If I understand your setup, this experiment is as follows:
- 2 independent variables (VR scenario experienced, time)
- VR scenario, two levels (A and B)
- Time (start, 5 minutes in, 10 minutes in, 15 minutes in, end, etc)
- 1 dependent variable (measure of discomfort) with multiple measurements taken per subject over time (repeated measures).
The first important question is the nature of your measure of discomfort. I assume you'll use something like a Likert-scale (on a scale from 1 to 5, with how much discomfort do you feel, with 1 being mild/no discomfort and 5 being extreme discomfort), so the measure will be parametric and on an interval/ratio scale. This is the most common (and usually the most useful) method, so we'll pretend that's what you had in mind.
You'll also of course have two possible ways to setup the human participants: 1) have every participant experience both conditions (you'll probably want to use counter-balanced ordering of experimental conditions), or 2) participants only experience one VR condition (either Scene A or Scene B, not both). You can do either one, but generally you'll need less participants if you go with option 1, as there will be less variance due to between-person factors (your experience of "carrots vs celery" will be more similar than "your experience of carrots" vs "my experience of celery", after all). You can use option 2 if necessary and this won't really change the test, but is generally avoided unless you have a good reason (like learning effects are just too great, etc).
If I've described your experimental scenario accurately, the most common test used for this is a two-way repeated measures ANOVA. This will allow you determine first if there is any statistically significant difference in any of the conditions (taking care of the issues you'd have by running repeated t-tests), and then the post-hoc tests will allow you to identify just what conditions are different from each other. If you decided to test only one VR scenario, then you'd use a one-way repeated measures ANOVA instead.
You might also reasonably ask a question like, "we also wonder how excited the participants feel", in which case you'd have participants respond to both a measure of discomfort and a measure of excitement. In this case you'd be adding a dependent variable, excitement, and this would change the test you'd need. In such a case what you'd likely want is a two-way repeated measures MANOVA if you kept both VR conditions, or if you dropped to one you'd just want a (one-way) repeated measures MANOVA. The more questions you ask (dependent variables) the more power you lose, so make sure you actually care about all the measures and don't just add them in willy-nilly.
Someone might be tempted to include one more independent variable, but generally I strongly warn you to avoid that temptation unless you have a lot of experience with such a beast, as heaven forbid you end up with a 3-way interaction of variables and need to interpret what is going on in a sensible fashion. It can get really messy and end up muddying the waters rather than clarifying them.
You'll naturally want to make note of all the assumptions of your chosen test, and SPSS will help you test the assumptions as well. These sorts of tests are very common in areas like HCI and cognitive psychology, and are not at all exotic. There are surely other approaches that could be used, but these are the classic approaches which are popularly published in these fields.
The test you are looking for is one-way repeated measures ANOVA. That is equivalent to two-way ANOVA, with repeated measures in one factor, with no replication. Following the ANOVA, you'll want to run followup tests to make the comparisons you are asking for, while adjusting for multiple comparisons.
Best Answer
As you already suggested yourself, you can model this problem with a linear mixed model (LMM). I don't think the sample size is small for an LMM at all. In fact, you'd have a much larger sample size than if you were to split the data and perform the tests you proposed on subsets (I advice against doing this in general).
You will want to reshape your data to be in long format for this.$^\dagger$ This also has the nice interpretation that columns represent variables (left, right and time point 1-3 in your example are actually categories of the variables side and time).
$\dagger$: I have included the $\textsf{R}$ code at the bottom of this answer to retain readability.
Although you mention these data are just an example, from this example you could already draw most of your conclusions using a single plot, labeled by subject:
There is no consistency in linepieces going up or down for either side ($\color{blue}{\text{left}}$ or $\color{red}{\text{right}}$) from any time point to the next. Hence it is unlikely you'll find any significant effects.
Using a random intercept for
subject
,$^\ddagger$ you'll indeed see that there is no effect of either time or side and there does not appear to be an interaction either. You could also try a random slope, or both, depending on your what you believe to be more correct.This model compares all other combinations to the right side of subjects at time point $1$ and gives the following output:
All $t$-values are small, suggesting none of these effects are significant. You can formally test this using the
lmerTest
package, or by bootstrapping confidence intervals, as I did below:Produces:
All of the 95%-CI for the fixed effects include zero, meaning there are no significant deviations from the reference group. You could try to change the reference group, but make sure you correct for the number of comparisons you perform.
Lastly, if you try to recreate this analysis for the actual data, also note that
time
need not be modeled as a factor if you can assumey
to linearly increase with time. This will ease the interpretation and requires less parameters.The $\textsf{R}$ code I used for this: