Final answer:
Trend analysis is the statistical method that examines time-series data to identify if variances are isolated events or part of longer movements. Analysis of variance (ANOVA), especially one-way ANOVA, is used to test equality of means across groups. Regression analysis is employed to determine the strength and direction of cause and effect relationships.
Step-by-step explanation:
The statistical method that examines data from different points in time to determine if a variance is an isolated event or if it is part of a longer movement is called trend analysis. This analysis is employed to identify trends in time-series data and to ascertain if movements in data are due to exogenous or endogenous influences. These trends can indicate if the movements are simply short-term fluctuations or part of a broader, longer-term cycle.
Analysis of variance (ANOVA) is another statistical method used to test whether the means of three or more groups are equal, assuming the populations are normally distributed with equal standard deviations; data are sampled randomly and independently. One-way ANOVA, in particular, is used when there is one independent variable and one dependent variable, employing the F ratio as the test statistic.
For understanding the nature of cause and effect relationships, regression analysis is typically used. It allows researchers to evaluate the strength and direction of relationships between a dependent (effect) variable and one or more independent (cause) variables. This can be done with software, like GIS in the case of geospatial data, which highlights how well the variables predict trends.