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.
What is the purpose of a Chi-square test for goodness of fit?
- To compare the means of two groups
- To compare the variance of two groups
- To determine the correlation between two variables
- To test if a data set follows a given theoretical distribution
The Chi-square test for goodness of fit is used to test whether the observed data fits a specific distribution. It compares the observed data with the values that would be expected under the theoretical distribution.
What does the slope of the regression line represent in simple linear regression?
- It represents the change in the dependent variable for a one-unit change in the independent variable
- It represents the error term
- It represents the independent variable
- It represents the strength of the correlation
The slope of the regression line in simple linear regression represents the change in the dependent variable for a one-unit change in the independent variable. It quantifies the strength and direction of the linear relationship between the two variables.
The ________ probability in Bayes' theorem is the revised probability of an event occurring after taking into account new information.
- joint
- marginal
- posterior
- prior
In Bayes' theorem, the posterior probability is the revised probability of an event occurring after taking into account new evidence.
What does a 95% confidence interval mean?
- That 95% of the population is within the interval
- That 95% of the sample data lies within the interval
- That the interval captures the true population parameter 95% of the time
- That there is a 95% chance that the interval contains the mean
A 95% confidence interval means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95% of the cases.
The _________ is crucial in hypothesis testing and the construction of confidence intervals.
- Central Limit Theorem
- Law of Large Numbers
- Probability Rule
- Sampling Distribution
The Central Limit Theorem is crucial in hypothesis testing and the construction of confidence intervals. By ensuring the normality of the distribution, it allows us to make inferences about the population from our sample data and to assess the likelihood that our sample mean is a reliable estimate of the population mean.
The _______ Rule is used when we want to find the probability of two events happening at the same time.
- Addition
- Division
- Multiplication
- Subtraction
The Multiplication Rule is used when we want to find the probability of two events happening at the same time. Specifically, it states that the probability of two independent events both occurring is the product of their individual probabilities.
What does skewness measure in a dataset?
- Central tendency
- Dispersion
- Kurtosis
- Symmetry or lack of symmetry
Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values. Negative skewness indicates a distribution with an asymmetric tail extending towards more negative values.