The Z-score and T-score are both types of _______ scores, which measure the number of standard deviations an observation is from the mean.
- mean
- median
- standard
- variance
The Z-score and T-score are both types of standard scores. They measure the number of standard deviations an observation or statistic is from the mean.
A ________ ANOVA is used when we have two independent variables and want to understand if there is an interaction between them.
- Factorial
- One-way
- Three-way
- Two-way
A two-way ANOVA is used when there are two independent variables. This type of ANOVA assesses the main effects of each independent variable and the interaction effect between the variables.
Can Pearson's Correlation Coefficient determine causality?
- No, never
- Yes, always
- Yes, but additional information is required
- Yes, but only if the coefficient is 1 or -1
No, Pearson's Correlation Coefficient cannot determine causality. It can only measure the degree of linear correlation between two variables. While two variables may be correlated, it does not mean that changes in one variable cause changes in the other. Correlation does not imply causation.
What does the range of a dataset represent?
- The average value
- The middle value
- The most frequent value
- The spread of the data
The range of a dataset is a measure of dispersion, representing the total spread of values in the dataset. It is calculated by subtracting the smallest value from the largest value in the dataset.
In a Venn diagram, the intersection of events A and B is represented by ________.
- The area only inside A
- The area only inside B
- The area outside of A and B
- The area where A and B overlap
In a Venn diagram, the intersection of events A and B is represented by the area where A and B overlap. This represents all outcomes that are in both A and B, or said another way, outcomes that satisfy both events A and B.
In which type of distribution are all outcomes equally likely?
- Exponential distribution
- Normal distribution
- Poisson distribution
- Uniform distribution
In a uniform distribution, all outcomes are equally likely. This is because the probability density function is constant within a certain range and zero elsewhere.
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.
What are confidence intervals used for in statistics?
- To determine the median of a sample
- To determine the spread of data in a sample
- To estimate the population parameter
- To find the mean of a sample
Confidence intervals are used to estimate the range within which the true population parameter lies with a certain degree of confidence. They do not specifically determine the mean, median, or spread of a sample.
How does skewness affect the mean and median of a dataset?
- In a positively skewed distribution, the mean is greater than the median
- In a positively skewed distribution, the median is greater than the mean
- Skewness affects only the mean
- Skewness does not affect the mean and median
In a positively skewed distribution, the mean is greater than the median as the mean gets pulled in the direction of the skew (towards the right tail). In a negatively skewed distribution, the mean is less than the median as the mean gets pulled towards the left tail.
What can cause the Chi-square test for goodness of fit to be biased?
- Having a large sample size
- Having a small sample size
- Having equal expected frequencies in all categories
- Having normally distributed data
A small sample size can lead to unreliable results in a Chi-square test for goodness of fit. This can be due to the fact that the test requires a sufficient number of observations in each category to provide a reliable estimate of the distribution.