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# Stats

TermDefinition
association: Values of one variable tend to occur with certain values of another variable; detected when the conditional distributions differ from the marginal distribution and from each other.
bias: A condition where the mean of the statistic values differs from the parameter that the statistic estimates.
bivariate data: Data collected on two variables for each individual in a study.
Central Limit Theorem: The name of the statement telling us that the sampling distribution of x is approximately normal whenever the sample is large and random.
conditional distribution: The distribution of the values in a single row (or a single column) of a two-way table.
control chart: A statistical tool for monitoring the input or output of a process.
control limits: μ − 3 σ/srn and μ + 3 σ/srn ; used to detect out-of-control signals in a control chart.
correlation coefficient: A measure of the strength of the linear relationship between two quantitative variables.
disjoint events: Events that cannot occur simultaneously.
distribution of a variable: A list of the possible values of a variable together with the frequency of each value. (Note: probabilities can be given instead of frequencies.)
event: A single outcome or a combination of outcomes from a random phenomenon.
extrapolation: Predicting a Y value using a value of X that is outside of the range of X values used to obtain the regression equation. This prediction could be very far off.
inference: Using results from a sample statistic value to draw conclusions about the population parameter.
influential observation: An observation that substantially alters the values of slope and y-intercept in the regression equation when it is included in the computations
law of large numbers: The fact that the average ( x ) of observed values in a sample will get closer and closer to μ as the sample size increases.
laws of probability: The basis for hypothesis testing and confidence interval estimation.
least squares: A method for finding the equation of a line that minimizes the sum of squared residuals.
least squares regression line: The line with the smallest sum of squared residuals.
lurking variable: A variable that is not measured but explains association between two variables that are measured.
marginal distribution: The distribution of the values in the “total” row (or the “total” column) of a two-way table.
mean of the sampling distribution of x the mean of all the sample means ( x =s) from all possible samples of size n from a population; equals μ
μ: The mean of the population
no association: A condition where values of one variable occur independent of values of another variable; detected when the conditionals of a two-way table equal the marginal distribution (and each other)
out-of-control process: One sample mean outside three standard deviations of x or nine sample means in a row above or below the center line.
outlier: An observation that falls outside the overall pattern of the data set.
parameter: A characteristic of a population that is usually unknown; this could be mean, median, proportion, standard deviation computed on all the data from the population.; a parameter does not have variability.
parameter symbols: μ, σ, and p (mean of population, standard deviation of population, proportion of a population, respectively)
positive association: High values of one variable tend to associate with high values of another variable.
probability of an outcome: A measure of the proportion of times an outcome occurs in a very long series of repetitions that gives us an indication of the likelihood of the outcome.
process: Sequence of operations used in production, manufacturing, etc.
process in statistical control: A process whose inputs and outputs exhibit natural variation when observed over time.
quality control chart: A chart plotting the means x of regular samples of size n against time; this chart is used to access whether the process is in control.
quantitative bivariate: The type of data required for regression analysis.
r: The symbol for correlation coefficient.
r2: The percentage of total variation in the response variable, Y, that is explained by the regression equation; in other words, the percentage of total variation in the response variable, Y, that is explained by the explanatory variable, X.
random: A phenomenon that describes the uncertainty of individual outcomes but gives a regular distribution of the outcomes in the long run.
regression equation: A formula for a line that models a linear relationship between two quantitative variables.
residual: The observed y minus the predicted y; denoted: y - yˆ
residual plot: A diagnostic plot of the explanatory variable versus the residuals used to access how well the regression line fits the data;
sample mean xbar : The random variable of the sampling distribution of xbar .
sample space: The list of all possible outcomes of a random phenomenon.
sampling distribution: A distribution of a statistic; a list of all the possible values of a statistic together with the frequency (or probability) of each value.
sampling distribution of xbar : A list of all the possible values for x together with the frequency (or probability) of each value; in other words, the distribution of all x ’s from all possible samples.
sampling variability: The variability of sample results from one sample to the next; something we must measure in order to effectively do inference.
scatterplot: A two dimensional plot used to examine strength of relationship between two variables as well as direction and type of relationship.
Simpson's paradox: A condition where the percentages reverse when a 3rd variable is ignored. a condition leading to misinterpretation of the direction of association between 2 variables caused by ignoring a 3rd variable that's associated with both of the reported variables.
simulation: Using random numbers to imitate chance behavior.
slope: A measure of the average change in the response variable for every one unit increase in the explanatory or independent variable.
standard deviation (s): A measure of the variability of data in a sample about xbar .
standard deviation of xbar (also called the standard deviation of the sampling distribution of xbar ): A measure of the variability of the values of the statistic x about μ; a measure of the variability of the sampling distribution of x ; in other words, the average amount that the statistic, x, deviates from its associated parameter. Computed as σ /SRn
statistic: A number computed from sample data (without any knowledge of the value of a parameter) used to estimate the value of the parameter.
statistic symbols: xbar , s, pˆ (mean of sample, standard deviation of sample, proportion of sample, respectively)
statistical process control: A procedure used to check a process at regular intervals to detect problems and correct them before they become serious.
sum of squared residuals (or error): the residuals are squared and added; denoted SSE.
total variation in Y: The sum of the squared deviations of the Y observations about their mean, y .
two-way table: A table containing counts for two categorical variables. It has r rows and c columns.
unbiased: A condition where the mean of the statistic values equals the parameter that the statistic estimates.
unexplained variation: The sum of squared residuals
X: The symbol for explanatory variable.
xbar -chart: A plot of sample means over time used to assess whether a process is in control.
Y: The symbol for response variable.
yˆ : The symbol for predicted y.
z-score: A measure of the number of standard deviations of a value or observation from the mean.
Created by: davidkentclark