Hello Staffan,

It sounds as if you have multiple questions about the driving behavior, as indicated by speed. It's up to you as to whether mean speed over any specified distance (e.g., 50m) is a plausible (and dependable) data point. Yes, averaged values may be used as data points.

So, to answer the question of whether average speed differed, you could:

1. run ordinary independent t-test on each case's average speed over some specific interval (50m, 3000m) for which you have all the data; or

2. run ordinary independent t-test on each case's average speed for the duration of their trial (whether they complete the circuit or not);

To answer the question about equality of variation, you could compute variance for each person using 50m (or some other length) averages and compare these (or SDs) across groups using a t-test (most likely will have to use robust t-method like Welch, or bootstrapped error estimate).

As well, you could get fancier, by applying a repeated measures framework, and testing whether there was any trend in the speeds (linear, quadratic, etc.) and determine whether the prevalence of one trend was comparable across dashboard/treatment groups.

Finally, to answer the question of whether completion of the circuit was related to type of dashboard, you could use odds ratio, logistic regression, Fisher exact test, or binomial test.

Good luck with your work.

I would like to add to David Morse answer: It is not entirely clear what your primary question is. Do you want to assess the differences between the groups at one specific time point or are you rather interested in the course of time and the differences between groups or the interaction of both or how similar individuals are? Each of your questions may need different models and a thorough interpretation of the results.

When I first read your question I immediately thought about a multilevel model (ML), which seems to me the most flexible way to answer your questions, but maybe also the most demanding to conduct the analyses. But with the ML model you can handle all of your time points (as displayed, otherwise, if you have „quasi“ continuous data with a high sampling rate and if this is import time-series analyses may be more appropriate), you can assess different functional forms for the time course (e.g. linear, quadratic….), you can assess the group differences AND the timeXgroup interaction. If you handle ID as a random effect, you can assess how similar participants are and if the differences can be explained by your other predictors (e.g. time, group or even other information available). Additionally, you can handle different autoregressive structures, which can be expected with the repeated measures. Missing data is not so much of a problem, since the slopes will be estimated with all available data points. (sounds a bit like a Swiss Army Knive, I know ;-) )

Sometimes a question can be boiled down to a simple t-test and answers all you need, but sometimes you need more advanced models to answer all of your (maybe more important/interesting) questions.

And I would like to add to both comments above: it seems that your experiment is more explorative than confirmative. You had not clear hypothesis in mind while designing the experiment that could be tested. So I advice not to go for testing at all. Better do a thorough explorative analysis and use this to generate hypotheses you could test in an appropriatel designed follow-up experiment.

Looking for interesting effects and testing these in the same data set is a common misbehaviour. It tells us little and such kind of "research" is the reason for journals being littered with irreproducible results. If you go that way, you would still need to repeat the experiment to confirm the hypotheses that were "tested" in your current data set - if you are interested in good scientific practice.