If the assumptions of a parametric test are violated, it might be appropriate to use a non-parametric statistical method. Non-parametric methods have fewer assumptions and can be used with different types of data.

The standard error is a statistical term that measures the standard deviation of the sampling distribution. In other words, it provides a measure of the variability or dispersion of sample means around the population mean. A smaller standard error indicates that the sample mean is likely to be a closer approximation to the population mean.

The probability of a Type I error (false positive) is the same as the significance level of a test. A significance level of 0.05, for instance, means there's a 5% chance of rejecting a true null hypothesis (Type I error).

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. It's used to observe and show the relationship between two numeric variables.

Conditional independence in probability theory refers to a situation where two events are independent given the occurrence of a third event. Mathematically, two events A and B are conditionally independent given a third event C if the probability of the intersection of A and B given C is the product of the probabilities of A given C and B given C.

The likelihood in Bayes' theorem represents the probability of the evidence given the event. It quantifies the extent to which the evidence supports the event.

Overfitting can occur when the degree of the polynomial is excessively high. Overfitting refers to a situation where a model is too complex and captures not just the underlying pattern but also the noise in the data. A high-degree polynomial may fit the training data very well, but it may perform poorly on new, unseen data.

In statistics, a sample is a smaller group or subset that is selected from the population of interest. It's a subset of the population that is used to represent the entire group as a whole. For example, if the population is all people living in a city, a sample might be 1,000 individuals selected randomly from that city.

A sample might not accurately represent the population when the sampling method is biased. In this case, the sample may not be diverse enough or inclusive of all relevant aspects of the population. This can lead to skewed results and inaccurate inferences about the population. Hence, it's essential to choose an unbiased sampling method.

In a uniform distribution, all outcomes are equally likely. This distribution is characterized by two parameters, a and b, which are the minimum and maximum values, respectively. The probability of any outcome is constant and equal across the entire range of the distribution.