In what scenarios is the use of Bayes' theorem considered controversial in statistics?
- All of the above
- When the events are independent
- When the prior is subjective or not based on data
- When the sample size is very large
The use of Bayes' Theorem is controversial when the prior probability is subjective or not based on data. Critics argue that this introduces personal bias into the statistical analysis. However, Bayesians argue that all modeling involves subjective choices.
When would you use a t-test instead of a Z-test?
- All of the above
- When the data is not normally distributed
- When the population standard deviation is unknown
- When the sample size is very large
T-tests are typically used when the population standard deviation is unknown. The sample size or normality of data isn't the primary deciding factor.
Which type of data is numerical: qualitative or quantitative?
- Both
- None
- Qualitative
- Quantitative
Quantitative data is numerical. It represents measurements or counts that can be quantified mathematically. For example, age, height, weight, or the number of objects are all quantitative data because they consist of numeric measurements.
What is a significant factor in a two-way ANOVA?
- An independent variable that affects the dependent variable
- The method of data collection
- The precision of the instruments used
- The size of the sample
In a two-way ANOVA, a significant factor is an independent variable that has a significant effect on the dependent variable. It is determined based on the calculated p-value for the effect of that factor.
The Wilcoxon Signed Rank Test requires the differences to be ________.
- continuous
- nan
- nominal
- ordinal or interval
The Wilcoxon Signed Rank Test requires the differences to be ordinal or interval, because it takes into account the magnitude of the differences.
How does the effect size influence the power of a test?
- Effect size has no influence on power
- It depends on the sample size
- Larger effect sizes decrease power
- Larger effect sizes increase power
The power of a test is influenced by the effect size - the magnitude of the difference or relationship you're testing for. Larger effect sizes increase the power of a test because they create a larger signal relative to the noise, making it easier to detect an effect if one exists.
How is the significance of Pearson's Correlation Coefficient determined?
- By calculating the standard deviation
- By comparing it to the mean
- By comparing to a critical value from the t-distribution
- By squaring the coefficient
The significance of Pearson's Correlation Coefficient is determined by conducting a hypothesis test, which involves comparing the calculated coefficient to a critical value from the t-distribution. If the absolute value of the coefficient is larger than the critical value, we can conclude that the correlation is statistically significant.
What is the primary use of the Wilcoxon Signed Rank Test?
- To compare the means of two groups
- To compare the medians of two groups
- To compare the mode of two groups
- nan
The Wilcoxon Signed Rank Test is a non-parametric test used to compare the medians of two related groups.
What kind of data is suitable for the Kruskal-Wallis Test?
- Binary data
- Nominal data
- Normal data
- Ordinal or continuous data
The Kruskal-Wallis Test is suitable for ordinal or continuous data that is not normally distributed.
What is the relationship between Cramér's V and the Chi-square test?
- Cramér's V is the inverse of the Chi-square statistic
- Cramér's V is the square of the Chi-square statistic
- Cramér's V is the square root of the Chi-square statistic divided by the sample size and the minimum of rows and columns minus 1
- There is no relationship between Cramér's V and the Chi-square test
Cramér's V is a measure of association between two nominal variables and it is based on the Chi-square statistic. It is calculated as the square root of the Chi-square statistic divided by the sample size and the minimum of rows and columns minus 1.
How is the confidence interval for a proportion calculated?
- nan
- p ± (z*√(p(1-p)/n))
- p ± z*(s/√n)
- p ± z*(σ/√n)
The confidence interval for a proportion is calculated using the formula: p ± (z*√(p(1-p)/n)), where p is the sample proportion, z is the z-score associated with the desired confidence level, and n is the sample size.
What is the primary purpose of conducting an ANOVA test?
- To calculate the standard deviation of a dataset
- To determine the mode of a set of data
- To find the correlation between two variables
- To test the equality of means among groups
The primary purpose of an ANOVA test is to compare the means of different groups and determine whether any of those means are significantly different from each other.