What better analysis could the authors have done?
They should take the women as the unit of analysis and for each woman find the mean volume for all the sessions using the same method. This would give 14 pairs of mean. Then they could apply the paired t method. If the 14 differences between these woman means display skewness and unequal variance, they could try a suitable transformation of the means (see Week 5). Finally, they could present the results as a confidence interval for the mean difference in volume expressed per session, in addition to a P value.
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