In hypothesis testing, a Type II error is committed when the null hypothesis is ______ but we ______ to reject it.
- False, fail to reject
- False, reject
- True, fail to reject
- True, reject
A Type II error, also known as a false negative, occurs when we fail to reject a false null hypothesis. This means we've missed evidence of an effect or difference that truly exists.
What kind of relationship does Pearson's Correlation Coefficient measure?
- Exponential
- Linear
- Monotonic
- Non-linear
Pearson's correlation coefficient measures linear relationships between variables. It measures the degree to which pairs of data for these two variables lie on a line.
What is the main difference between the Wilcoxon Signed Rank Test and the paired t-test?
- All of the above
- The Wilcoxon test is non-parametric while the t-test is parametric
- The Wilcoxon test is used for ordinal data while the t-test is used for continuous data
- The Wilcoxon test uses ranks while the t-test uses actual values
The Wilcoxon Signed Rank Test is a non-parametric test that uses ranks and is used for ordinal data, while the paired t-test is a parametric test that uses actual values and is typically used for continuous data.
The ________ in a two-way ANOVA can reveal whether the effect of one independent variable depends on the level of the other independent variable.
- Effect size
- Interaction effect
- Main effect
- Post-hoc test
The interaction effect in a two-way ANOVA reveals whether the effect of one independent variable depends on the level of the other independent variable. This allows us to understand how the independent variables relate to each other.
How is Bayes' theorem related to conditional probability?
- Bayes' theorem and conditional probability are not related
- Bayes' theorem cannot be used with conditional probability
- Bayes' theorem is a specific type of conditional probability
- Bayes' theorem is used to calculate the complement of the conditional probability
Bayes' theorem is a way of finding a probability when we know certain other probabilities. The probabilities that we know are usually conditional probabilities, and Bayes' theorem is used to 'reverse' these probabilities.
The ________ is the most frequent value in a data set.
- Mean
- Median
- Mode
- nan
The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.
What is a uniform distribution?
- A distribution in which all outcomes are equally likely
- A distribution in which all outcomes follow a linear pattern
- A distribution where outcomes are not related
- A distribution where outcomes have a bell-shaped pattern
A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. This distribution is often used in the cases where all outcomes are equally likely.
How is the 'mean' calculated for a data set?
- By arranging the values in ascending order
- By finding the middle value
- By finding the most frequent value
- By summing all values and dividing by the number of values
The mean of a data set is calculated by summing all the values and then dividing by the number of values. It gives the 'average' of the data and can be used for both discrete and continuous data sets. However, it can be heavily influenced by outliers or extreme values.
How can the effects of interaction be investigated in a two-way ANOVA?
- By calculating the F-statistic for each independent variable
- By checking the interaction term in the ANOVA table
- By conducting a one-way ANOVA
- By conducting post-hoc tests
The effects of interaction in a two-way ANOVA can be investigated by examining the interaction term in the ANOVA table. If the p-value for the interaction term is significant, it suggests that the effect of one independent variable on the dependent variable depends on the level of the other independent variable. Post-hoc tests can then be conducted to investigate the interaction effects further.
How does the presence of multicollinearity affect the standard errors of the regression coefficients?
- It does not affect the standard errors.
- It makes them equal to zero.
- It makes them larger.
- It makes them smaller.
In the presence of multicollinearity, the standard errors of the affected coefficients are inflated, leading to less precise and unstable estimates of the regression coefficients.