What is the rank-based method in non-parametric statistics?
- A method of handling data that involves converting the data to ranks
- A method that involves converting data to percentages
- A method that involves cubing the data values
- A method that involves taking the logarithm of the data
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.
How can you check for the independence assumption in simple linear regression?
- By calculating the mean of the residuals
- By calculating the standard deviation of the residuals
- By checking the correlation coefficient
- By examining a scatter plot of the residuals
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 ________ measures the proportion of the variance in the dependent variable that is predictable from the independent variables in a multiple linear regression.
- Correlation coefficient
- F-statistic
- R-squared value
- Regression coefficient
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.
What are the consequences of violating the assumption of independence in a Chi-square test for goodness of fit?
- It can cause the test to be biased, leading to incorrect conclusions
- It can cause the test to be overly sensitive to small differences
- It can cause the test to have a lower power
- It can cause the test to incorrectly reject the null hypothesis
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.
A point estimate is a single value that serves as an estimate of the ________.
- Median
- Population parameter
- Sample
- Variable
A point estimate is a single value used as an estimate of a population parameter. The sample mean, for instance, might be used as a point estimate of the population mean.
ANOVA assumes that all populations being compared have the same ________.
- All of these
- Mean
- Sample size
- Variance
One of the assumptions of ANOVA is the assumption of homogeneity of variances, which means that all populations being compared have the same variance.
What is the primary purpose of Principal Component Analysis (PCA)?
- To calculate the mean of data
- To classify data
- To reduce dimensionality of data
- To visualize data
The primary purpose of PCA is to reduce the dimensionality of data while maintaining as much information as possible. It transforms the data into a new, lower-dimensional set of variables that are uncorrelated and that explain the maximum possible amount of variance in the data.
The measure of dispersion that is the square root of the variance is known as the _______.
- Mean
- Median
- Range
- Standard Deviation
The standard deviation is the square root of the variance. It measures the average distance between each data point and the mean. Like the variance, it expresses the dispersion of data around the mean, but unlike the variance, its units are the same as the original data, making it easier to interpret.
In hierarchical clustering, a ________ is used to visualize the hierarchy of clusters.
- bar chart
- dendrogram
- histogram
- pie chart
In hierarchical clustering, a dendrogram is used to visualize the hierarchy of clusters. It is a tree-like diagram that records the sequences of merges or splits.
What is the difference between a one-tailed and a two-tailed test?
- The directionality of the hypothesis
- The number of samples being compared
- The number of times the test is performed
- The types of data being used
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.