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.
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.
In what scenarios might Spearman's rank correlation coefficient be a better choice than Pearson's?
- When both variables are normally distributed
- When the data contains outliers or is not normally distributed
- When the relationship between variables is linear
- When the relationship between variables is non-linear and non-monotonic
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.
A ________ test is a common non-parametric statistical method.
- ANOVA
- Mann-Whitney U
- Regression
- T
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 ________ result in the Chi-square test for goodness of fit indicates that the observed distribution does not significantly differ from the expected distribution.
- negative
- non-significant
- significant
- skewed
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.
What is the purpose of a Chi-square test for goodness of fit?
- To compare the means of two groups
- To compare the variance of two groups
- To determine the correlation between two variables
- To test if a data set follows a given theoretical distribution
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.
What does the slope of the regression line represent in simple linear regression?
- It represents the change in the dependent variable for a one-unit change in the independent variable
- It represents the error term
- It represents the independent variable
- It represents the strength of the correlation
The slope of the regression line in simple linear regression represents the change in the dependent variable for a one-unit change in the independent variable. It quantifies the strength and direction of the linear relationship between the two variables.
The ________ probability in Bayes' theorem is the revised probability of an event occurring after taking into account new information.
- joint
- marginal
- posterior
- prior
In Bayes' theorem, the posterior probability is the revised probability of an event occurring after taking into account new evidence.
What does a 95% confidence interval mean?
- That 95% of the population is within the interval
- That 95% of the sample data lies within the interval
- That the interval captures the true population parameter 95% of the time
- That there is a 95% chance that the interval contains the mean
A 95% confidence interval means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95% of the cases.