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Views of these variations can change enormously between cultures over time. For example, nineteenth-century European and American ideas of race and eugenics culminated in the attempts of the Nazi-led German society of the 1930s to deny not just reproduction, but life itself to a variety of people with "differences" attributed in part to ...
In continuous-time dynamics, the variable time is treated as continuous, and the equation describing the evolution of some variable over time is a differential equation. [7] The instantaneous rate of change is a well-defined concept that takes the ratio of the change in the dependent variable to the independent variable at a specific instant.
Longitudinal studies are often used in social-personality and clinical psychology, to study rapid fluctuations in behaviors, thoughts, and emotions from moment to moment or day to day; in developmental psychology, to study developmental trends across the life span; and in sociology, to study life events throughout lifetimes or generations; and ...
Visualization of Simpson's paradox on data resembling real-world variability indicates that risk of misjudgment of true causal relationship can be hard to spot. Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined.
Statistical modeling for nonstationary time series was developed in the 1990s. [33] Methods for nonstationary multivariate extremes have been introduced more recently. [34] The latter can be used for tracking how the dependence between extreme values changes over time, or over another covariate. [35] [36] [37]
It supports the modern evolutionary synthesis—the current scientific theory that explains how and why life changes over time. Evolutionary biologists document evidence of common descent, all the way back to the last universal common ancestor , by developing testable predictions, testing hypotheses, and constructing theories that illustrate ...
Trend analysis can be also used for word usage, how words change in the frequency of use in time (diachronic analysis), in order to find neologisms or archaisms. It relates to diachronic linguistics, a field of linguistics which examines how languages change over time.
For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity itself. Often the independent variable is time.