Glossary of Terms

Certainty Equivalent

The certainty equivalent represents the maximum amount of money we are willing to pay for some gamble. In other words, it is the minimum amount of money I would rather have for certain instead of taking some risk.

A friend offers you the following bet: He will flip a coin. If it lands on heads you win nothing, but if it lands on tails he will award you \$100. How much would you be willing to pay for this chance?

Conditional Probabilities

The conditional probability of an event B in relationship to an event A is the probability that event B occurs, given that event A has already occurred. Information presented as conditional probabilities is often misinterpreted.

"If a woman has breast cancer, the probability that she will test positive on a screening mammogram is 90 percent." People often misinterpret this to mean: "If a woman tests positive on a screening mammogram, the probability that she has breast cancer is 90 percent."

Control Group

In an experiment, the control group is the group of subjects (people or objects) that exist in the same conditions as the experimental group, but do not undergo the treatment or factor being studied.

In an experiment on how plants react to limited light, the control plant and the experimental plant would receive the same amount of water and plant food. However, the experimental plant would sit in a windowless room to keep out sunlight, while the control plant would sit by a window and receive normal levels of light.

Coverage Error

Coverage error is the failure to accurately characterize the population that the survey or poll is trying to study through the omission, over-representation or wrongful inclusion of particular groups of people in the sample (1).

Coverage error occurs in web surveys because they exclude people without internet access.

Decimal

Decimals are numbers expressed in base-10 math. Decmials, when used as statistics, are representations with denominator some power of 10.

Major League Baseball indicates batting average as a decimal quantity.

Denominator

The denominator is the bottom number of a fraction that describes the number of equal parts that make up the whole.

In the fraction 3/8, for example, '8' is the denominator, indicating that it will take eight total portions to have one complete whole.

Digital Divide

The digital divide refers to the socio-economic gap between communities that have access to computers and the internet and those who do not (c).

The digital divide refers to the unequal adoption of technology and access to the internet because of disparities in income and opportunity.

Experiment

Experiments test whether one factor causes another by randomly assigning participants to control groups and experimental groups.

To see if a certain type of plant needs sunlight to grow, a researcher divides 10 of the plants into two groups of 5: an experimental group that sits in the sun, and a control group that sits in the dark. In order to prove that the difference in plant growth was not caused by initial differences in the two groups of plants, the researcher gives each of the ten plants a number 1 to 10, has a computer arbitrarily clump the numbers into 2 groups, then flips a coin to see which group will be the experimental group.

Experimental Group

In an experiment, the experimental group is the group of subjects (people or objects) that undergo the treatment or factor being studied. The experimental group exists in the same conditions as the control group.

In an experiment on how plants react to limited light, the control plant and the experimental plant would receive the same amount of water and plant food. However, the experimental plant would sit in a windowless room to keep out sunlight, while the control plant would sit by a window and receive normal levels of light.

Experimental Probability

Experimental probability is the chance of something happening based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested.

To find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played.

Fraction

Fractions are simply ways of representing portions of whole quantities. Composed of a numerator and a denominator, they indicate how much of a certain object is being considered.

3/8 is a fraction indicating three portions out of eight total, or three eighths of a whole.

Frequency View

The frequency view is an approach taken by mathematicians and scientists to determine the chances of an event happening by repeating the experiment many times and using the results to calculate the probability. This view opposes the personal approach to probability.

To find the probability of rolling a 3 with a six-sided die, you roll the die 1,000,000 times. Out of these rolls, you roll a three 166,549 times. You find the proportion of 3's by dividing: 166,549 / 1,000,000 = 0.166549. You conclude that the probability of rolling a 3 on this particular die is 1/6.

Innumeracy

The opposite of numeracy, innumeracy is "the inability or unwillingness to understand basic mathematical ideas involving numbers or logic as they apply in everyday life" (5).

Knowing that 4 out of 5 dentists recommend Trident, an innumerate person would take at face value that a relitavely large quantity of dentists recommend Trident, and not be able to make critical inferences as to the relitave merit of this quoted statistic.

Natural Frequencies

A natural frequency is a way of representing a number as a part of another number.

1 out of 4.

Numeracy

Numeracy is the knowledge of basic number skills and the ability to apply those skills in contexts that require high levels of literacy to interpret situations and make judgments (20).

Knowing that 4 out of 5 dentists recommend Trident, a person exhibiting numeracy would realize that the practical meaning of this statistic depends on the sample size and other research factors.

Numerator

The numerator is the top number of a fraction that describes the number of parts considered.

In the fraction 3/8, for example, '3' is the numerator, and indicates that we are considering three equal portions of a whole that has eight total portions.

Objective

Objective means focused on facts and conditions. Theoretically, objective studies and assessments are not distorted by personal feelings, prejudices, or interpretations (11). Objective is the oppossite of subjective.

An objective survey evaluating the effectiveness of a new medication might record changes in participants' blood pressure or days absent from work. A subjective survey evaluating the same medication might interview participants to ask them how they feel or what they remember.

Outcome

An outcome is any one of the possible results of an experiment.

When you flip a coin, there are two possible outcomes: heads and tails.

Percent

Percents are representations that have been adjusted to have a denominator of 100. They indicate the number of times a specific outcome occurs given one hundred attempts.

An outcome that occurs with 44% frequency means that it will occur fourty four times out of one hundred.

Personal View

An approach taken by mathematicians and philosophers to calculate probability, the personal view is an individual's belief about the chances that an event will occur. People who define probabilities use their knowledge about the world to make the best possible guess. The personal view is another name for subjective probability.

