Ap Stats

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Alternative Hypothesis

Back 1

The Hypothesis which states the Null Hypothesis is incorrect in a significance test.

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Block design

Back 2

The random assignment of subjects to treatments is carried out separately within each block.

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Boxplot

Back 3

Displays the 5-number summary as a central box with whiskers that extend to the non-outly ingredients data values.

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Causation

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

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Center

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A descriptive feature which describes the placement and relationships of the median to the other parts of the graphic representation.

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Central Limits Theorem

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The sampling distribution of the mean will approach the normal distribution as n increases (n>30).

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Chi-Squared Goodness of Fit

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

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Cluster Sample

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A sampling design in which entire groups are chosen at random.

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Coefficient of Determination

Back 9

Measures the percentage of variation in a dependent variable explained by one or more independent variables (r^2).

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Conditional Probability

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The probability that a particular event will occur, given that another event has already occurred.

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Confidence Variable

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The range of values within which a population parameter is estimated to lie.

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Confounded Variable

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An intended difference between the conditions of an experiment that could have affected the dependent variable.

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Convenience Sample

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A sample that includes members of the population that are easily accessed.

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Correlation

Back 14

The measure of a relationship between two variables or sets of data.

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Data

Back 15

Information gathered from observations.

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Degrees of Freedom

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A parameter of the t distribution. When the t distribution is used in the computation of an interval estimate of a population mean, the appropriate t distribution has n-1 degrees of freedom. Where n is the size of the sample random sample.

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Descriptive Statistics

Back 17

Statistical procedures used to describe characteristics and responses of group of subjects.

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Discrete Random Variable

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Variable where the number of outcomes can be counted and each outcome has a measurable and positive probability.

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Dotplot

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Graphs and dot for each case against a single axis.

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Empirical Rule

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States that, in a 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 (normal curve).

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Experiment

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The act of conducting a controlled test or investigation.

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Experimental Probability

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Probability based on what happens when an experiment is actually done.

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Extrapolation

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Estimating a value outside the range of measured data.

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Histogram

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A bar graph that shows frequency of data within equal intervals.

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Independent

Back 25

A relationship between two sets of data or datum which states the outcome of one has no effect on the outcome of the other.

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Inferential Statistics

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Statistics that are used to interpret data and draw conclusions.

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Interpolation

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Using the Least Squares Regression Line to predict a y-value for an x-value within the x-dada set.

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IQR

Back 28

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

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Joint frequency

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The number of responses for a given characteristic.

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Law of Large Numbers

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

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Least Squares Regression Line

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The line that minimizes the sum of squared residuals.

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Lurking Variable

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A variable other than x and y that simultaneously affect both variables, accounting to the correlation between the two.

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Margin of Error

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The range of percentage points in which the sample accurately reflects the population, the range surrounding a sample's response within which researchers are confident the larger population's true response would fall.

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Marginal Frequency

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Row and column totals in a contingency table (cross-tabulation) that represents the unitarian frequency distributions of responses the row and column variables.

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Matched Pairs

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Either two measurements are taken on each individual such as pre and post OR two individuals are matched by a third variable (different from explanatory variable and the response variable) such as identical twins.

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Mean

Back 36

The arithmetic average of a distribution, obtained by adding the scores and then dividing the number of scores.

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Median

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The middle score in the distribution; half the scores are above it and half are below it.

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Mode

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That datum which occurs the most in a set of data.

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Mutually Exclusive

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Each event or variable is independent from one another. No event or variable will have an effect on the probability of outcome for any other event or variable.

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Non-Response Bias

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A bias caused by a number of people who did not respond to the survey.

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Normal

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A sample which follows the Empirical Rule for distribution.

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Null Hypothesis

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The Hypothesis that states there is no difference between two or more sets of data in a significance test.

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Observational Study

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An experiment which observes individuals and measures variables of interest but does not attempt to influence the responses.

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Outlier

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An extreme deviation from the mean.

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P-Value

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The probability of getting a result at least as extreme as the result given from the test. The lower the value the stronger the evidence.

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Parameter

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A numerical measurement describing some characteristic of a population.

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Placebo Effect

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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.

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Population

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The entire aggregation of items from which samples can be drawn.

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Probability

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The likelihood that a particular event will occur.

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Qualitative

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Data identified by something other than numbers.

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Quantitative

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Dad or datum being numerically defined.

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Quota Sample

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A sample deliberately constructed to reflect several of the major characteristics of a given population.

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Random Sample

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A sample in which every element in the sample has an equal chance of being selected.

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Residual

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The difference between an observed value of the response variable and the value predicted by the Regression Line.

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Response Bias

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Anything in the survey design that influences the responses from the sample.

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Sample

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

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Sample Space

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All possible outcomes of an experiment.

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Sampling distribution

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The distribution of values taken by the statistic in all possible samples of the same size from the same population.

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Scatterplot

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

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Simple Random Sample

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Ever member of the population has a known and equal chance of selection.

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Simulation

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The act of repeating an experiment to get more accurate statistical evidence

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Spread

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A descriptive feature in which describes the range of data graphically.

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Standard Deviation

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A measure of variability that describes an average distance of every score from the mean (r).

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Standard Error

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5he standard deviation of a sampling distribution.

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Standardized Value (z-score)

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

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Statistic

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A numerical value measurement describing some characteristic of a sample.

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Statistical Significance

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When your discovered p- value is less than your alpha (.05 if not given). States that chance alone would rarely produce an equally extreme results.

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Stemplot

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A graphical representation of a quantitative data set. Leading values of each data point are presented as stems and second digits are give as leaves.

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Stratified Sample

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A sample drawn by selecting individuals systematically from a sampling frame.

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t-test

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A parametric inferential statistical test of the null hypothesis for a single sample where the population standard deviation is unknown.

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Theoretical Probability

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The ratio of the number of favorable outcomes to the number of possible outcomes if all outcomes have ever the same chance of happening.

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Two-way Table

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

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Type I Error

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An error that occurs when a researcher concludes that the independent variable had an effect on the dependent variable, when no such relation exists; a false positive.

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Type II Error

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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 positive.

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Undercoverage

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Occurs when some groups in the population are left out of the process of choosing the sample.

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Voluntary Response Bias

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

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Wording Bias

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A type of response Bias where the question is posed to achieve a desired result.

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z-test

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A parametric inferential statistical test of the null hypothesis for a single sample where the population standard deviation is know.

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Cumulative Frequency Plot

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A line graph that depicts cumulative Frequencies.

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Census

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A sample that consists of the entire population.

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Experimental Control

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Aspects of the experiment that we know. May have an effect on the response, but that are not the factors being stated.

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Grammatical Factor

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Variable whose levels are controlled by the experimenter.

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Double Blind

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Neither the subjects nor the people who have contact with then know which treatment a subject has received.

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Randomization

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Process by which each individual is given a fair chance of selection.

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Small Variance

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Cluster; the data is around the mean.

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Large Variance

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Data is spread out.

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Residual (error)

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The sum of the residuals is always 0.

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Methods for Gathering Data

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Surveys

Interviews

Experiments

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Multistage Sample

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Unbiased and easy to conduct.

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Stratified Sample Advantages

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Less variability

Unbiases

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Categorical Variable Examples

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Eye color

Zip code

Race

Type of pet

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Number of successes observed

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k (from the binomial formula)

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The 25 percentile

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Q1 (the first quartile)