# #StackBounty: #hypothesis-testing #correlation #statistical-significance #anova #multilevel-analysis Correlation or difference? appropr…

### Bounty: 50

In a comparative study on human motion and perception in both reality and virtual reality, I am examining differences and relations between specific entities.

In two separate experiments, TTG Estimation and Distance Estimation data were collected from the same set of test persons who had following tasks:

• *TTG Estimation task: Estimation for a Time-To-Go in [seconds] – test subjects are asked to signal the point of time (in Reality and Virtual Reality) at which they feel there’s just not enough time for securely crossing
the street until the arrival of a vehicle (at 3 different
speeds).
• *Distance Estimation task: Test subjects are asked to estimate the distance in [m] between them and a pylon (in Reality and
Virtual Reality)

Following table shall give a visualisation of the experiment design with the corresponding variables to be examined:

``````+-----------------+-----------------------------+---------------------------------+
|                 | TTG Estimation Experiment   | Distance Estimation Experiment  |
+                 +-----------------------------+---------------------------------+
|                 | 30 km/h | 35 km/h | 40 km/h | 8m | 9m | 10m | 11m | 12m | 13m |
+-----------------+---------+---------+---------+----+----+-----+-----+-----+-----+
| Reality         |         |         |         |    |    |     |     |     |     |
+-----------------+---------+---------+---------+----+----+-----+-----+-----+-----+
| Virtual Reality |         |         |         |    |    |     |     |     |     |
+-----------------+---------+---------+---------+----+----+-----+-----+-----+-----+
| Test Variables  |     abs(TTG_R - TTG_VR)     |      abs(Dist_R - Dist_VR)      |
+-----------------+-----------------------------+---------------------------------+
``````

So in general I’m interested in the answer to the following question:
Is there a relation between the estimation ability/quality for TTG and the estimation ability/quality for Distance? Or in other words …
Do test persons with a good estimation for the TTG also give a good estimation for the Distance?

So my questions are:
a) What hypothesis approach is more appropriate? A comparison between two test variables OR a correlation analysis?
I am confused by the fact that the test variables |TTG_R – TTG_VR| and |Dist_R – Dist_VR| have different levels (TTG: 3 different vehicle speeds; Distance: 6 different distances) and that the test variables are measured in different units (TTG: s; Distance: m).

b) What exact method/test can I use to adress my point of interest? Does difference hypothesis make sense? (e.g. ANOVA for multiple factors?)
I have thought of normalising the test variables via zscore and check for bivariate correlation but then immediately I realise there are different test levels for each variable TTG: 3 different vehicle speeds; Distance: 6 different distances).
And regarding a difference hypothesis I am not sure if test levels can be used as factors?

Available software for evaluation:

• Matlab
• SPSS

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