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If the trend can be assumed to be linear, trend analysis can be undertaken within a formal regression analysis, as described in Trend estimation. If the trends have other shapes than linear, trend testing can be done by non-parametric methods, e.g. Mann-Kendall test, which is a version of Kendall rank correlation coefficient.
Because of the stochastic nature of the trend it is not possible to break up integrated series into a deterministic (predictable) trend and a stationary series containing deviations from trend. Even in deterministically detrended random walks spurious correlations will eventually emerge. Thus detrending does not solve the estimation problem.
If the estimated trend, ^, is larger than the critical value for a certain significance level, then the estimated trend is deemed significantly different from zero at that significance level, and the null hypothesis of a zero underlying trend is rejected. The use of a linear trend line has been the subject of criticism, leading to a search for ...
A systematic review focuses on a specific research question to identify, appraise, select, and synthesize all high-quality research evidence and arguments relevant to that question. A meta-analysis is typically a systematic review using statistical methods to effectively combine the data used on all selected studies to produce a more reliable ...
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
It details the aims, hypothesis, and research method clearly so as to remain transparent and neutral. [6] This review format adheres to explicit criteria when selecting what research is included in the review. Common methods used to analyse selected research articles include text mining, citation, co-citation analysis, and topic modelling ...
Then one can use [5] [6] [7] linear regression to obtain an estimate ^ of the true underlying trend slope and an estimate ^ of the underlying intercept term b; if the estimate ^ is significantly different from zero, this is sufficient to show with high confidence that the variable Y is non-stationary.
The trend test exploits the suspected effect direction to increase power, but this does not affect the sampling distribution of the test statistic under the null hypothesis. Thus, the suspected trend in effects is not an assumption that must hold in order for the test results to be meaningful.