What does a P-P plot compare?

What does a P-P plot compare?

• A. A plot of the density function against cumulative probabilities.
• B. A scatter plot of observed frequencies against expected frequencies.
• C. A histogram of observed values.
• D. A graph plotting the cumulative probability of the variable against the cumulative probability of a particular distribution.

Answer: (D)

P-P plots assess how well data fit a specified distribution by comparing their empirical probabilities to the theoretical probabilities from that distribution. You plot the cumulative probability of each observed value (empirical CDF) against the cumulative probability you’d expect under the hypothesized distribution (theoretical CDF). If the data come from that distribution, the points fall roughly along the 45-degree line. Deviations indicate where the data diverge, revealing whether discrepancies occur in the center or in the tails. This is different from plots that show observed versus expected frequencies (chi-square context) or a histogram, and from a plot that mixes density with cumulative probabilities. In short, a P-P plot directly compares the empirical CDF to the theoretical CDF.

P-P plots assess how well data fit a specified distribution by comparing their empirical probabilities to the theoretical probabilities from that distribution. You plot the cumulative probability of each observed value (empirical CDF) against the cumulative probability you’d expect under the hypothesized distribution (theoretical CDF). If the data come from that distribution, the points fall roughly along the 45-degree line. Deviations indicate where the data diverge, revealing whether discrepancies occur in the center or in the tails. This is different from plots that show observed versus expected frequencies (chi-square context) or a histogram, and from a plot that mixes density with cumulative probabilities. In short, a P-P plot directly compares the empirical CDF to the theoretical CDF.