How does the Spearman’s Rank Correlation test handle ties in data ranks?
- Assigns the maximum rank to ties
- Assigns the minimum rank to ties
- Averages the tied ranks
- Ignores the tied ranks
The Spearman’s Rank Correlation test handles ties in data ranks by averaging the ranks. For example, if two values tie for a place in the ranking, they are assigned a rank equal to the average of those places.
__________ in multiple linear regression refers to the proportion of the variance in the dependent variable that is predictable from the independent variables.
- Beta coefficient
- F-statistic
- R-squared
- T-statistic
R-squared is a statistical measure in regression models that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables.
What strategies can be employed to reduce both Type I and Type II errors?
- Decrease sample size, use a more lenient significance level
- Decrease sample size, use a more stringent significance level
- Increase sample size, use a more lenient significance level
- Increase sample size, use a more stringent significance level
Increasing the sample size makes the test more sensitive, reducing both Type I and Type II errors. Similarly, a more stringent significance level (lower α) reduces the chance of a Type I error. However, it's important to note that decreasing Type I error probability often leads to an increase in Type II error probability, and vice versa. This is known as the Type I/Type II tradeoff.
What does the interquartile range in a box plot represent?
- The middle 50% of the data
- The range of the top 25% of the data
- The range within one standard deviation from the mean
- The total range of the dataset
The interquartile range (IQR) in a box plot represents the middle 50% of the data. It is the range within which the central half of the values fall and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
What is the purpose of non-parametric statistical methods?
- To analyze data without making assumptions about the population distribution
- To make the calculation process more complex
- To provide less accurate results
- To use less data in the analysis
Non-parametric statistical methods are used to analyze data without making assumptions about the population distribution. These tests are based on differences in medians or ranks rather than differences in means.
A value of 0 in Pearson's Correlation Coefficient means there's no ________ correlation between the two variables.
- linear
- negative
- perfect
- visible
A value of 0 in Pearson's Correlation Coefficient means there's no linear correlation between the two variables. However, it's important to note that this doesn't necessarily mean there is no relationship at all, it could be that the relationship is nonlinear.
How is a probability distribution defined?
- It is the average value of a dataset
- It is the highest and lowest value of a dataset
- It is the likelihood of each possible outcome of a random variable
- It is the spread of possible values in a dataset
A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. For a random variable, the probability distribution is the probability that the variable takes a particular value.
What does a Principal Component represent in a dataset?
- A combination of original features
- A feature of the dataset
- A group of similar data points
- A target variable
A Principal Component is a linear combination of the original features in a dataset. Each principal component is orthogonal to each other, meaning they are uncorrelated and each represents a different direction in which the data varies.
Can the Mann-Whitney U test be used for paired samples?
- No
- Only if the data is normally distributed
- Only if the variances are equal
- Yes
No, the Mann-Whitney U test is not used for paired samples. It is designed for two independent samples. For paired samples, a different test, such as the Wilcoxon signed-rank test, would be more appropriate.
When is it more appropriate to use the Mann-Whitney U test than a t-test?
- When data is normally distributed
- When data is not normally distributed
- When sample sizes are equal
- When the variances of the two groups are equal
The Mann-Whitney U test is more appropriate to use than a t-test when the data is not normally distributed. This test is a non-parametric alternative to the independent t-test and does not assume normality.