Conditional independence of A and B given C means that knowing that C has occurred does not change the ________ between A and B.
- Difference
- Intersection
- Ratio
- Relationship
Conditional independence of A and B given C means that knowing that C has occurred does not change the relationship between A and B. In other words, the occurrence of event C does not affect the independence of events A and B.
What is the assumption made when computing the Pearson correlation coefficient?
- The correlation is zero
- The variables are independent
- The variables are normally distributed
- There is a linear relationship between variables
When computing the Pearson correlation coefficient, it is assumed that there is a linear relationship between the variables. Furthermore, it's also assumed that the variables are continuous and that the data is homoscedastic (i.e., the variance of the errors is the same across all levels of the variables).
How is the variance related to the standard deviation in a data set?
- The variance is the average of the standard deviation
- The variance is the square of the standard deviation
- The variance is the square root of the standard deviation
- The variance is twice the standard deviation
The variance is the square of the standard deviation. Standard deviation is a measure of dispersion in a dataset and variance is a square of it, meaning that they both represent the same concept of dispersion, but in different units.
What does kurtosis measure in a dataset?
- Central tendency
- Dispersion
- Skewness
- The "tailedness" of the distribution
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values.
What is the effect of outliers on PCA?
- It depends on the distribution of the data
- They can distort the principal components
- They enhance the performance of PCA
- They have no effect on PCA
Outliers can significantly distort the principal components identified by PCA, as they can artificially inflate the variance along their direction. It's generally a good practice to address outliers before applying PCA.
What is the concept of "Type I" error in the context of hypothesis testing?
- Failing to reject a false null hypothesis
- Failing to reject a true alternative hypothesis
- Rejecting a false alternative hypothesis
- Rejecting a true null hypothesis
A Type I error in hypothesis testing is the incorrect rejection of a true null hypothesis, often signified by the Greek letter alpha (α). In other words, a Type I error happens when the researcher incorrectly concludes that the null hypothesis is false when, in fact, it is true.
When can we apply the Chi-square test for goodness of fit?
- When the data are continuously distributed
- When the data are normally distributed
- When we have categorical data and want to see if it follows a specific distribution
- When we want to compare means
The Chi-square test for goodness of fit is used when we have categorical data and we want to see if the data follows a specific distribution.
How does Spearman's Rank Correlation react to outliers as compared to Pearson's correlation?
- Both are equally sensitive to outliers
- Less sensitive to outliers
- More sensitive to outliers
- Neither is sensitive to outliers
Spearman's Rank Correlation is less sensitive to outliers than Pearson's correlation. This is because Spearman's correlation is based on rank orders rather than raw data values, making it more robust against outliers.
What does a null hypothesis represent in statistical testing?
- A condition of no effect or no difference
- A specific outcome of the experiment
- An effect or difference exists
- The sample size is large enough for the test
The null hypothesis is a statement in statistical inference which asserts that there is no significant difference between the set of observed and expected data.
How does the rate parameter affect the shape of a Poisson distribution?
- All of the above
- It determines the kurtosis of the distribution
- It determines the skewness of the distribution
- It does not affect the shape of the distribution
The rate parameter (lambda) in a Poisson distribution determines the average rate of occurrence per interval, which directly affects the shape of the distribution. Higher lambda values result in distributions that are less skewed to the right.