## AP Stats

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orangechicken4ever  on April 10, 2012

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# AP Stats

 Alternative HypothesisThe theory that the researcher hopes to confirm by rejecting the null hypothesis. (Ha)
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#### Definitions

Alternative Hypothesis The theory that the researcher hopes to confirm by rejecting the null hypothesis. (Ha)
Association When some of the variability in one variable can be accounted for by the other.
Bar Graph Graph in which the frequencies of categories are displayed with bars; analogous to histogram for numerical data.
Bimodal Distribution with two (or more) most common values.
Binomial Distribution Probability distribution for a random variable X in a binomial setting where n is the number of independent trials, p is the probability of success on each trial, and x is the count of successes out of the n trials. {on the formula sheet}
Binomial Setting (experiment) When each of a fixed number, n, of observations either succeeds or fails, independently, with probability p.
Bivariate Data Having to do with two variables
Block A grouping of experimental units thought to be related to the response to the treatment.
Block Design (Blocking) Procedure by which experimental units are put into homogeneous groups in an attempt to control for the effects of the group on the response.
Boxplot Graphical representation of the 5-number summary of a data set. Each value in the 5-number summary is located over its corresponding value on a number line. A box is drawn that ranges from QI to Q3 and "whiskers" extend to the maximum and minimum values from QI and Q3.
Categorical Data (Qualitative Data) Data whose values range over categories rather than values.
Censuns Attempt to contact every member of a population.
Center The "middle" of a distribution; either the mean or the median.
Central Limit Theory (CLT) Theorem that states that the sampling distribution of a sample mean becomes approximately normal when the sample size is large. {on the formula sheet}
Chi-Square (x²) Goodness-of-Fit Test Compares a set of observed categorical values to a set of expected values under a set of hypothesized proportions for the categories.
Coefficient of Determination (r²) Measures the proportion of variation in the response variable explained by regression on the explanatory variable.
Complement of an event Set of all outcomes in the sample space that are not in the event.
Completely Randomized Design When all subjects (or experimental units) are randomly assigned to treatments in an experiment.
Conditional Probability The probability of one event succeeding given that some other event has already occurred.
Confidence Interval An interval that, with a given level of confidence, is likely to contain a population value (estimate) +/- (margin of error)
Confidence Level The probability that the procedure used to construct an interval will generate an interval that does contain the population value.
Confounding Variable Has an effect on the outcomes of the study but whose effects cannot be separated from those of the treated variable.
Contingency Table (Two-Way Table) Table that lists the outcomes of two categorical variables; the values of one category are given as the row variable, and the values of the other category are given as the column variable; also called a contingency table.
Continuous Random Variable A random variable whose values are continuous data; tales all values in an interval.
Control (Statistical Control) Holding constant variables in an experiment that might effect the response but are not one of the treatment variables.
Convenience Sample Sample chosen without any random mechanism; chooses individuals based on ease of selection.
Correlation Coefficient (r) Measures the strength of the linear relationship between two quantitative variables.
Correlation is not Causation Just because two variables correlate strongly does not mean that one caused the other.
Critical Value Values in a distribution that identify certain specified areas of the distribution.
Degrees of Freedom Number of independent data-points in a distribution.
Density Function A function that is everywhere non-negative and has a total area equal to 1 underneath it and above the horizontal axis.
Descriptive Statistics Process of examining data analytically and graphically.
Dimension Size of a two way table; (rows)*(columns)
Discrete Data Data that can be counted (possibly infinite) or placed in order.
Discrete Random Variable Random variable whose values are discrete data.
Dotplot Graph in which data values are identified as dots placed above their corresponding values on a number line.
Empirical Rule (68-95-99.7 Rule) States that, in normal distribution, about 68% of the terms are within one standard deviation of the mean, about 95% are within two standard deviations, and about 99.7% are within three standard deviations.
Estimate Sample value used to approximate a value of a parameter.
Event In probability, a subset of a sample space; a set of one or more simple outcomes.
Expected Value Mean value of a discrete random variable.
Experiment Study in which a researcher measures the responses to a treatment variable, or variables, imposed and controlled by the researcher.
