Results

Descriptive Statistics

The Q-Q plots suggest that for both films the expected quantile points are close to those that would be expected from a normal distribution (i.e. the dots fall close to the diagonal line). The descriptive statistics confirm this conclusion. The skewness statistics gives rise to a z-score of -0.302 / 0.512 = -0.59 for The Notebook, and 0.04 / 0.512 =0.08 for a documentary about notebooks. These show no excessive (or significant) skewness. For kurtosis these values are -0.281 / 0.992 = -0.28 for The Notebook, and -1.024 / 0.992 = -1.03 for a documentary about notebooks. None of these z-scores are large enough to concern us. More important the raw values of skew and kurtosis are close enough to zero.

To assess equal variances, we can look at the two observed variances (52.011 and 50.829) and look at their ratio. The ratio here is fairly close to 1 so not any cause for worry. If this ratio is greater than 2, or lower than 0.5, you can start to worry about this assumption.

In the Chapter we talk a lot about NOT using significance tests of assumptions, so proceed with caution here. The Shapiro-Wilk test shows no significant deviation from normality for both films. If you chose to ignore my advice and use these sorts of tests then you might assume normality. However, the sample is small and these tests would have been very underpowered to detect a deviation from normal.