The Mann-Whitney U test is a ________ test.
- Chi-square
- correlation
- non-parametric
- parametric
The Mann-Whitney U test is a non-parametric test, meaning it does not assume that the underlying data follows a specific distribution.
How does the concept of "updating" apply in Bayesian statistics?
- It means changing the data after analysis
- It means replacing old hypotheses with new ones
- It refers to modifying the statistical model
- It refers to the process of using new evidence to update a prior probability
Updating in Bayesian statistics refers to the process of using new evidence to update a prior probability to a posterior probability. Bayes' theorem provides the mathematical framework for this updating process.
What are the implications of having a small expected frequency in a Chi-square test for goodness of fit?
- It can cause the Chi-square distribution approximation to be inaccurate
- It increases the degrees of freedom
- It leads to a higher power of the test
- It leads to a smaller Chi-square statistic
If the expected frequency in any category is too small (common rule of thumb is less than 5), the Chi-square distribution approximation may be inaccurate, leading to incorrect conclusions.
If the calculated Chi-square statistic is greater than the critical Chi-square value, we ________ the null hypothesis.
- accept
- adjust
- reject
- retain
If the calculated Chi-square statistic is greater than the critical Chi-square value (based on the chosen significance level and the degrees of freedom), we reject the null hypothesis. This means the observed distribution significantly differs from the expected distribution.
Factor analysis reduces the dimensions of data by combining similar _______ into groups or factors.
- eigenvalues
- factors
- observations
- variables
Factor analysis reduces the dimensions of data by combining similar variables into groups or factors.
The ________ distribution is symmetric and its mean, median and mode are equal.
- Binomial
- Normal
- Poisson
- Uniform
The normal distribution, also known as the Gaussian distribution, is symmetric, and its mean, median, and mode are all equal. It is shaped like a bell curve, with the data evenly distributed about the mean.
What are the key assumptions for applying the Sign Test?
- Data must be at least ordinal
- Data must be categorical
- Data must be continuous
- Data must be normally distributed
The key assumption for applying the Sign Test is that the data must be at least ordinal. The Sign Test is a non-parametric test and does not require the assumption of normality.
How does the Law of Large Numbers impact the calculation of probabilities?
- It changes the probability of an event based on previous outcomes.
- It doesn't affect the calculation of probabilities.
- It guarantees that the experimental probability gets closer to the theoretical probability as the number of trials increases.
- It states that all probabilities must be equal.
The Law of Large Numbers impacts the calculation of probabilities by asserting that as the number of trials (or observations) increases, the experimental probabilities will get closer and closer to the theoretical (or true) probabilities. It gives validity to the notion of probability in practical applications.
The Sign Test is based on the direction of the _________ between pairs.
- differences
- medians
- ranks
- signs
The Sign Test is based on the direction of the differences between pairs.
What techniques can be used to detect multicollinearity in a multiple regression model?
- Analysis of Variance (ANOVA)
- Chi-square test
- T-test
- Variance Inflation Factor (VIF)
The Variance Inflation Factor (VIF) is commonly used to detect multicollinearity in regression analysis.