In Exercises 5–16, use analysis of variance for the indicated test.


Clancy, Rowling, and Tolstoy Ease of Reading Pages were randomly selected from three books: The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J.K. Rowling, and War and Peace by Leo Tolstoy. Listed below are Flesch Reading Ease Scores for those pages. Use a 0.05 significance level to test the claim that pages from books by those three authors have the same mean Flesch Reading Ease score. Given that higher scores correspond to text that is easier to read, which author appears to be different, and how is that author different?

Verified step by step guidance

1. Step 1: Organize the data into groups based on the authors (Clancy, Rowling, Tolstoy). Each group contains the Flesch Reading Ease Scores provided in the table.
2. Step 2: Calculate the mean Flesch Reading Ease score for each group (author). This involves summing the scores for each author and dividing by the number of scores in that group.
3. Step 3: Compute the overall mean of all the scores combined. This is done by summing all the scores across the three groups and dividing by the total number of scores.
4. Step 4: Perform an Analysis of Variance (ANOVA) test. This involves calculating the between-group variance (how much the group means differ from the overall mean) and the within-group variance (how much the scores within each group differ from their respective group mean). Use these variances to compute the F-statistic.
5. Step 5: Compare the calculated F-statistic to the critical value from the F-distribution table at a 0.05 significance level. If the F-statistic exceeds the critical value, reject the null hypothesis that the means are the same. Identify which author is different by examining the group means and their relationship to the overall mean.

Key Concepts

Analysis of Variance (ANOVA)

ANOVA is a statistical method used to compare the means of three or more groups to determine if at least one group mean is significantly different from the others. It assesses the impact of one or more factors by comparing the variance within groups to the variance between groups. In this context, ANOVA will help test the claim regarding the Flesch Reading Ease scores of the books by Clancy, Rowling, and Tolstoy.

Flesch Reading Ease Score

The Flesch Reading Ease Score is a readability test designed to indicate how easy a text is to read. The score is calculated based on the average number of syllables per word and the average number of words per sentence. Higher scores indicate easier readability, which is crucial for understanding how the texts from different authors compare in terms of accessibility to readers.

Significance Level

The significance level, often denoted as alpha (α), is the threshold for determining whether a statistical result is significant. In this case, a significance level of 0.05 means that there is a 5% risk of concluding that a difference exists when there is none. This level will guide the decision on whether to reject the null hypothesis that the mean Flesch Reading Ease scores of the three authors are the same.