In a positively skewed distribution, the mean is usually greater than the median. A positive skew means the right tail of the distribution is longer or fatter. The mean, being affected by the values of the data points, gets dragged in the direction of the tail, and hence is typically greater than the median in a positively skewed distribution.

The standard error is the standard deviation of the sampling distribution of a statistic. It measures the dispersion of the sample means around the true population mean.

Factor analysis is typically used when dealing with high-dimensional data. It is used to identify a smaller number of factors that explain the pattern of correlations within a set of observed variables, thus helping in dimensionality reduction.

The variance of each Principal Component corresponds to the eigenvalues of the covariance matrix. A larger eigenvalue corresponds to a larger amount of variance explained by that Principal Component.

Factor loadings are the correlation coefficients between the factors and the variables. It is a measure of how much the variable is "explained" by the factor.

A T-test is typically used when the population variance is unknown. It's based on the t-distribution, which is a family of distributions that resemble the normal distribution but have heavier tails.

In a symmetric distribution, the skewness is zero. The distribution is neither left-skewed (negative skewness) nor right-skewed (positive skewness) but symmetric.

The Kruskal-Wallis Test is used when the assumptions of the ANOVA (like normality, homogeneity of variances) are not met. It's a non-parametric alternative to the one-way ANOVA.

A sampling distribution is the distribution of a statistic (like a mean, median, or proportion) over many samples drawn from the same population. It is a distribution of all possible samples of the same size that can be obtained from a population.

The two main branches of statistics are descriptive and inferential. Descriptive statistics involves methods of organizing, picturing, and summarizing information from data. It provides simple summaries about the sample and measures, such as mean, median, mode, etc. Inferential statistics, on the other hand, involves methods of using information from a sample to draw conclusions (inferences) about the population. It includes various techniques like hypothesis testing, regression analysis, etc.

The Mann-Whitney U test and the Wilcoxon rank-sum test are essentially the same test, although they use slightly different methods of calculation. Both are non-parametric tests used to determine if two independent samples were drawn from a population with the same distribution.

In a histogram, the area under the curve represents the total number of observations in the dataset. The height of each bar corresponds to the frequency of a bin, and the width of the bar corresponds to the size of the bin. So the total area of all bars equals the total number of observations.