A statistical test has more power to detect an effect if the effect size is ______.
- Equal to the sample size
- Large
- Small
- Unchanged
The power of a test is influenced by the effect size - the magnitude of the difference or relationship you're testing for. Larger effect sizes increase the power of a test because they create a larger signal relative to the noise, making it easier to detect an effect if one exists.
How does the height of a bar in a histogram relate to the frequency of the data?
- It has no relation with the frequency
- It represents the cumulative frequency
- It represents the mean frequency
- It represents the relative frequency
The height of a bar in a histogram represents the frequency (or relative frequency) of data for that particular bin. This means the taller the bar, the more data falls into that specific interval.
What is the purpose of 'normalization' or 'standardization' in the pre-processing step of cluster analysis?
- To decrease the number of clusters
- To ensure that all features contribute equally to the distance calculation
- To handle missing values
- To increase the computational complexity
Normalization or standardization ensures that all features contribute equally to the final distance calculation, regardless of their original scale. Without this step, features with larger scales would dominate the distance calculation, potentially leading to misleading clusters.
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 does a residual plot tell us about the fit of the model?
- It indicates how well the model's predictions match the actual data
- It indicates the variance of the residuals
- It shows the correlation between the dependent and independent variables
- It shows the relationship between the dependent and independent variables
A residual plot shows the residuals on the y-axis and the independent variable on the x-axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.
Can PCA be used for both supervised and unsupervised learning?
- No
- Only for supervised learning
- Only for unsupervised learning
- Yes
No, PCA is a technique for unsupervised learning. It does not use any class label information in its algorithm, making it unsupervised. However, the transformed dataset from PCA can be used for subsequent supervised learning tasks.
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.