Interval estimation provides a range (or interval) of values for the parameter of interest. This is more informative than a point estimate, as it gives a measure of uncertainty.

To detect the presence of interaction effects in your data, you can include interaction terms in your regression model and then check the significance of these terms. If the interaction term is statistically significant, this suggests that the effect of one variable on the dependent variable depends on the level of another variable.

For continuous random variables, the probability density function (PDF) is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value.

Violating the assumption of homoscedasticity (equal variances across groups) in ANOVA can lead to incorrect conclusions about the differences between group means, i.e., the results of the ANOVA test could be misleading. This might cause Type I errors (rejecting a true null hypothesis) or Type II errors (failing to reject a false null hypothesis).

The silhouette score is a measure of the similarity of an object to its own cluster (cohesion) compared to other clusters (separation). It represents how similar an object is to its own cluster compared to other clusters. The score ranges from -1 to 1, with high values indicating that the object is well matched to its own cluster and poorly matched to neighboring clusters.

The Wilcoxon Signed Rank Test is a non-parametric test used to compare the medians of two related groups.

The significance of Pearson's Correlation Coefficient is determined by conducting a hypothesis test, which involves comparing the calculated coefficient to a critical value from the t-distribution. If the absolute value of the coefficient is larger than the critical value, we can conclude that the correlation is statistically significant.

The power of a test is influenced by the effect size - the magnitude of the difference or relationship you're testing for. Larger effect sizes increase the power of a test because they create a larger signal relative to the noise, making it easier to detect an effect if one exists.

The Wilcoxon Signed Rank Test requires the differences to be ordinal or interval, because it takes into account the magnitude of the differences.

In a two-way ANOVA, a significant factor is an independent variable that has a significant effect on the dependent variable. It is determined based on the calculated p-value for the effect of that factor.