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).
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).
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.
What is a Type I error in the context of hypothesis testing?
- Accepting a false null hypothesis
- Accepting a true null hypothesis
- Rejecting a false null hypothesis
- Rejecting a true null hypothesis
A Type I error occurs when the null hypothesis is true, but it is rejected. It is also known as a "false positive" result.
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.
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.
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.
A numerical summary of a sample, as opposed to a population, is known as a ________.
- mean
- mode
- parameter
- statistic
In the field of statistics, a statistic is a numerical summary of a sample, as opposed to a population. It's a measure that is calculated from the sample data. For example, if we have data for a certain number of individuals from a larger group, the average of this data is a statistic.
Does the Kruskal-Wallis Test require the data to be normally distributed?
- No
- Only for large sample sizes
- Only for small sample sizes
- Yes
No, the Kruskal-Wallis Test does not require the data to be normally distributed. This is why it is classified as a non-parametric test.