The main difference between one-tailed and two-tailed tests is the directionality of the hypothesis. One-tailed tests look for an effect in a specific direction, while two-tailed tests look for an effect in either direction.

A rank-based method in non-parametric statistics is a method of handling data that involves converting the data to ranks. The original data values are replaced by their ranks (e.g., the smallest value gets a rank of 1, the second smallest gets a rank of 2, etc.), and these ranks are used in the statistical analysis.

The independence assumption in simple linear regression can be checked by examining a scatter plot of the residuals. The residuals should be randomly scattered with no clear pattern. If there is a clear pattern (like a curve or a trend), it indicates that the residuals are not independent and the assumption of independence is violated.

The R-squared value, also known as the coefficient of determination, measures the proportion of the variance in the dependent variable that can be predicted from the independent variables in a multiple linear regression. It ranges from 0 to 1, with 1 indicating perfect prediction.

Violating the assumption of independence in a Chi-square test for goodness of fit can lead to biased results and incorrect conclusions. This is because the test assumes that the observations are independent, and this assumption is necessary for the test's validity.

Yes, a symmetrical distribution can have nonzero kurtosis. Kurtosis is a measure of the weight in the tails, or the extreme values, which can occur in both directions, thus not affecting the symmetry. For example, a normal distribution is symmetric and has a kurtosis greater than zero.

Spearman's rank correlation coefficient is a non-parametric measure of correlation, meaning it can be used when the data is not normally distributed. It is also less sensitive to outliers compared to Pearson's coefficient. Further, it can be used to measure monotonic relationships, whether they are linear or not.

The Mann-Whitney U test is a common non-parametric statistical method used to compare two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.

A non-significant result in the Chi-square test for goodness of fit indicates that the observed distribution does not significantly differ from the expected distribution. In other words, we do not have enough evidence to reject the null hypothesis.

The Chi-square test for goodness of fit is used to test whether the observed data fits a specific distribution. It compares the observed data with the values that would be expected under the theoretical distribution.