Hi, it's Margriet Groen here and in this video I'd briefly like

to talk about the concepts of
centering and standardizing.

Now, centering and standardizing
are linear transformations of

data, and they allow you to
represent your data in a metric

that is suitable to you and to

your audience. So for instance

in a figurehead. Response
durations on the Y axis.

Ann is measured in milliseconds.
Now. If you wanted to talk about

that in seconds instead, you'd
simply divide each result

response by 1000.

That won't affect the
theoretical conclusions drawn

from your regression model.

A bit more about centering.

Now, centering is a particularly
common linear transformation.

It's frequently applied to
continuous predictor variables.

When you do regression.

So how do you do it?

You subtract the mean of that
predictor variable in the sample

from each data point.

Now and as a result, each
data point is expressed in

terms of how much it is
above or below the mean.

So you might notice that the
value of 0 has now changed. It

has a new meaning. It is at the
center of the variable

distribution, which is the mean.

But this is clearly visible in
the figures here on the slide.

Say I'm on the Y axis, we have
reaction time and on the X axis

we have work frequency.

Now in the figure on the
left, The Intercept, so that

is where why? That is the Y
value here for Axis zero,

that's The Intercept an so
on the left the Intercept is

at about 870 milliseconds.

Now in the figure on the right.

The expert active X the X
predict is a word. Frequency has

been centered, so now the
Intercept is the predicted Y

value for the mean of X.

Say predicted Y value for the
meaning of acts, so you can

see the mean of X is about
680 milliseconds an you can

see that this now is since
exactly at a middle.

So notice that this slope of the
regression line has not changed.

Now sometimes unsent and
uncentered into sets make

no sense whatsoever, for
example when performance in

sports game is modeled as a
function of height of the

players, The Intercept is
the predicted performance

for someone of zero height.

Now, after centering, the
Intercept becomes the

predicted performance of a
person of every tight and that

is a much more meaningful
quantity.

OK, about standardizing.

So the second common linear
transformation is

standardizing or sometimes
called zed scoring. How do

you do that? You divide the
centered variable by the

standard deviation of the
sample.

So standardization involves re
expressing the data in terms of

how many standard deviations
they are away from the mean.

It's sometimes called sat
scoring because the result of

numbers are in standard units
and they are often represented

by the letters sent.

Now in the figure in the figure

here. Can you see histogram of
the distribution of a data set

from Warner Cooperman Ambrish

Board 2013? They asked native
English speakers to rate

positivity or negativity of
words on a scale from 1 to 9.

And that's referred to
as emotional balance.

And they have to normal.

Instagram, Sophie scores from
1:00 to 9:00.

An and below here you see two
additional X axes.

And this one is for the centered

data. And the this one is for
the standardized data.

And that highlights how
linear transformations just

change the units on the X
axis. Then they leave the

overall shape of the data.
This completely in in intact.

That's all for now, thank you.