cannot be predicted with precise accuracy. It involves randomness and uncertainty.

Front 3

Statistics

Back 3

The science of measuring, controlling, drawing conclusions based on the data, and communicating uncertainty.

Front 4

Statistical analysis

Back 4

The study of the likelihood and probability of events occurring based on known information and inferred by taking a limited number of samples.

Front 5

Qualitative

Back 5

Data that fall into categories.

Ex. What is your major?

Front 6

Quantitative

Back 6

Data that are numbers.

Ex. How many units are you taking?

Front 7

Discrete data

Back 7

Data that results from a finite, or infinite, “countable” number of possibilities.

Front 8

Continuous data

Back 8

Data that result from an infinite number of possibilities with no gaps or jumps.

Ex. The number of stairs on campus is discrete, your weight, height, and age are continuous.

Front 9

Nominal level

Back 9

Data that are in categories that have no obvious order.

Ex. What is your major?What is your favorite color?

Front 10

Ordinal level

Back 10

Data that are in categories but the categories can be ordered. Involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless.

Ex. What grade did you get in the class?What floor is the classroom on?

Front 11

Interval level

Back 11

Numerical data where differences are meaningful but there is no natural zero.

Ex. What year were you born?What temperature is it?

Front 12

Ratio level

Back 12

Numerical data where there is a natural zero.

Ex. How much money do you have in your pocket?How many units are you enrolled in?

Front 13

Population

Back 13

The complete collection of data to be studied.

Front 14

Sample

Back 14

Collection of a subset of the population.

Front 15

Parameter

Back 15

A numerical measure describing a characteristic of a population.

Front 16

Statistic

Back 16

A numerical measure describing a characteristic of a sample.

Front 17

Population parameter

Back 17

The true value of a population attribute.

Front 18

Sample statistics

Back 18

An estimate, based on sample data, of a population parameter.

Front 19

Sample survey

Back 19

The reason for conducting a sample survey is to estimate the value of some attribute of a population.

Front 20

Sampling method

Back 20

The way that observations are selected from a population to be in the sample.

Front 21

Survey

Back 21

A survey produces a sample statistic, which is used to estimate a population parameter. If you repeated a survey many times, using different samples each time, you might get a different sample statistic with each replication. And each of the different sample statistics would be an estimate for the same population parameter.

Front 22

Unbiased

Back 22

If the statistic is unbiased, the average of all the statistics from all possible samples will equal the true population parameter; even though any individual statistic may differ from the population parameter.

Front 23

Bias

Back 23

Bias often occurs when the survey sample does not accurately represent the population.

Front 24

Selection bias

Back 24

The bias that results from an unrepresentative sample.

Front 25

Sampling error

Back 25

The variability among statistics from different samples.

Front 26

Probability sampling methods

Back 26

This sampling method relys on random sampling. The only sampling method that permits standard statistical analysis.

Front 27

Non-probability sampling methods

Back 27

This sampling method offers two potential advantages - convenience and cost. But, the main disadvantage is they do not allow you to estimate the extent to which sample statistics are likely to differ from population parameters.

Ex. Two of the main types of non-probability sampling methods are voluntary samples and convenience samples.

Front 28

Random sample

Back 28

Selection such that each unit has an equal chance of being selected

Front 29

Simple random sampling

Back 29

Refers to any sampling method that has the following properties. The population consists of N objects.The sample consists of n objects. With a simple random sample of n items, all possible samples of n items have the same chance of being selected

Front 30

Voluntary sample

Back 30

A sample made up of people who self-select into the survey. Often, these people have a strong interest in the main topic of the survey. 


Ex. A news show asks viewers to participate in an on-line poll. This would be a volunteer sample. The sample is chosen by the viewers, not by the survey administrator.

Front 31

Convenience sample

Back 31

A sample made up of people who are easy to reach. 



Ex. Consider the following example. A pollster interviews shoppers at a local mall. If the mall was chosen because it was a convenient site from which to obtain survey participants because it was close to the pollster's home or business, this would be a convenience sample.

Front 32

Systematic sampling

Back 32

This sample creates a list of every member of the population. From the list, we randomly select the first sample element from the first k elements on the population list. Thereafter, we select every kth element on the list. 

This method is different from simple random sampling since every possible sample of n elements is not equally likely

Front 33

Stratified sampling

Back 33

The population is divided into groups, based on some characteristic. Then, within each group, a probability sample (often a simple random sample) is selected. The groups are called strata. 



Ex. We conduct a national survey. We might divide the population into groups or strata, based on geography - north, east, south, and west. Then, within each stratum, we might randomly select survey respondents.

Front 34

Cluster sampling

Back 34

Every member of the population is assigned to one, and only one, group. Each group is called a cluster. A sample of clusters is chosen, using a probability method (often simple random sampling). Only individuals within sampled clusters are surveyed. 



Note the difference between cluster sampling and stratified sampling. With stratified sampling, the sample includes elements from each stratum. With cluster sampling, in contrast, the sample includes elements only from sampled clusters.

Front 35

Sampling error (or random sampling error)

Back 35

Occurs when the sample has been selected with a random method but there is still discrepancy between a sample result and the true population result; such an error results from chance sample fluctuations.

Front 36

Nonsampling error

Back 36

The result of human error, including such factors as wrong data entries, computing error, questions with biased wording, false data provided by responders, forming biased conclusions, or applying statistical methods that are not appropriate for the circumstances.

Front 37

Nonrandom sampling error

Back 37

The result of using a sampling method that is not random, such as using a convenience sample or a voluntary response sample.

Front 38

Potential Pitfalls - Small Samples

Back 38

Conclusions should not be based on samples that are far too small.

Ex. Basing a customer sales rate on a sample of only three customers.

Front 39

Potential Pitfalls - Loaded Questions

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If survey questions are not worded carefully, the results of a study can be misleading.

Ex. 97% yes: “Should the President have the line item veto to eliminate waste?”57% yes: “Should the President have the line item veto, or not?”

Front 40

Potential Pitfalls - Nonresponse

Back 40

Occurs when someone either refuses to respond to a survey question or is unavailable.

Ex. People who refuse to talk to pollsters have a view of the world around them that is markedly different than those who will let pollsters into their homes.

Front 41

Potential Pitfalls - Missing Data

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Can dramatically affect results.Subjects may drop out for reasons unrelated to the study.

Ex. People with low incomes are less likely to report their incomes.

Ex. U.S. Census suffers from missing people (tend to be homeless or low income).

Front 42

Statistical significance

Back 42

The outcome of the event is unlikely and happens in a study when we get a result that is very unlikely to occur by chance

Ex. Mr. O flipped a coin 100 times and tails came up 52 times.Not statistically significant

Ex. Mr. O flipped a coin 100 times and tails came up 92 times.Statistically significant

Front 43

Statistical literacy

Back 43

A clear understanding of such important terms as sample, population, statistic, parameter, quantitative data, categorical data, voluntary response sample, and simple random sample