What does probability measure?
- Degree of difference between groups
- Likelihood of an event occurring
- Speed of an event
- Strength of a relationship
Probability measures the likelihood or chance of an event occurring. It is a mathematical concept that is fundamental to statistics and data science, helping to predict outcomes and guide decision-making.
The Mann-Whitney U test can be used when the assumptions of the ________ test are not met.
- ANOVA
- F
- chi-square
- t
The Mann-Whitney U test can be used as an alternative when the assumptions of the t-test (e.g., normality, homogeneity of variance) are not met.
When is it more appropriate to use the Wilcoxon Signed Rank Test rather than the Sign Test?
- When data is nominal
- When data is normally distributed
- When data is ordinal or interval
- When sample size is large
The Wilcoxon Signed Rank Test is more appropriate to use when data is ordinal or interval because it takes into account the magnitude of the differences between paired observations, unlike the Sign Test which only considers the sign of the differences.
The Kruskal-Wallis Test ranks all the data from all groups together; it then tests whether the ________ ranks differ significantly between the groups.
- average
- mean
- median
- mode
The Kruskal-Wallis Test ranks all the data from all groups together; it then tests whether the mean ranks differ significantly between the groups.
When two variables increase and decrease together, they are said to have a ________ correlation.
- negative
- positive
- strong
- zero
When two variables increase and decrease together, they are said to have a positive correlation. This is indicated by a positive Pearson's Correlation Coefficient.
If the null hypothesis is false, but we fail to reject it, what type of error have we made?
- Both Type I and Type II error
- Neither Type I nor Type II error
- Type I error
- Type II error
If the null hypothesis is false, but we fail to reject it, we have made a Type II error. This is also known as a "false negative" result.
What are the assumptions of the Mann-Whitney U test?
- Equal variances and independent observations
- Independent observations and normally distributed residuals
- Independent observations and similarly shaped distributions
- Normal distribution, equal variances, and independent observations
The assumptions of the Mann-Whitney U test are that observations are independent and that the distributions are similarly shaped. It does not require the assumption of normal distribution or equal variances.
Spearman's Rank Correlation is used when the variables are measured on a ________ scale.
- Interval
- Nominal
- Ordinal
- Ratio
Spearman's Rank Correlation is used when the variables are measured on an ordinal scale, as it compares the ranks of data. It can also be used with interval and ratio scales, particularly when a non-parametric measure of association is desired.
What is the impact of a large sample size on the confidence interval of the mean?
- Larger sample size has no impact on the confidence interval
- Larger sample size leads to a narrower interval
- Larger sample size leads to a wider interval
- Larger sample size makes the interval skewed
Larger sample sizes lead to narrower confidence intervals. With more data, we're able to estimate the population parameter more precisely, thus the range of values within which we believe the parameter lies (the confidence interval) gets smaller.
What are the key properties of a Bernoulli distribution?
- It can only take positive integer values
- It has a bell-shaped curve
- It has a single trial with two possible outcomes
- It models a series of independent trials
A Bernoulli distribution is a discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q=1-p. It models a single trial with two possible outcomes, often labelled 'success' and 'failure'.