### Re: What is considered significant in the measurement of reaction times?

Date: Wed Feb 2 15:18:19 2000
Posted By: Paul Thompson, Faculty, Biostatistics, Med School
Area of science: Neuroscience
ID: 949267221.Ns
Message:
```
Hi, Matt.  Sounds like a great project.  This is a really standard question
in statistics: How big is big?

Here is my suggestion:
1) Organize the data into two columns: a) Dominant b) Non-Dominant.
So, now we have 32 pairs.
2) Compute a difference between them.
3) Compute the mean difference and the standard deviation of the
difference.  These are the important basic quantities which describe the
problem of interest.

The mean is computed as (sum diffs)/# diffs.  So, it would be the total of
all diffs, divided by 32.

The standard deviation is computed as sqrt(sum(Diff - mean diff)^2 / 31].
There are other formulas as well, but this is easy to use.  Here is another
formula:  sqrt([sum (diff^2) - n*(mean diff)^2]/31).  Maybe do it both
ways, and check them - they should be the same.  Watch those parentheses!!

If you have a calculator with statistics functions, both can be computed
from the calculator.

4) Compute the STANDARD ERROR.  This is a measure of the amount of variance
you get the same mean diff?  Of course not!!

Std err = Std dev / sqrt(32)

5) t = mean / std err.  If t > 2.042, you have a significant result.
Or if t < -2.042, again significant.

We start by assuming that, if there is no difference between dom and
nondom, mean diff = 0.  If the mean diff REALLY IS 0, the actual observed
diff will be close to 0, but probably not exactly 0.  Sometimes it will be
a little > 0, sometimes a little < 0.  If the observed t > 2.042 or t <
-2.042, this is unlikely to occur by chance; such a value only occurs BY
CHANCE 5 % of the time.  So, we say that "This result is significant.  That
means that, if the real diff is 0, this result would occur 5 % of the
time.  That is pretty unusual, so I think the beginning idea (mean diff =
0) is not true, and I reject it."

Good luck.  If you have any other qs, paul@wubios.wustl.edu

```

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