To find the probability of getting 3 on a six-sided die, you sit down and think. You reason that all of the sides of the die are the same, and that you can believe that the die does not have holes or heavy objects inserted into it. You conclude that each side of the die should have the same chance of landing face up, and therefore, that when you roll the die, you have one chance in six to get a 3. Your answer is that the probability of getting 3 is 1/6.

Practical Significance

Practical significance refers to the usefulness of a research finding in real life. See statistical significance for more information.

In a study, a researcher finds a small relationship between happiness and time spent outdoors. In real life, however, the actual influence of time outdoors on happiness proves so small that being out all day has little affect. In this example, the research findings are statistically significant, but not practically significant.

Probability

Probability means: 1. being probable, 2. something that is probable, 3. a ratio expressing the chances that a certain event will occur, and 4. a branch of mathematics studying chances of random events.

To find the probability of rolling a 3 on a six-sided die, you roll the die 1,000,000 times. You roll a 3 166,549 times. You find the proportion of 3's by dividing: 166,549 / 1,000,000 = 0.166549. The probability of rolling a 3 on this particular die is about 1/6.

Public Opinion

Public opinion is an aggregate of the individual views, attitudes, and beliefs about a particular topic expressed by a significant proportion of a community (14).

During the 2000 elections, it was not clear whether the Presidential candidate was elected as a result of public opinion or due to some discrepency in the system.

Random Digit Dialing

Random digit dialing is when researchers sample from a compilation of all possible telephone numbers, including unlisted ones (17).

Some researchers try to measure public opinion by calling every 50th residential number in a telephone book. This survey method excludes cell phone users, unlisted numbers, and people who do not have a telephone.

Regression to the Mean

Regression to the mean refers to the phenomenon that extreme results tend to sway back toward normal.

An outstanding is movie is most likely followed by a not-so- brilliant sequel.

Relative Risks

Relative risk is the "probability of an event in the active group divided by the probability of the event in the control group" (12).

Consider a woman's risk of developing breast cancer compared to women who do not have the same risk factors. If you hear a report stating that "breast cancer was found to be increased 10-fold... or by 76%... or 5 times as common" you are listening to relative risks.

Risk

Risk is the potential harm that may arise from some present process or from some future event. It is often mapped to the probability of some event which is seen as undesirable. See uncertainty for more information

A woman's risk of developing breast cancer is X%, depending on various risk factors such as smoking, sun bath, etc..

Sample

The sample is the group of participants considered in a research study.

Studies of psychological disorders conducted on college campuses often have a sample of college undergraduates.

Single-Event Probabilities

A single event probability is the probability that a specific event will occur. The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes.

When a weather reporter says "there is a 30 percent chance that it will rain tomorrow," some people think that it will rain 30 percent of the time, others that it will rain in 30 percent of the area, and still others that it will rain on 30 percent of the days that are like tomorrow. Although the third option is the intended message, approximately two thirds of the people will interpret this statement incorrectly.

Statistical Significance

Statistical significance refers to the scientific legitimacy of a research finding. Research findings are typically considered statistically significant only if the results would occur by chance less than five times out of one hundred. Statistical significance is based on a mathematical cut-off. It communicates very little about whether or not the finding is useful in real life (21). See practical significance for more information.

In a study, a researcher finds a small relationship between happiness and time spent outdoors. In real life, however, the actual influence of time outdoors on happiness proves so small that being out all day has little affect. In this example, the research findings are statistically significant, but not practically significant.

Statistics

Statistics are/is 1. facts or data assembled and classified so as to present significant information. 2. collection, calculation, description, manipulation, and interpretation of the mathematical attributes of large sets or populations, and 3. a branch of mathematics dealing with collection, analysis and interpretation of data.

According to sociologist David Phillips of the University of California San Diego, Christmas is the deadliest day of the year for Americans with 12.4 percent more deaths than normal (15).

Subjective

The opposite of objective, subjective means influenced by personal beliefs and experiences (11).

An objective survey evaluating the effectiveness of a new medication might record changes in participants' blood pressure or days absent from work. A subjective survey evaluating the same medication might interview participants to ask them how they feel, what they remember, etc.

Subjective Probability

Subjective probability is equivalent to personal view. A person's subjective probability of an event describes his or her degree of belief in the event.

A Rangers fan might say, "I believe that the Rangers have a probability of 0.9 of winning the Scottish Premier Division this year since they have been playing really well."

Survey

A survey is a systematic method for gathering information from a sample of people for the purposes of constructing quantitative descriptors of the attributes of the larger population of which they are member (4).

Before an election, pollsters question a sample of voters to determine how the public perceives the candidates and the issues (17).

Theoretical Probability

Theotetical probability is the chance of events happening as determined by calculating results as they would occur under ideal circumstances.

The theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4. Under ideal circumstances, one out of every four rolls would be a 4.

Theories of Probability

A theory of probability is a way of understanding probability statements. A theory of probability connects the mathematics of probability with the real world of observation and experiment.

The frequency view is one theory of probability.

Uncertainty

The probabilities of the various possible outcomes are not known. By that definition, most real-life situations involve uncertainty. You usually don't know the probabilities of the different things that can happen in real life, such as accidents, for example. Uncertainty is related to risk.

Everybody take a coin, flip it. Heads or tails? In principle, we should be able to determine the outcome if we knew exactly how the coin was thrown. This is elementary physics, laws of motion. In practice, we either can't measure these initial conditions sufficiently precisely, or we don't care to do it. As a result, our knowledge about the outcome of this phenomenon is uncertain.