In which situations would you use the Kruskal-Wallis Test instead of ANOVA?
- When data is normally distributed
- When sample sizes are large
- When the assumptions of ANOVA are violated
- When there is only one independent variable
You would use the Kruskal-Wallis Test when the assumptions of ANOVA (like normality or equal variances) are violated.
What is the role of interaction effects in a two-way ANOVA?
- They calculate the variance within each group
- They correct for multiple comparisons
- They show how the levels of one independent variable affect the effect of the other variable on the dependent variable
- They show the distribution of residuals
In a two-way ANOVA, interaction effects show how the levels of one independent variable affect the effect of the other variable on the dependent variable. Essentially, it shows whether the effect of one independent variable depends on the level of the other independent variable.
What are the characteristics of a Poisson distribution?
- All outcomes are equally likely
- It describes the distribution of non-overlapping events in an interval
- It describes the distribution of rare events
- It describes the events that are not independent
The Poisson distribution is used for describing the distribution of rare events in a large population or time/space interval. It also describes events that are independent, meaning the occurrence of one event doesn't affect the occurrence of another.
When the population variance is unknown, a _______ test is typically used.
- Chi-square
- F
- T
- Z
A T-test is typically used when the population variance is unknown. It's based on the t-distribution, which is a family of distributions that resemble the normal distribution but have heavier tails.
What is a factor loading in the context of factor analysis?
- The correlation between a factor and a variable
- The difference between a factor and a variable
- The percentage of variance in a variable explained by a factor
- The ratio between a factor and a variable
Factor loadings are the correlation coefficients between the factors and the variables. It is a measure of how much the variable is "explained" by the factor.
The variance of each Principal Component corresponds to the _______ of the covariance matrix.
- determinant
- diagonal elements
- eigenvalues
- trace
The variance of each Principal Component corresponds to the eigenvalues of the covariance matrix. A larger eigenvalue corresponds to a larger amount of variance explained by that Principal Component.
In which situations is factor analysis typically used?
- When dealing with categorical variables
- When dealing with high-dimensional data
- When the data distribution is skewed
- When there is a need to predict an outcome
Factor analysis is typically used when dealing with high-dimensional data. It is used to identify a smaller number of factors that explain the pattern of correlations within a set of observed variables, thus helping in dimensionality reduction.
The ________ is the standard deviation of the sampling distribution of a statistic.
- Median deviation
- Population deviation
- Sample deviation
- Standard error
The standard error is the standard deviation of the sampling distribution of a statistic. It measures the dispersion of the sample means around the true population mean.
What are the two branches of statistics?
- Descriptive and hypothetical
- Descriptive and inferential
- Inferential and hypothetical
- Predictive and inferential
The two main branches of statistics are descriptive and inferential. Descriptive statistics involves methods of organizing, picturing, and summarizing information from data. It provides simple summaries about the sample and measures, such as mean, median, mode, etc. Inferential statistics, on the other hand, involves methods of using information from a sample to draw conclusions (inferences) about the population. It includes various techniques like hypothesis testing, regression analysis, etc.
What is a sampling distribution?
- A distribution of all possible samples
- A distribution of sample proportions
- A distribution of sample variances
- A distribution of the population
A sampling distribution is the distribution of a statistic (like a mean, median, or proportion) over many samples drawn from the same population. It is a distribution of all possible samples of the same size that can be obtained from a population.