Experimental Units Individuals on which experiments are conducted.
Explanatory Variable (Independent Variable) (Treatment Variable) Explains changes in response variable; treatment variable; independent variable.
Extrapolation Predictions about the value of a variable based on the value of another variable outside the range of measured values.
First Quartile 25th Percentile
Five Number Summary For a dataset: [minimum value, Q1, median, Q3, maximum value]
Geometric Setting Independent observations, each of which succeeds or fails with the same probability p; number of trials needed until the first success is variable of interest.
Histogram Graph in which the frequencies of numerical data are displayed with bars; analogous to a bar graph for categorical data
Homogeneity of Proportions Chi-square hypothesis in which proportions of a categorical variable are tested for homogeneity across two or more populations.
Independent Events Knowing one event occur does not change the probability that the other occurs: P(A) = P(A|B)
Inferential Statistics Use of sample data to make inferences about populations.
Influential Observation Observation, usually in the x direction whose removal would have a marked impact on the slope of the regression line.
Interpolation Predictions about the value of a variable based on the value of another variable within the range of measured values.
Inter-quartile Range Value of the third quartile minus the value of the first quartile; contains middle 50% of data.
Least-Squares Regression Line (Line of Best Fit) Of all possible lines, the line that minimizes the sum of squared errors (residuals) from the line.
Lurking Variable One that has an effect of the outcomes of the study but whose influence was not part of the investigation.
Margin of Error Measure of uncertainty in the estimate of a parameter; (critical value)*(standard error)
Marginal Totals Row and Column totals in a two-way table.
Matched Pairs Experimental units paired by a researcher based on some common characteristic or characteristic.
Matched Pairs Design Experimental design that utilizes each pair as a block; one unit receives one treatment, and the other unit receives the other treatment.
Mean Sum of all the values in a dataset divided by the number of values.
Median Halfway through an ordered dataset, below and above which there lie an equal number of data values; 50th percentile.
Mode Most common value in a distribution.
Mount-Shaped (Bell-Shaped) Distribution in which data values tend to cluster about the center of the distribution; characteristic of a normal distribution.
Mutually Exclusive Events Events that cannot occur simultaneously; if one occurs, the other doesn't.
Negatively Associated Large values of one variable are associated with smaller values of the other.
Non-response Bias Occurs when subjects selected for a sample do not respond.
Normal Curve Familiar bell-shaped density curve; symmetric about its mean; defined in terms of its mean and standard deviation.
Normal Distribution Distribution of a random variable X so that P(a < X < b) is the area under the normal curve between a and b.
Null Hypothesis Hypothesis being tested- usually a statement that there is no effect or difference between treatments; what a researcher wants to disprove to support his/her alternative.
Numerical Data (Quantitative Data) Data whose value are numerical.
Observational Study When variables of interest are observed and measured but no treatment is imposed in an attempt to influence the response.
Observed Values Counts of outcomes in an experiment or study; compared with expected values in a chi-square analysis.
One-Sided Alternative Alternative hypothesis that varies from the null in only one direction.
One-Sided Test Used when an alternative hypothesis states that the true value is less than or greater than the hypothesized value.
Outcome Simple events in a probability experiment.
Outlier A data value that is far removed from the general pattern of the data.
P(A and B) Probability that both A and B occur; P(A and B)= P(A)*P(A|B)
P(A or B) Probability that either A or B occurs; P(A or B)= P(A) + P(B) - P(A and B).
P-Value Probability of getting a sample value at least as extreme as obtained by chance alone assuming the null hypothesis is true.
Parameter Measure that describes a population.
Percentile Rank Proportion of terms in the distribution less than the value being considered.
Placebo An inactive procedure or treatment.
Placebo Effect Effect, often positive, attributable to the patient's expectation that the treatment will have an effect.
Point Estimate Value based on sample data that represents a likely value for a population parameter.
Positively Associated Large values of one variable are associated with larger values of the other.
Power of the Test Probability of rejecting a null hypothesis against a specific alternative.
Probability Histogram Histogram for a probability distribution; horizontal axis are the outcomes, vertical axis are the probabilities of those outcomes.
Probability of an Event Relative frequency of the number of ways an event can succeed to the total number of ways it can succeed or fail.
Probability Sample Sampling technique that uses a random mechanism to select the the members of the sample.
Proportion Ratio of the count of a particular outcome to the total number of outcomes.
