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).
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.
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 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.
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 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.
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.
The ________ of an event A is the event that A does not occur.
- Complement
- Mirror
- Opposite
- Substitute
In probability theory, the "complement" of an event A is the event that A does not occur, often denoted as A'. If the probability of event A happening is P(A), then the probability of it not happening, or its complement, is P(A') = 1 - P(A).
The Mann-Whitney U test assumes that the samples are ________ and ________.
- dependent, heterogeneous
- dependent, homogeneous
- independent, heterogeneous
- independent, homogeneous
The Mann-Whitney U test assumes that the samples are independent (not paired or related) and heterogeneous (can have different variances).
When are the Addition and Multiplication Rules of Probability applicable?
- Both are used for mutually exclusive events
- Only for dependent events
- Only for independent events
- The Addition Rule is for mutually exclusive events and the Multiplication Rule is for independent events
The Addition Rule is applicable when calculating the probability of the occurrence of at least one of two mutually exclusive events, while the Multiplication Rule is used to calculate the probability of two independent events both occurring.
What happens to the range of a dataset if an outlier is added?
- The effect on the range is unpredictable
- The range decreases
- The range increases
- The range remains the same
If an outlier is added to a dataset, it can significantly increase the range, as the range is calculated as the difference between the maximum and minimum values in the dataset.
How does the power of a test relate to Type II errors?
- The power of a test is the probability of making a Type II error
- The power of a test is the probability of not making a Type II error
- The power of a test is unrelated to Type II errors
- nan
The power of a test is the probability that it correctly rejects a false null hypothesis, i.e., it is the probability of not making a Type II error.