# Comparison of repeated measure

I have driving-related data from 100 people for 3 months. I want to see if the driving miles from weekdays are different than weekends. As the sample is not independent I cannot use normal Chi-sq. Can I use repeated measure ANOVA to test the difference of VMT between weekday and weekend? What are the other statistics to do it?

## 1 Answer

It sounds like what you want is a paired t-test. You have two samples $$S_1$$ of weekday driving total hours over 3 months and $$S_2$$ of weekend driving total hour over 3 months. Each of these can be "paired up." Driver $$i$$ has a value for both weekday and weekend.

The formula for a paired t-test is $$t_{calc}= \frac{ \sum x_{1i}-x_{2i}}{\sqrt {\frac{n(\sum d_i^2)-(\sum d_i)^2}{n-1}}}$$

here $$x_{1i}$$ is the weekday value of individual $$i$$ and $$x_{2i}$$ is the weekend value of individual $$i$$. $$d_i$$ is the difference between those two values.

Don't worry about memorizing this formula or anything. Any program you use will have it. The basic idea is that you take the difference (numerator) of the two values of the individuals and then calculate the standard deviation of the differences between those two values (denominator). This often minimizes your variance since you are comparing the same individual with themselves.

In short, use a paired t-test.

• Paired t-test would actually compare means across the user. I am trying to see if I can compare across trips. In that case, wouldn't repeated Anova be more appropriate? – Msilvy Dec 6 '19 at 17:44
• It does depend on what you want as an outcome. If you are simply interested in change across trips, repeated measure would be appropriate. It sounded to me like you were interested in the difference between weekend and weekday. – Tanner Phillips Dec 7 '19 at 15:50