What does it mean when results are significantly different?
Not Due to Chance In principle, a statistically significant result (usually a difference) is a result that’s not attributed to chance. More technically, it means that if the Null Hypothesis is true (which means there really is no difference), there’s a low probability of getting a result that large or larger.
Is a difference statistically significant?
But statistical significance is not the same as practical significance. Often times, when differences are small but statistically significant, it is due to a very large sample size; in a sample of a smaller size, the differences would not be enough to be statistically significant.
How to measure the significance of a difference?
Calculate how far each observation is from the average, square each difference, and then average the results and take the square root. This is the standard deviation, and it measures how spread out the measurements are from their mean. The standard error of some estimator. For example, perhaps the error bars are the standard error of the mean.
Is it wise to obtain multiple measurements over a wide range?
Physical variations (random) — It is always wise to obtain multiple measurements over the widest range possible. Doing so often reveals variations that might otherwise go undetected. These variations may call for closer examination, or they may be combined to find an average value.
What happens when two results have identical statistical significance?
Two results with identical statistical significance can nonetheless contradict each other. Instead, think about statistical power. If we compare our new experimental drugs Fixitol and Solvix to a placebo but we don’t have enough test subjects to give us good statistical power, then we may fail to notice their benefits.
When are differences in significance aren’t significant?
There is a statistically significant difference between the groups, even though the confidence intervals overlap. [1] Unfortunately, many scientists skip hypothesis tests and simply glance at plots to see if confidence intervals overlap.