One common feature of non-parametric methods is the use of ________ rather than raw data points.
- averages
- frequencies
- medians
- ranks
One common feature of non-parametric methods is the use of ranks rather than raw data points, which makes them more robust to outliers and does not require the assumption of a specific distribution.
The ________ of a box plot are used to indicate variability outside the upper and lower quartiles.
- Bars
- Outliers
- Tails
- Whiskers
The whiskers of a box plot are used to indicate the variability of the data outside the upper and lower quartiles. They often extend to the maximum and minimum data values (excluding outliers), or 1.5 times the interquartile range.
What does a p-value represent in a t-test or Z-test?
- All of the above
- The probability of observing the sample data if the null hypothesis is true
- The probability of rejecting the null hypothesis when it is true
- The probability of the sample mean being equal to the population mean
In a t-test or Z-test, the p-value represents the probability of obtaining a sample statistic as extreme or more extreme than the observed statistic, assuming the null hypothesis is true.
A Type I error occurs when we reject the null hypothesis, even though it is _______.
- FALSE
- Not applicable
- Not proven
- TRUE
A Type I error occurs when we reject the null hypothesis, even though it is true. This is also known as a "false positive" error.
What are the two main types of data in statistics?
- Categorical and Numerical
- Discrete and Continuous
- Parametric and Nonparametric
- Qualitative and Quantitative
The two main types of data in statistics are Qualitative and Quantitative. Qualitative data, also known as categorical data, represents characteristics or attributes and cannot be mathematically quantified. Quantitative data, on the other hand, is numerical, representing measurements or counts that can be quantified mathematically.
What is the difference between mutually exclusive and independent events?
- Mutually exclusive events always happen together; independent events never happen together
- Mutually exclusive events can't occur at the same time; independent events don't influence each other
- Mutually exclusive events influence each other; independent events can't occur at the same time
- There is no difference
Mutually exclusive events are events that cannot occur at the same time - the occurrence of one event excludes the occurrence of the other(s). On the other hand, independent events are those where the occurrence of one event does not affect the probability of the occurrence of the other event(s). The concepts are related but distinct.
What does the Addition Rule of Probability help calculate?
- The average of two probabilities
- The difference between two probabilities
- The probability that at least one of two events will occur
- The probability that both events will occur
The Addition Rule in probability is used to calculate the probability that at least one of two (or more) events will occur. It states that the probability of the occurrence of at least one of two mutually exclusive events is the sum of their individual probabilities.
The _________ states that as a sample size grows, the sample mean will be closer to the population mean.
- Central Limit Theorem
- Law of Large Numbers
- Probability Rule
- Sampling Distribution
The Law of Large Numbers states that as a sample size grows, the sample mean will be closer to the population mean. This means that the larger the sample size, the more the sample mean approximates the population mean.
When would it be more appropriate to use a two-way ANOVA instead of a one-way ANOVA?
- When the dependent variable is categorical
- When the sample size is very large
- When there are two independent variables to consider
- When there is only one group to study
It is more appropriate to use a two-way ANOVA instead of a one-way ANOVA when there are two independent variables. Two-way ANOVA is used to observe the interaction effect between the two independent variables on the dependent variable.
What is the primary objective of cluster analysis?
- To classify variables into different groups
- To group similar instances into clusters
- To predict the output variable
- To visualize high-dimensional data
The primary objective of cluster analysis is to group similar instances (observations, data points, etc.) into clusters.