Quartiles 25th, 50th, and 75th percentiles of a data set.
Random Phenomenon Unclear how any one trial will turn out, but there is a regular distribution of outcomes in a large number of trials.
Random Sample Sample in which each member of the sample is chosen by chance and each member of the population has an equal chance to be in the sample.
Random Variable Numerical outcome of a random phenomenon (random experiment).
Randomization Random assignment of experimental units to treatments.
Range Difference between the maximum and minimum values of a data set.
Replication Repetition of each treatment enough times to help control for chance variation.
Representative Sample Sample that possess the essential characteristics of the population from which it was taken.
Residual In regression, the actual value minus the predicted value.
Resistant Statistics One whose numerical value is not influenced by extreme values in the data set.
Response Bias Bias that stems from respondents inaccurate or untruthful response.
Response Variable Measures the outcome of a study.
Robust When a procedure may still be useful even if the conditions needed to justify it are not completely satisfied.
Robust Procedure Procedure that still works reasonably well even if the assumptions needed for it are violated; the t-procedures are robust against the assumption of normality as long as there are no outliers or severe skewness.
Sample Space Set of all possible mutually exclusive outcomes of a probability experiment.
Sample Survey Using a sample from a population to obtain responses to questions from individuals.
Sampling Distribution of a Statistic Distribution of all possible values of a statistic for samples of a given size.
Sampling Frame List of experimental units from which the sample is selected.
Scatterplot Graphical representation of a set of ordered pairs; horizontal axis is first element in the fair, vertical axis is the second.
Shape Geometric description of a data set: mound-shaped; symmetric; uniform; skewed; etc.
Significance Level (α) Probability value that, when compared to the P value, determines whether a finding is statistically significant.
Simple Random Sample (SRS) Sample in which all possible samples of the same size are equally likely to be the sample chosen.
Simulation Random imitation of a probabilistic situation.
Skewed Distribution that is asymmetrical.
Skewed (Left/Right) Asymmetrical with more of a tail on the left (right) than on the right (left).
Standard Deviation Square-root of the variance. {on the formula sheet}
Standard Error Estimate of population standard deviation based on sample data.
Standard Normal Distribution Normal distribution with a mean of 0 and a standard deviation of 1.
Standard Normal Probability Normal probability calculated from the standard normal distribution.
Statistic Measure that describes a sample (e.g., sample mean)
Statistically Significant A finding that is unlikely to have occurred by chance.
Statistics Science of data.
Stemplot Graph in which ordinal data are broken into "stems" and "leaves"; visually similar to a histogram except that all the data are retained.
Stratified Random Sample Groups of interest (strata) chosen in such a way that they appear in approximately the same proportions in the sample as in the population.
Subjects Human experimental units.
Survey Obtaining responses from to questions from individuals.
Symmetric Data values distributed above and below the center of the distribution.
Systematic Bias The mean of the of the sampling distribution of a statistic does not equal the mean of the population.
Systematic Sample Probability sample in which one of the first n subjects is chosen at random for the sample and then each nth person after that is chosen for the sample.
T-Distribution The distribution with n-1 degrees of freedom for the t-statistic.
T-Statistic T-Value
Test Statistic (estimator - hypothesized value) / (standard error)
Third Quartile 75th percentile
Tree Diagram Graphical technique for showing all possible outcomes in a probability experiment.
Two-Sided Alternative Alternative hypothesis that can vary from the null in either direction; values much greater than or much less than the null provide evidence against the null
Two-Sided Test A hypothesis test with a two-sided alternative.
Type-I Error The error made when a true hypothesis is rejected.
Type-II Error The error made when a false hypothesis is not rejected.
Unbiased Estimate Mean of the sampling distribution of the estimate equals the parameter being estimated.
Undercoverage Some groups in a population are not included in a sample from that population.
Uniform Distribution in which all data values the same frequency occurrence.
Univariate Data Having to do with a single variable.
Variance Average of the squared deviations from their mean of a set of observation.
Voluntary Response Bias Bias inherent when people choose to respond to a survey or poll; bias is typically toward opinions of those who feel most strongly.
Voluntary Response Sample Sample in which participants are free to respond or no to respond to a survey or a poll.
Wording Bias Creation of response bias attributable to the phrasing of a question.
z-Score Number of standard deviations a term is above or below the mean.

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