What is a significant factor in a two-way ANOVA?
- An independent variable that affects the dependent variable
- The method of data collection
- The precision of the instruments used
- The size of the sample
In a two-way ANOVA, a significant factor is an independent variable that has a significant effect on the dependent variable. It is determined based on the calculated p-value for the effect of that factor.
Which type of data is numerical: qualitative or quantitative?
- Both
- None
- Qualitative
- Quantitative
Quantitative data is numerical. It represents measurements or counts that can be quantified mathematically. For example, age, height, weight, or the number of objects are all quantitative data because they consist of numeric measurements.
When would you use a t-test instead of a Z-test?
- All of the above
- When the data is not normally distributed
- When the population standard deviation is unknown
- When the sample size is very large
T-tests are typically used when the population standard deviation is unknown. The sample size or normality of data isn't the primary deciding factor.
In what scenarios is the use of Bayes' theorem considered controversial in statistics?
- All of the above
- When the events are independent
- When the prior is subjective or not based on data
- When the sample size is very large
The use of Bayes' Theorem is controversial when the prior probability is subjective or not based on data. Critics argue that this introduces personal bias into the statistical analysis. However, Bayesians argue that all modeling involves subjective choices.
What is the difference between one-way and two-way ANOVA?
- One-way ANOVA compares one group, two-way ANOVA compares two groups
- One-way ANOVA compares two groups, two-way ANOVA compares more than two groups
- One-way ANOVA considers one independent variable, two-way ANOVA considers two independent variables
- One-way ANOVA considers two independent variables, two-way ANOVA considers one independent variable
The key difference between one-way and two-way ANOVA lies in the number of independent variables they consider. A one-way ANOVA is used when there is one independent variable, whereas a two-way ANOVA is used when there are two independent variables.
What is the Durbin-Watson statistic used for in residual analysis?
- To check for autocorrelation
- To check for heteroscedasticity
- To check for linearity of the relationship
- To check for normality of residuals
The Durbin-Watson statistic is a test statistic used to detect the presence of autocorrelation (a relationship between values separated from each other by a given time lag) in the residuals (prediction errors) from a regression analysis.
The Mann-Whitney U test is primarily used for comparing ________ distributions.
- binomial
- dependent
- independent
- normal
The Mann-Whitney U test is used for comparing independent distributions, particularly to determine whether two independent samples were drawn from a population with the same distribution.
What is the difference between a discrete and a continuous probability distribution?
- Discrete distributions are always normal; continuous distributions are always uniform
- Discrete distributions are for qualitative data; continuous distributions are for quantitative data
- Discrete distributions involve countable outcomes; continuous distributions involve uncountable outcomes
- There is no difference
Discrete probability distributions are used when the outcomes are countable or discrete. Examples include the number of heads when flipping coins or the number of defective items in a batch. Continuous probability distributions are used when outcomes are uncountably infinite, typically involving measurements. Examples include the height of individuals or the time it takes to run a mile.
What are the dependent and independent variables in simple linear regression?
- Both variables are dependent
- Both variables are independent
- The dependent variable is the outcome we are trying to predict, and the independent variable is the predictor
- The dependent variable is the predictor, and the independent variable is the outcome we are trying to predict
In simple linear regression, the dependent variable is the outcome we are trying to predict, and the independent variable is the predictor. The dependent variable is also known as the response or target variable, and the independent variable is also known as the explanatory or feature variable.
When is it appropriate to use a binomial distribution?
- When each trial in an experiment has exactly two possible outcomes
- When the data is continuous
- When the outcomes are not independent
- When the probability of success changes with each trial
A binomial distribution is appropriate when conducting an experiment where each trial has exactly two possible outcomes (often termed success and failure), the trials are independent, and the probability of success is constant across trials.