How do non-parametric statistical methods deal with outliers compared to parametric methods?
- They are more robust to outliers
- They are more sensitive to outliers
- They don't handle outliers
- They eliminate outliers before analysis
Non-parametric statistical methods are more robust to outliers compared to parametric methods. This is because non-parametric tests often use medians and ranks, which are less sensitive to extreme values, compared to means which are used in parametric tests.
How does the concept of geometric mean differ from the arithmetic mean?
- Geometric mean cannot be used for negative numbers, arithmetic mean can
- Geometric mean uses addition, arithmetic mean uses multiplication
- Geometric mean uses multiplication, arithmetic mean uses addition
- There is no difference
The arithmetic mean involves the sum of the values divided by the number of values, while the geometric mean involves multiplying all the values together, and then taking the nth root of the product (where n is the total number of values). Geometric mean is especially useful when comparing different items with extremely variable ranges.
What are some real-world implications of kurtosis in a dataset?
- Datasets with high kurtosis are easier to interpret
- High kurtosis can indicate a bias in data collection
- High kurtosis can indicate the presence of outliers
- Kurtosis does not have real-world implications
In real-world data analysis, kurtosis is used to identify the presence of outliers. High kurtosis in a dataset may signal an increase in tail risk. This is particularly relevant in fields like finance, where tail risk could translate into heavier losses than the normal distribution would predict.
What does the Wilcoxon Signed Rank Test compare in paired samples?
- Means
- Medians
- Modes
- Variance
The Wilcoxon Signed Rank Test compares the medians in paired samples.
What is the measure of central tendency that divides a data set into two equal halves?
- Mean
- Median
- Mode
- Range
The median is the measure of central tendency that divides a data set into two equal halves. When the observations are ordered from smallest to largest, the median is the middle value, ensuring that 50% of the data falls below and 50% above the median value.
The larger the number of observations, the closer the sample mean will be to the population mean, according to the _________.
- Central Limit Theorem
- Law of Large Numbers
- Probability Rule
- Sampling Distribution
According to the Law of Large Numbers, the larger the number of observations, the closer the sample mean will be to the population mean. This law is a fundamental principle of probability and statistics that states that as the size of a sample is increased, the estimate of certain parameters obtained from the sample will tend to approach the true value for the population.
What happens if the Kruskal-Wallis Test results in a statistically significant H value?
- It means nothing
- It means the groups are different
- It means the groups are the same
- It means the test failed
A statistically significant H value in the Kruskal-Wallis Test suggests that at least one of the sample distributions is different from the others.
How is the Chi-square distribution related to the normal distribution?
- The Chi-square distribution is a special case of the normal distribution
- The Chi-square distribution is the distribution of the square of a standard normal random variable
- The Chi-square distribution is the distribution of the sum of two standard normal random variables
- The normal distribution is a special case of the Chi-square distribution
The Chi-square distribution is related to the normal distribution in that it is the distribution of the square of a standard normal random variable.
Quantitative data can be broken down into two types: ________ and ________.
- Continuous, Categorical
- Discrete, Continuous
- Nominal, Ordinal
- Ratio, Interval
Quantitative data can be broken down into two types: Discrete and Continuous. Discrete data can only take specific values (like whole numbers) while Continuous data can take any value (within a range).
How does the Kruskal-Wallis Test handle ties between ranks?
- Assigns them average ranks
- Discards them
- Ignores them
- Treats them as errors
When two or more data points have the same value, they are considered tied. The Kruskal-Wallis Test assigns them the average of the ranks that the tied values would have received had they been different.