The ________ in a two-way ANOVA can reveal whether the effect of one independent variable depends on the level of the other independent variable.
- Effect size
- Interaction effect
- Main effect
- Post-hoc test
The interaction effect in a two-way ANOVA reveals whether the effect of one independent variable depends on the level of the other independent variable. This allows us to understand how the independent variables relate to each other.
How is Bayes' theorem related to conditional probability?
- Bayes' theorem and conditional probability are not related
- Bayes' theorem cannot be used with conditional probability
- Bayes' theorem is a specific type of conditional probability
- Bayes' theorem is used to calculate the complement of the conditional probability
Bayes' theorem is a way of finding a probability when we know certain other probabilities. The probabilities that we know are usually conditional probabilities, and Bayes' theorem is used to 'reverse' these probabilities.
A Chi-square test for independence is used to determine if there is a significant relationship between two ________ variables.
- categorical
- continuous
- nominal
- ordinal
A Chi-square test for independence is used to determine if there is a significant relationship between two categorical variables. It is not applicable for continuous, ordinal, or nominal variables.
A probability must be a number between ________ and ________.
- #NAME?
- -1, 1
- 0, 1
- 1, 100
By definition, the probability of an event is a number between 0 and 1. A probability of 0 means the event will never occur, and a probability of 1 means the event is certain to occur.
What is the effect of having small expected frequencies in a Chi-square test?
- It does not affect the test
- It increases the power of the test
- It invalidates the test
- It reduces the power of the test
In a Chi-square test, having small expected frequencies can reduce the power of the test and potentially lead to erroneous conclusions. This is because the Chi-square test is based on the assumption that the expected frequency of each category is at least 5.
What is the role of standard error in interval estimation?
- Standard error determines the shape of the distribution of the sample means
- Standard error is not related to interval estimation
- Standard error is used to calculate the margin of error, which determines the width of the confidence interval
- Standard error is used to calculate the sample mean, which is the center of the confidence interval
The standard error plays a crucial role in interval estimation. It is used to calculate the margin of error, which determines the width of the confidence interval. The standard error measures the variability of the sample mean around the population mean. A smaller standard error will result in a narrower confidence interval, assuming the confidence level is constant.
What type of correlation does the Spearman's Rank Correlation test measure?
- Correlation of variances
- Linear correlation
- Monotonic correlation
- Polynomial correlation
Spearman's Rank Correlation test measures monotonic correlation, which indicates whether an increase in one variable will increase or decrease the other variable. It does not require the relationship between the variables to be linear.
The _______ of a confidence interval corresponds to the total area under the curve that is excluded on both sides of the curve.
- Confidence level
- Margin of error
- Population parameter
- Standard error
The margin of error of a confidence interval corresponds to the total area under the curve that is excluded on both sides of the curve. This margin of error determines the width of the confidence interval.
What happens if the assumption of homoscedasticity is violated in simple linear regression?
- It has no effect on the regression model
- It makes the regression model more accurate
- It makes the regression model perfectly fit the data
- It makes the standard errors and confidence intervals invalid
Homoscedasticity is the assumption that the variance of the residuals is constant across all levels of the independent variable. If this assumption is violated (a condition known as heteroscedasticity), it can lead to unreliable and inefficient estimates of the standard errors. This, in turn, can make the confidence intervals and hypothesis tests invalid.
In the context of a continuous random variable, the ________ function gives the probability that the variable takes a value less than or equal to a certain value.
- Cumulative Distribution Function
- Probability Density Function
- Probability Mass Function
- Random Function
The Cumulative Distribution Function (CDF) of a random variable is defined as the probability that the variable takes a value less than or equal to a certain value. The difference between discrete and continuous random variables is the way their probabilities are assigned.