What is the purpose of a Z-test?
- To assess the relationship between categorical variables
- To calculate the correlation between two variables
- To compare sample and population means when the population standard deviation is known
- nan
A Z-test is used to compare the mean of a sample to the mean of a population when the population standard deviation is known. It's not used to calculate correlations or assess relationships between categorical variables.
If the occurrence of A does not affect the occurrence of B, we say A and B are ________.
- Dependent
- Independent
- Joint
- Mutually exclusive
If the occurrence of A does not affect the occurrence of B, we say A and B are independent. This is a key concept in probability theory where the occurrence of one event does not change the probability of another.
What are the ways to check the assumptions of an ANOVA test?
- By calculating the F-statistic
- By calculating the mean and variance of each group
- By checking normality of residuals, homogeneity of variance, and independence of observations
- By conducting post-hoc tests
The assumptions of an ANOVA test can be checked by: 1. Checking the normality of residuals using a normal probability plot or a statistical test like the Shapiro-Wilk test; 2. Checking the homogeneity of variance using a Levene's test or Bartlett's test; 3. Checking the independence of observations which usually pertains to the study design (random sampling, random assignment).
How does the Spearman’s Rank Correlation test handle ties in data ranks?
- Assigns the maximum rank to ties
- Assigns the minimum rank to ties
- Averages the tied ranks
- Ignores the tied ranks
The Spearman’s Rank Correlation test handles ties in data ranks by averaging the ranks. For example, if two values tie for a place in the ranking, they are assigned a rank equal to the average of those places.
__________ in multiple linear regression refers to the proportion of the variance in the dependent variable that is predictable from the independent variables.
- Beta coefficient
- F-statistic
- R-squared
- T-statistic
R-squared is a statistical measure in regression models that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables.
What is the purpose of non-parametric statistical methods?
- To analyze data without making assumptions about the population distribution
- To make the calculation process more complex
- To provide less accurate results
- To use less data in the analysis
Non-parametric statistical methods are used to analyze data without making assumptions about the population distribution. These tests are based on differences in medians or ranks rather than differences in means.
A value of 0 in Pearson's Correlation Coefficient means there's no ________ correlation between the two variables.
- linear
- negative
- perfect
- visible
A value of 0 in Pearson's Correlation Coefficient means there's no linear correlation between the two variables. However, it's important to note that this doesn't necessarily mean there is no relationship at all, it could be that the relationship is nonlinear.
How is a probability distribution defined?
- It is the average value of a dataset
- It is the highest and lowest value of a dataset
- It is the likelihood of each possible outcome of a random variable
- It is the spread of possible values in a dataset
A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. For a random variable, the probability distribution is the probability that the variable takes a particular value.
What does a Principal Component represent in a dataset?
- A combination of original features
- A feature of the dataset
- A group of similar data points
- A target variable
A Principal Component is a linear combination of the original features in a dataset. Each principal component is orthogonal to each other, meaning they are uncorrelated and each represents a different direction in which the data varies.
Can the Mann-Whitney U test be used for paired samples?
- No
- Only if the data is normally distributed
- Only if the variances are equal
- Yes
No, the Mann-Whitney U test is not used for paired samples. It is designed for two independent samples. For paired samples, a different test, such as the Wilcoxon signed-rank test, would be more appropriate.