Discrete (Statistics) Vocab
Terms
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- labeled scatterplot
- device for including information from a categorical variable into a scatterplot; assigns different labels to the dots in a scatterplot
- scatterplot
- the simplest graph for displaying two quantitative variables simultaneously; it uses a vertical axis for one of the variables and a horizontal axis for the other. A dot is placed for each observational pair at the intersection of its two values.
- response variable
- the variable to be predicted; the convention is to place this variable on the vertical axis
- explanatory variable
- the variable to do the predicting; the convention is to place this variable on the horizontal axis
- positively associated
- if larger values of one variable tend to occur with larger values of the other variable
- negatively associated
- if larger values of one variable tend to occur with smaller values of the other
- correlation coefficient
-
a measure of the linear relationship between two quantitative variables
has to be between +1 and -1. It can equal one of those values when the observations form a perfectly straight line. - difference between association and causation
- two variables may be strong associated without a cause-and-effect relationship existing between them. Often the explanation is that both variables are related to a third variable not being measured; this variable is often called a lurking or confounding variable.
- least squares regression
- a technique for modeling the relationship between two quantitative variables
- least squares
- a criterion that says to choose the line that minimizes the sum of squared vertical distances from the points to the line
- prediction
- one can use the regression line to predict the value of the y-variable for a given value of the x-variable simply by plugging that value of x into the equation of the regression line; finding the y-value of the point on the regression line corresponding to the x-value of interest
- extrapolation
- trying to predict y for values of x beyond those contained in the data
- fit
- the part that is explained by the model
- residual
- the difference between the actual y-value and the fitted value y; measures the vertical distance from the observed y-value to the regression line
- fitted value
- the y-value that the regression line would predict for the x-value of that observation
- proportion of variability
- the square of the correlation coefficient, written r^2; provides a measure of how closely the points fall to the least squares line and thus also provides an indication of how confident one can be of predictions made with the line
- residual plots
- can be used to indicate when the linear relationship is not a satisfactory model for describing the relationship between two variables
- transformation
- can be used to create a linear relationship between variables
- outliers
- observations with large (in absolute value) residuals; outliers fall far from the regression line, not following the pattern of the relationship apparent in the others
- influential observation
- one whose removal would substantially affect the regression line
- side-by-side stemplot
-
a common set of stems is used in the middle of the display with leaves for each category branching out in either direction, one to the left and one to the right
the convention is to order the leaves from the middle out toward either side - statistical tendency
- pertains to average or typical cases but not necessarily to individual cases
- outlier
- observation lying more than 1.5 times the interquartile range away from the nearer quartile
- modified boxplot
- treats outliers differently by marking them with a special symbol (*) and then extending the boxplot's "whiskers" only to the most extreme non-outlying value
- two-way table
-
classifies each person according to two variables
it is a 2 x 3 table; the first number represents the number of categories of the row variable, and the second number represents the number of categories of the column variable
the explanatory variable should be in columns and the response variable in rows - marginal and conditional distributions
- conditional distributions: distributions of one variable for given categories of the other variable
- segmented bar graph
-
conditional distributions can be represented visually
contain segments whose lengths correspond to the conditional proportions - Simpson's paradox
- aggregate proportions can reverse the direction of the relationship seen in the individual pieces
- independence
- two categorical variables are said to be independent if the conditional distributions of one variable are identical for every category of the other variable
- relative risk
- the ratio of the proportions having the disease between the two groups of the explanatory variable