Converting ________ data into quantitative data involves the process of coding.
- Continuous
- Discrete
- Qualitative
- Quantitative
Converting Qualitative data into quantitative data involves the process of coding. This process involves assigning numerical values to qualitative information (such as categories or themes) so that they can be manipulated and analyzed statistically. For example, if you have data on types of pets (dogs, cats, etc.), you can assign a numerical code (1 for dogs, 2 for cats, etc.) to transform this qualitative data into quantitative data.
The _______ measures the variability of the point estimate.
- Mean
- Median
- Mode
- Standard error
Standard error is a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates.
What are the assumptions for conducting a Kruskal-Wallis Test?
- All of the above
- Data must be normally distributed
- Samples must be independent
- Variances must be equal
The key assumption for conducting a Kruskal-Wallis Test is that the samples must be independent.
The ________ distribution is used when there are exactly two mutually exclusive outcomes of a trial.
- Binomial
- Normal
- Poisson
- Uniform
A binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial (often referred to as a success or a failure). It models the total number of successes in a fixed number of independent trials.
A ________ is a smaller group selected from the population of interest.
- distribution
- parameter
- population
- sample
In statistics, a sample is a smaller group or subset that is selected from the population of interest. It's a subset of the population that is used to represent the entire group as a whole. For example, if the population is all people living in a city, a sample might be 1,000 individuals selected randomly from that city.
In polynomial regression, overfitting can occur when the degree of the polynomial is excessively ________.
- High
- Low
- Middle
- Zero
Overfitting can occur when the degree of the polynomial is excessively high. Overfitting refers to a situation where a model is too complex and captures not just the underlying pattern but also the noise in the data. A high-degree polynomial may fit the training data very well, but it may perform poorly on new, unseen data.
What does the likelihood in Bayes' theorem represent?
- The posterior probability of the event
- The prior probability of the event
- The probability of the event given the evidence
- The probability of the evidence given the event
The likelihood in Bayes' theorem represents the probability of the evidence given the event. It quantifies the extent to which the evidence supports the event.
Explain the concept of conditional independence in probability theory.
- It is another term for mutual exclusivity
- It means that the independence of two events does not depend on the occurrence of any other events
- It means that two events are independent only when a third event does not occur
- It means that two events are independent only when a third event occurs
Conditional independence in probability theory refers to a situation where two events are independent given the occurrence of a third event. Mathematically, two events A and B are conditionally independent given a third event C if the probability of the intersection of A and B given C is the product of the probabilities of A given C and B given C.
A negative value of skewness indicates that the distribution is skewed to the ________.
- Left
- Middle
- Right
- nan
A negative value of skewness indicates that the distribution is skewed to the left, meaning that the left tail of the distribution is longer or fatter than the right tail.
What does ANOVA stand for in statistics?
- Analysis of Variance
- Analytic Normality of Variables
- Automatic Number Variance Analysis
- Average Numerical Outcome Variance
ANOVA stands for Analysis of Variance. It's a statistical method used to test the differences between two or more means.
What does the shape of the probability density function of a normal distribution look like?
- It is skewed to the left
- It is skewed to the right
- It is symmetric and bell-shaped
- It is uniform
The probability density function of a normal distribution is symmetric and bell-shaped. It is characterized by its mean and standard deviation, with the mean indicating the center of the distribution and the standard deviation indicating the width or spread.
What are the consequences of using too large or too small a sample size in hypothesis testing?
- The sample size does not influence hypothesis testing
- Too large a sample size can dilute the effect size, and too small can exaggerate it
- Too large a sample size can lead to overfitting, and too small can lead to underfitting
- Too large a sample size can overstate evidence against the null hypothesis, and too small can lack the power to detect an effect
With a large sample size, small differences may become statistically significant, which can lead to overstating the evidence against the null hypothesis. In contrast, with a small sample size, we might not have enough power to detect an effect, even if one exists.