If two events are independent, the conditional probability of one event given the other is simply the probability of the event itself. This is because in independent events, the occurrence of one event does not affect the occurrence of the other event.

A Type II error, also known as a false negative, occurs when the null hypothesis is false, but we fail to reject it.

The mode can be misleading or irrelevant especially with continuous data. Since the mode is the most frequently occurring value, with continuous data the frequency of each value is often the same (i.e., 1), hence it becomes difficult to define a mode in a traditional sense.

A VIF greater than 5 is often taken as an indication of high multicollinearity among the predictors in a regression model. This could lead to imprecise and unreliable estimates of the regression coefficients.

The type of factor analysis in which the researcher assumes that all variance in the observed variables is common variance is known as common factor analysis.

The Kruskal-Wallis Test is used to compare three or more independent samples. It's an extension of the Mann-Whitney U Test for more than two groups.

Spearman's Rank Correlation is preferable to Pearson's correlation when the relationship between variables is non-linear but monotonic. Pearson's correlation measures linear relationships, while Spearman's can capture non-linear relationships.

The z-value associated with a 95% confidence interval in a standard normal distribution is approximately 1.96. This means that we are 95% confident that the true population parameter lies within 1.96 standard deviations of the sample mean.

The interquartile range, which is the difference between the upper quartile (Q3) and the lower quartile (Q1), represents the middle 50% of the data and is not affected by outliers. The range, on the other hand, is the difference between the maximum and minimum data values and is significantly affected by outliers.

Outliers can have a significant impact on the result of K-means clustering. They can distort the shape and size of the clusters, as they may pull the centroid towards them, creating less accurate and meaningful clusters.