What is the impact of data transformation on the decision to use non-parametric tests?
- A suitable data transformation may make it possible to use a parametric test
- Data transformation always leads to non-parametric tests
- Data transformation always makes data normally distributed
- Data transformation does not affect the choice between parametric and non-parametric tests
A suitable data transformation may make it possible to use a parametric test instead of a non-parametric test. Transformations can help to stabilize variances, normalize the data, or linearize relationships between variables, allowing for the use of parametric tests that might have more statistical power.
The Kruskal-Wallis Test is used to compare ________ independent samples.
- four
- three
- three or more
- two
The Kruskal-Wallis Test is used to compare three or more independent samples. It's an extension of the Mann-Whitney U Test for more than two groups.
In which situation is Spearman's Rank Correlation preferable to Pearson's correlation?
- When the data is normally distributed
- When the relationship between variables is non-linear and monotonic
- When the relationship is linear
- When there are no ties in the ranks
Spearman's Rank Correlation is preferable to Pearson's correlation when the relationship between variables is non-linear but monotonic. Pearson's correlation measures linear relationships, while Spearman's can capture non-linear relationships.
What is the z-value associated with a 95% confidence interval in a standard normal distribution?
- 1.64
- 1.96
- 2
- 2.33
The z-value associated with a 95% confidence interval in a standard normal distribution is approximately 1.96. This means that we are 95% confident that the true population parameter lies within 1.96 standard deviations of the sample mean.
How is the interquartile range different from the range in handling outliers?
- Both exclude outliers
- Both include outliers
- The interquartile range does not include outliers, the range does
- The interquartile range includes outliers, the range does not
The interquartile range, which is the difference between the upper quartile (Q3) and the lower quartile (Q1), represents the middle 50% of the data and is not affected by outliers. The range, on the other hand, is the difference between the maximum and minimum data values and is significantly affected by outliers.
How can 'outliers' impact the result of K-means clustering?
- Outliers can distort the shape and size of the clusters
- Outliers can lead to fewer clusters
- Outliers can lead to more clusters
- Outliers don't impact K-means clustering
Outliers can have a significant impact on the result of K-means clustering. They can distort the shape and size of the clusters, as they may pull the centroid towards them, creating less accurate and meaningful clusters.
A positive Pearson's Correlation Coefficient indicates a ________ relationship between two variables.
- inverse
- linear
- perfect
- positive
A positive Pearson's Correlation Coefficient indicates a positive relationship between two variables. This means that as one variable increases, the other variable also increases, and vice versa.
What are the assumptions made in simple linear regression?
- Homogeneity, normality, and symmetry
- Independence, homogeneity, and linearity
- Linearity, homoscedasticity, and normality
- Symmetry, linearity, and independence
The assumptions made in simple linear regression include linearity (the relationship between the independent and dependent variables is linear), homoscedasticity (the variance of the residuals is constant across all levels of the independent variable), and normality (the residuals are normally distributed).
Principal Component Analysis (PCA) is a dimensionality reduction technique that projects the data into a lower dimensional space called the _______.
- eigen space
- feature space
- subspace
- variance space
PCA is a technique that projects the data into a new, lower-dimensional subspace. This subspace consists of principal components which are orthogonal to each other and capture the maximum variance in the data.
The range of a dataset is sensitive to _______.
- Mean
- Median
- Mode
- Outliers
The range of a dataset is sensitive to outliers. Because the range is calculated as the difference between the maximum and minimum values, an outlier (an extremely high or low value) can greatly increase the range.