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.
The Kruskal-Wallis Test is a non-parametric method used when the assumptions of the ________ are not met.
- ANOVA
- Correlation analysis
- Regression analysis
- t-test
The Kruskal-Wallis Test is used when the assumptions of the ANOVA (like normality, homogeneity of variances) are not met. It's a non-parametric alternative to the one-way ANOVA.
In a symmetric distribution, the skewness is ________.
- -1
- 0
- 1
- It varies
In a symmetric distribution, the skewness is zero. The distribution is neither left-skewed (negative skewness) nor right-skewed (positive skewness) but symmetric.
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 assumptions must be met for a Chi-square test for independence to be valid?
- The data must be continuous
- The data must be normally distributed
- The observations must be independent and the expected frequency of each category must be at least 5
- The sample size must be larger than 30
For a Chi-square test for independence to be valid, the observations must be independent, and the expected frequency of each category must be at least 5.