The standard error of a statistic is a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates. It is used to test hypotheses on the grounds of a set of data. For sample means, the standard error tells us how the mean varies from one sample to another.

Changing the units of measurement will change the scale of the data, and hence will affect the values of standard deviation and variance. If the data is scaled up, both measures will increase, and if the data is scaled down, they will decrease. However, the relative dispersion, as measured by the coefficient of variation, will remain the same.

The principle of equally likely outcomes is a basic assumption in the classical definition of probability. It states that if an experiment has n outcomes, and there's no reason to believe that any one outcome is more likely than any other, then each outcome is assumed to have an equal probability of 1/n. For example, in tossing a fair coin, heads and tails are equally likely.

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering method that can find arbitrary shaped clusters and is less affected by outliers. It works based on the density of points in a region, growing clusters according to the density estimate.

The standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The skewness of a distribution can be determined using a box plot by looking at the position of the median in the box. If the median is not in the center of the box (i.e., the quartiles are not equidistant from the median), the data is skewed. If the median is closer to the bottom of the box, the data is positively skewed, and if it's closer to the top, the data is negatively skewed.

The silhouette score is a measure of how close each point in one cluster is to the points in the neighboring clusters. It ranges from -1 (incorrect clustering) to +1 (highly dense clustering). 0 indicates overlapping clusters.

Non-parametric tests can be used with nominal, ordinal, interval, and ratio scales of measurement. This is one of the reasons why non-parametric tests are sometimes chosen over parametric ones, as they can handle data that are not interval or ratio (which are required for many parametric tests).

If the p-value from a Mann-Whitney U test is less than the significance level (often 0.05), you would reject the null hypothesis, suggesting there is a significant difference between the groups.

The Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population. In other words, as the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.