The Chi-square test for goodness of fit is used to determine whether the observed distribution of data follows an expected distribution.

PCA can be implemented using SVD. Both techniques can be used for dimensionality reduction, and they both rely on eigenvalue decomposition, but SVD decomposes the data matrix directly, while PCA works on the covariance matrix of the data.

A wider confidence interval suggests a higher level of uncertainty about the estimate because the range of values for the population parameter is larger.

In multiple linear regression, each coefficient represents the average change in the dependent variable for one unit of change in the independent variable, while holding all other independent variables constant.

Bartlett's Test of Sphericity is used in factor analysis to test the hypothesis that the variables are uncorrelated in the population. In other words, the population correlation matrix is an identity matrix. A significant test indicates that a factor analysis may be useful with your data.

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.

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).

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.

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 key difference between parametric and non-parametric statistical methods is the assumptions they make about the data distribution. Parametric methods assume that the data follow a certain distribution, while non-parametric methods do not make these assumptions.

Converting Qualitative data into quantitative data involves the process of coding. This process involves assigning numerical values to qualitative information (such as categories or themes) so that they can be manipulated and analyzed statistically. For example, if you have data on types of pets (dogs, cats, etc.), you can assign a numerical code (1 for dogs, 2 for cats, etc.) to transform this qualitative data into quantitative data.

Standard error is a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates.