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.
In a two-way ANOVA, ________ refers to the effect of one independent variable on the dependent variable, adjusting for the effects of the other independent variables.
- Interaction effect
- Main effect
- Simple effect
- nan
In a two-way ANOVA, the main effect refers to the effect of one independent variable on the dependent variable, adjusting for the effects of the other independent variables. It provides the overall effect of one factor on the outcome, irrespective of the levels of other factors.
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.
The ________ in Spearman's Rank Correlation indicates the strength and direction of association between two ranked variables.
- Coefficient
- Median
- P-value
- Rank
The coefficient in Spearman's Rank Correlation indicates the strength and direction of the association between two ranked variables. This coefficient can range from -1 (perfect negative correlation) to 1 (perfect positive correlation).
What is the purpose of a scatter plot?
- To compare two numerical variables
- To display a distribution
- To show the relationship between three variables
- To visualize categorical variables
A scatter plot is a graphical representation that uses dots to represent the values obtained for two different variables - one plotted along the x-axis and the other plotted along the y-axis. It helps to identify the type of relationship (if any) between two numerical variables.
Does PCA require the features to be on the same scale?
- Depends on the algorithm used
- Depends on the data
- No
- Yes
Yes, PCA requires the features to be on the same scale. If features are on different scales, PCA might end up giving higher weightage to features with higher variance, which could lead to incorrect principal components. So, it's typically a good practice to standardize the data before applying PCA.
What are communalities in factor analysis?
- They are the shared variance between variables
- They are the unique variances of variables
- They are the variances of the factors after rotation
- They represent the total variance of the factors
In factor analysis, communalities are the proportion of variance in each variable that is accounted for, or shared among the factors. They represent the shared variance between variables.
What is the difference between a positively skewed and a negatively skewed distribution?
- Positively skewed has a longer tail on the left, negatively skewed has a longer tail on the right
- Positively skewed has a longer tail on the right, negatively skewed has a longer tail on the left
- Positively skewed has a peak on the left, negatively skewed has a peak on the right
- Positively skewed has a peak on the right, negatively skewed has a peak on the left
In a positively skewed distribution, the right tail is longer or fatter (i.e., the mass of the distribution is concentrated on the left). In a negatively skewed distribution, the left tail is longer or fatter (i.e., the mass of the distribution is concentrated on the right).
The square of the standard deviation gives the _______.
- Mean
- Median
- Range
- Variance
The square of the standard deviation gives the variance. Variance is the average of the squared differences from the mean, and standard deviation is the square root of this variance. Hence, squaring the standard deviation gives us the variance.