Untitled Flashcard Set

Why analyze the median instead of the mean?

The median is less sensitive to outliers and skewness, making it a better measure of center for skewed distributions, such as this dataset with a potential outlier (7), which pulls the mean upward.

What is the key idea behind the Sign Test for median hypothesis testing?

If the true median is hypothesized, each data point has a 50% chance of being above or below that median, allowing for a binomial distribution of counts.

What are the steps in the Sign Test?

1. Count values below the hypothesized median. 2. Count values above. 3. State n. 4. Observe p=0.5 under H₀. 5. Calculate extreme probabilities for tails.

What is the formula for the binomial probability in the Sign Test?

P(X=k) = \binom{n}{k}(0.5)^n, where n is the number of trials and k is the number of successes.

What is the significance of the p-value in hypothesis testing?

The p-value indicates the strength of evidence against the null hypothesis. A small p-value suggests rejecting H₀, while a large p-value indicates insufficient evidence against it.

What is the Wilcoxon Signed Rank Test used for?

It is used to test whether the median of one sample differs from a hypothesized median or to analyze paired data by looking at the differences within pairs.

What are the assumptions for using the Wilcoxon Signed Rank Test?

Data should be continuous or ordinal, and the distribution of differences should be approximately symmetric; observations must be independent.

When is the Kruskal-Wallis Test appropriate?

When comparing three or more independent groups to determine if they come from the same distribution.

What is the main difference between the Wilcoxon Signed Rank Test and the Wilcoxon Rank Sum Test?

The Signed Rank Test analyzes paired data differences while the Rank Sum Test compares two independent groups by ranking all observations together.

What is the relationship between s²_B and s²_W in ANOVA?

s²_B (between-group variance) measures variability of group means around the overall mean, while s²_W (within-group variance) measures variability of individuals within the same group. A large s²_B relative to s²_W implies significant differences in group means.

What are post-hoc methods?

Post-hoc methods are statistical tests applied after an overall test (like ANOVA) indicates that differences exist, required to determine which specific groups differ.

What is the constraint in the One-Way ANOVA model?

A constraint like Στᵢ = 0 is required to eliminate redundancy in model parameters, ensuring that the effects are uniquely identifiable.

List the three assumptions of ANOVA.

1. Normality of residuals (εᵢⱼ are normally distributed). 2. Homoscedasticity (equal variances across groups). 3. Independence of observations.

Why might the Wilcoxon test p-value be 'better' than the Sign Test?

The Wilcoxon test uses both the sign and magnitude of deviations, resulting in more statistical power and a more precise p-value compared to the Sign Test.

What does a confidence interval (CI) that does not include 1 for variance ratios imply?

It suggests that the populations have unequal variances.

What does a CI not including 0 imply for differences in two population means?

It suggests that the means are likely significantly different.