On Significance III

"Given the important role that correlation plays in structural equation modeling, we need to understand the factors that affect establishing relationships among multivariable data points. The key factors are the level of measurement, restriction of range in data values (variability, skewness, kurtosis), missing data, nonlinearity, outliers, correction for attenuation, and issues related to sampling variation, confidence intervals, effect size, significance, sample size, and power." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"There are three possible reasons for [the] absence of predictive power. First, it is possible that the models are misspecified. Second, it is possible that the model’s explanatory factors are measured at too high a level of aggregation [...] Third, [...] the search for statistically significant relationships may not be the strategy best suited for evaluating our model’s ability to explain real world events [...] the lack of predictive power is the result of too much emphasis having been placed on finding statistically significant variables, which may be overdetermined. Statistical significance is generally a flawed way to prune variables in regression models [...] Statistically significant variables may actually degrade the predictive accuracy of a model [...] [By using] models that are constructed on the basis of pruning undertaken with the shears of statistical significance, it is quite possible that we are winnowing our models away from predictive accuracy." (Michael D Ward et al, "The perils of policy by p-value: predicting civil conflicts" Journal of Peace Research 47, 2010)

"Another way to secure statistical significance is to use the data to discover a theory. Statistical tests assume that the researcher starts with a theory, collects data to test the theory, and reports the results - whether statistically significant or not. Many people work in the other direction, scrutinizing the data until they find a pattern and then making up a theory that fits the pattern." (Gary Smith, "Standard Deviations", 2014)

"These practices - selective reporting and data pillaging - are known as data grubbing. The discovery of statistical significance by data grubbing shows little other than the researcher’s endurance. We cannot tell whether a data grubbing marathon demonstrates the validity of a useful theory or the perseverance of a determined researcher until independent tests confirm or refute the finding. But more often than not, the tests stop there. After all, you won’t become a star by confirming other people’s research, so why not spend your time discovering new theories? The data-grubbed theory consequently sits out there, untested and unchallenged." (Gary Smith, "Standard Deviations", 2014)

"With fast computers and plentiful data, finding statistical significance is trivial. If you look hard enough, it can even be found in tables of random numbers." (Gary Smith, "Standard Deviations", 2014)

"In short, statistical significance does not mean your result has any practical significance. As for statistical insignificance, it doesn’t tell you much. A statistically insignificant difference could be nothing but noise, or it could represent a real effect that can be pinned down only with more data." (Alex Reinhart, "Statistics Done Wrong: The Woefully Complete Guide", 2015)

"Statistical significance is a concept used by scientists and researchers to set an objective standard that can be used to determine whether or not a particular relationship 'statistically' exists in the data. Scientists test for statistical significance to distinguish between whether an observed effect is present in the data (given a high degree of probability), or just due to chance. It is important to note that finding a statistically significant relationship tells us nothing about whether a relationship is a simple correlation or a causal one, and it also can’t tell us anything about whether some omitted factor is driving the result." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)

"Statistical significance refers to the probability that something is true. It’s a measure of how probable it is that the effect we’re seeing is real (rather than due to chance occurrence), which is why it’s typically measured with a p-value. P, in this case, stands for probability. If you accept p-values as a measure of statistical significance, then the lower your p-value is, the less likely it is that the results you’re seeing are due to chance alone." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)