What is the purpose of a scatter plot?
- To compare two numerical variables
- To display a distribution
- To show the relationship between three variables
- To visualize categorical variables
A scatter plot is a graphical representation that uses dots to represent the values obtained for two different variables - one plotted along the x-axis and the other plotted along the y-axis. It helps to identify the type of relationship (if any) between two numerical variables.
Does PCA require the features to be on the same scale?
- Depends on the algorithm used
- Depends on the data
- No
- Yes
Yes, PCA requires the features to be on the same scale. If features are on different scales, PCA might end up giving higher weightage to features with higher variance, which could lead to incorrect principal components. So, it's typically a good practice to standardize the data before applying PCA.
What are communalities in factor analysis?
- They are the shared variance between variables
- They are the unique variances of variables
- They are the variances of the factors after rotation
- They represent the total variance of the factors
In factor analysis, communalities are the proportion of variance in each variable that is accounted for, or shared among the factors. They represent the shared variance between variables.
What is the difference between a positively skewed and a negatively skewed distribution?
- Positively skewed has a longer tail on the left, negatively skewed has a longer tail on the right
- Positively skewed has a longer tail on the right, negatively skewed has a longer tail on the left
- Positively skewed has a peak on the left, negatively skewed has a peak on the right
- Positively skewed has a peak on the right, negatively skewed has a peak on the left
In a positively skewed distribution, the right tail is longer or fatter (i.e., the mass of the distribution is concentrated on the left). In a negatively skewed distribution, the left tail is longer or fatter (i.e., the mass of the distribution is concentrated on the right).
The square of the standard deviation gives the _______.
- Mean
- Median
- Range
- Variance
The square of the standard deviation gives the variance. Variance is the average of the squared differences from the mean, and standard deviation is the square root of this variance. Hence, squaring the standard deviation gives us the variance.
In a histogram, what does the area under the curve represent?
- The average value of observations
- The median of the data
- The total number of observations
- The total range of the data
In a histogram, the area under the curve represents the total number of observations in the dataset. The height of each bar corresponds to the frequency of a bin, and the width of the bar corresponds to the size of the bin. So the total area of all bars equals the total number of observations.
How does the Mann-Whitney U test compare to the Wilcoxon rank-sum test?
- They are identical tests
- They are used for different types of data
- They handle ties differently
- They make different assumptions about the data
The Mann-Whitney U test and the Wilcoxon rank-sum test are essentially the same test, although they use slightly different methods of calculation. Both are non-parametric tests used to determine if two independent samples were drawn from a population with the same distribution.
What is a Type I error in the context of hypothesis testing?
- Accepting a false null hypothesis
- Accepting a true null hypothesis
- Rejecting a false null hypothesis
- Rejecting a true null hypothesis
A Type I error occurs when the null hypothesis is true, but it is rejected. It is also known as a "false positive" result.
How does the power of a test relate to Type II errors?
- The power of a test is the probability of making a Type II error
- The power of a test is the probability of not making a Type II error
- The power of a test is unrelated to Type II errors
- nan
The power of a test is the probability that it correctly rejects a false null hypothesis, i.e., it is the probability of not making a Type II error.
What happens to the range of a dataset if an outlier is added?
- The effect on the range is unpredictable
- The range decreases
- The range increases
- The range remains the same
If an outlier is added to a dataset, it can significantly increase the range, as the range is calculated as the difference between the maximum and minimum values in the dataset.