A point estimate is a single value that serves as an estimate of the ________.
- Median
- Population parameter
- Sample
- Variable
A point estimate is a single value used as an estimate of a population parameter. The sample mean, for instance, might be used as a point estimate of the population mean.
ANOVA assumes that all populations being compared have the same ________.
- All of these
- Mean
- Sample size
- Variance
One of the assumptions of ANOVA is the assumption of homogeneity of variances, which means that all populations being compared have the same variance.
What is the primary purpose of Principal Component Analysis (PCA)?
- To calculate the mean of data
- To classify data
- To reduce dimensionality of data
- To visualize data
The primary purpose of PCA is to reduce the dimensionality of data while maintaining as much information as possible. It transforms the data into a new, lower-dimensional set of variables that are uncorrelated and that explain the maximum possible amount of variance in the data.
The measure of dispersion that is the square root of the variance is known as the _______.
- Mean
- Median
- Range
- Standard Deviation
The standard deviation is the square root of the variance. It measures the average distance between each data point and the mean. Like the variance, it expresses the dispersion of data around the mean, but unlike the variance, its units are the same as the original data, making it easier to interpret.
In hierarchical clustering, a ________ is used to visualize the hierarchy of clusters.
- bar chart
- dendrogram
- histogram
- pie chart
In hierarchical clustering, a dendrogram is used to visualize the hierarchy of clusters. It is a tree-like diagram that records the sequences of merges or splits.
What is the difference between a one-tailed and a two-tailed test?
- The directionality of the hypothesis
- The number of samples being compared
- The number of times the test is performed
- The types of data being used
The main difference between one-tailed and two-tailed tests is the directionality of the hypothesis. One-tailed tests look for an effect in a specific direction, while two-tailed tests look for an effect in either direction.
Can a symmetrical distribution have nonzero kurtosis?
- No
- Only if it's a normal distribution
- Only if it's not a normal distribution
- Yes
Yes, a symmetrical distribution can have nonzero kurtosis. Kurtosis is a measure of the weight in the tails, or the extreme values, which can occur in both directions, thus not affecting the symmetry. For example, a normal distribution is symmetric and has a kurtosis greater than zero.
In what scenarios might Spearman's rank correlation coefficient be a better choice than Pearson's?
- When both variables are normally distributed
- When the data contains outliers or is not normally distributed
- When the relationship between variables is linear
- When the relationship between variables is non-linear and non-monotonic
Spearman's rank correlation coefficient is a non-parametric measure of correlation, meaning it can be used when the data is not normally distributed. It is also less sensitive to outliers compared to Pearson's coefficient. Further, it can be used to measure monotonic relationships, whether they are linear or not.
A ________ test is a common non-parametric statistical method.
- ANOVA
- Mann-Whitney U
- Regression
- T
The Mann-Whitney U test is a common non-parametric statistical method used to compare two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.
A ________ result in the Chi-square test for goodness of fit indicates that the observed distribution does not significantly differ from the expected distribution.
- negative
- non-significant
- significant
- skewed
A non-significant result in the Chi-square test for goodness of fit indicates that the observed distribution does not significantly differ from the expected distribution. In other words, we do not have enough evidence to reject the null hypothesis.