AP Statistics

Statistical Significance

An observed effect too large to attribute plausibly to chance.

Non-Response Bias

Bias introduced to a sample when a large fraction of those sampled fails to respond.

P-Value

found by substituting the x-value in the regression equation; they're the values on the fitted line

Empirical Rule

A statistical rule stating that for a normal distribution, almost all data will fall within three standard deviations of the mean.

Lurking Variable

a variable that is not explicitly part of a model but affects the way the variables in the model appear to be related

Null Hypothesis

The null hypothesis attempts to show that no variation exists between variables, or that a single variable is no different than zero. It is presumed to be true until statistical evidence nullifies it for an alternative hypothesis.

Quota Sample

A sampling method of gathering representative data from a group. As opposed to random sampling, quota sampling requires that representative individuals are chosen out of a specific subgroup.

Probability

Quantifiable likelihood (chance) of the occurrence of an event expressed as odds, or a fraction of 1.

Descriptive Statistics

The branch of statistics that includes numerical, graphical, and tabular methods for organizing and summarizing data

Median

the middle value with half of the data above and half below it

Stemplot

A table in which data values are divided into either a "leaf" or a "stem." In a stem and leaf plot, the stem values appear on the vertical axis and the leaf values are listed on the horizontal axis.

Data

systematically recorded information, whether numbers or labels, together with its context

Margin of Error

Analytical technique that accounts for the number of acceptable errors in an experiment.

Normal

Normal distribution with mean of zero and variance of one.

Simple Random Sample (SRS)

this of sample size n is one in which each set of n elements in the population has an equal chance of selection

Sampling Distributon

A type of distribution that involves the probability distribution of sample statistics based on randomly selected samples.

Interpolation

Estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from the available information.

Qualitative

involving distinctions based on qualities

Theoretical Probability

Probability based on comparing the number of possible favorable outcomes to the number of total possible outcomes

Block Design

the random assignment of units to treatments is carried out separately within each block

Least Squares Regression Line

the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible

Type II Error

An error that occurs when a researcher concludes that the independent variable had no effect on the dependent variable, when in truth it did; a "false negative" (Source: CHH, 2 Ed).

Histogram

a bar chart representing a frequency distribution

Undercoverage

A sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population

Joint Frequency

Number of cases with given values on two or more variables.

Matched Pairs

a technique whereby each participant is identical to one other participant in terms of a third variable

Conditional Probability

the probability that an event will occur given that one or more other events have occurred

Mode

the most frequent value of a random variable

Systematic Sample

A sample drawn by selecting individuals systematically from a sampling frame

Sample Space

the set of all possible outcomes of a probability experiment

Confounded Variable

A variable whose effect on the response variable cannot be separated from the effect of the explanatory variable on the response variable. (Note: Usually confounded variables are lurking variables but only a few lurking variables are also confounded.)

Experimental Probability

Probability based on data from repeating an event (doing an experiment)

Placebo Effect

experimental results caused by expectations alone; any effect on behavior caused by the administration of an inert substance or condition, which is assumed to be an active agent

Marginal Frequency

A set of intervals, usually adjacent and of equal width, into which the range of a statistical distribution is divided, each associated with a frequency indicating the number of measurements in that interval.

Parameter

a constant in the equation of a curve that can be varied to yield a family of similar curves

Voluntary Response Bias

bias introduced to a sample when individuals can choose on their own whether to participate in the sample

Mean

an average of n numbers computed by adding some function of the numbers and dividing by some function of n

Alternative Hypothesis

The hypothesis that states there is a difference between two or more sets of data.

Correlation

a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other

Response Bias

anything in the survey design that influences the responses from the sample

Coefficient of Determination

The statistic or number determined by squaring the correlation coefficient. Represents the amount of variance accounted for by that correlation.

Random Sample

a sample in which every element in the population has an equal chance of being selected

Binomial

a quantity expressed as a sum or difference of two terms

Experiment

the act of conducting a controlled test or investigation

Law of Large Numbers

(statistics) law stating that a large number of items taken at random from a population will (on the average) have the population statistics

Outlier

an extreme deviation from the mean

Extrapolation

an inference about the future (or about some hypothetical situation) based on known facts and observations

Snowball Sample

Samples in which informants provide contact information about other people who share some of the characteristics necessary for a study

Independent

not dependent on or conditioned by or relative to anything else

IQR

Range of the middle 50% of the values; Q3-Q1 = 75th percentile - 25th percentile

Ogive

a line graph of a cumulative frequency or cumulative relative frequency distribution.

Confidence Interval

The level of certainty that the true score falls within a specific range. The smaller the range the less the certainty.

Standard Error

the standard deviation of a sampling distribution

Observational Study

observes individuals and measures variables of interest but does not attempt to influence the responses

Residual

relating to or indicating a remainder

Convenience Sample

a form of nonprobability sample using respondents who are convenient or readily accessible to the researcher—for example, employees, friends, or relatives

Simulation

representation of something (sometimes on a smaller scale)

Degrees of Freedom

The number of individual scores that can vary without changing the sample mean. Statistically written as 'N-1' where N represents the number of subjects.

Dotplot

A one dimensional plot of a quantitative data set where each value in the data set is represented by a dot above its corresponding location on the x axis.

Two-way Table

A table containing counts for two categorical variables. It has r rows and c columns.

Geometric

characterized by simple geometric forms in design and decoration

Inferential Statistics

numerical methods used to determine whether research data support a hypothesis or whether results were due to chance

Spread

become distributed or widespread

Discrete Random Variable

a random variable that may assume either a finite number of values or an infinite sequence of values

Population

(statistics) the entire aggregation of items from which samples can be drawn

Sample

items selected at random from a population and used to test hypotheses about the population

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

Standard Deviation

a computed measure of how much scores vary around the mean score

Cluster Sample

population is split into parts or clusters usually based on geography and then entire clusters are selected randomly and sampled

Type I Error

Stating that the null hypothesis is false when it is in fact true.

Standardized Value

value found by subtracting the mean and dividing by the standard deviation

Boxplot

displays the 5-number summary as a central box with whiskers that extend to the non-outlying data values

Mutually Exclusive

necessitating a choice between mutually exclusive possibilities

Scatterplot

a graphed cluster of dots, each of which represents the values of two variables

Stratified Sample

the population is divided into strata and a random sample is taken from each stratum

Quantitive

Provides data and answers questions about relationships among measured variables. Also called traditional experimental approach.

Wording Bias

a type of response bias where the question is posed to achieve a desired result

Causation

A cause and effect relationship in which one variable controls the changes in another variable.

Statistic

A numerical measurement describing some characteristic of a sample

Center

an area that is approximately central within some larger region

Z-Test

The statistical formula to determine the z-score of a particular raw score.

T-Test

A group of statistics used to determine if a significance difference exists between the means of two sets of data.

Chi-Squared Goodness of Fit

uses sample data to test hypotheses about the shape or proportions of a population distribution. The test determines how well the obtained sample proportions fit the population proportions specified by the null hypothesis.