James Doodson wrote:
> Hi all,
>
> Does anybody have any advice on a) techniques, b) fun activities, or c)
> pitfalls/common problems with helping undergraduate psychology students
> understand 'what significance is' (some of the theory, significance
> framed in terms of probability, p-values, parametric vs. non-parametric).
Dear James,
This is probably not in the "fun" category... but one key idea that
students don't get: how a statistic can have different values in a
/sample/ given than the null hypothesis is true (in the /population/).
You can convey the idea by simulation. For instance for the correlation
coefficient, r, set things up so that two variables are completely
independent, and then run a bunch of simulated studies testing the
correlation.
In the statistical package R, you can do this for correlations as follows:
sampleSize = 20 # sample size
numOfSims = 1000 # how many simulations to run
rs = c() # for storing the r's
for (i in 1:numOfSims) {
x1 = rnorm(sampleSize) # generate random x1
x2 = rnorm(sampleSize) # generate random x2
rs[i] = cor(x1,x2) # store the correlation between x1 and x2
}
hist(rs) # draw a histogram
Hopefully even if you don't know R, this is reasonably straightforward.
I'm sure you can do something similar in SPSS, or Excel, or even
probably on an applet online somewhere.
Then students hopefully start to see that every now and again, even
though we know in the population there is no relationship between x1 and
x2, sometimes in the sample we get values for r quite far away from 0.
Here's another for a two-sample t-test:
sampleSize = 20
numOfSims = 1000
mean1 = 50 # mean of group 1
mean2 = 50 # group 2
sd1 = 10 # sd of group 1
sd2 = 10 # group 2
ts = c()
for (i in 1:numOfSims) {
x1 = rnorm(sampleSize/2, mean1, sd1)
x2 = rnorm(sampleSize/2, mean2, sd2)
ts[i] = t.test(x1,x2)$statistic
}
hist(ts)
The code's not dramatically different.
And so on...
Fingers crossed, the extra step of why we typically want to a find a
value of t, or of r, etc, which is exceedingly unlikely in a world where
the null hypothesis is true, is easy to convey.
Cheers,
Andy
--
Andy Fugard, Postdoctoral researcher, ESF LogICCC project
"Modeling human inference within the framework of probability logic"
Department of Psychology, University of Salzburg, Austria
http://www.andyfugard.info
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