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from now on I'm gonna be free to do a pop quiz in class where I say
"Do a frequency distribution of...almost
anything." and expect you to be able to. Let's make sure you understand
what a frequency distribution is. it's just a fancy word
for listing all the possible values that could happen in a sample or study or
population,
and telling how frequently each one occurs.
So that's why the word "frequency" is there.
It tells how many. It's like a tally. The reason it's called a
"distribution" is, it tells how those items
get distributed. Or, if you put them in a pile
in the right order how they pile up. That's all a frequency distribution is.
Let's do a couple examples to illustrate so you know how to do a frequency
distribution.
If you do frequency distribution of grades. Say I was giving test in class.
The first step in making a frequency distribution is, list all the possible items.
Those are all the possible Grades. Then either in a table or in a graph,
you would then
put a place for how frequently or how often
each one happens. I take the first persons test, It's a C. second one's a B.
And I'm just gonna tally, or drop along this line in
a pile in the right place, where each one goes. This guy got a D.
This guy got a B this guy got a C.
A D. So as you can see it's simply how
frequently each of these grades
occurs in this given situation. That's all a frequency distribution is.
List all the possible items and either put
as a number or tally or in this case a graph how often each happens.
In this case it's 2, 35, 5, 3 and 2 respectively for each of these grades.
An A happens twice. C happens 5 times. you can draw a curve to see how
the shape is. Here's what's really useful for your statistics class:
Say I want to know what grade do 5 percent the top five students in my class
fall at or above? Now that I know
how the scores are distributed, Ican count 1,2
3, 4, 5 of the highest scores. draw a line
and shade a region, then say this region over here
with the B or higher, 5 of my students. It's actually not a percent here is it?
Because we don't have a hundred scores. But I'll say, 5 of my ,
oh, 15 or 20 students are at a B or above. My top five students are.
You can do for you see distribution on statistics as well. So if you were doing
one of the means
you put a place for the frequency and then you have to actually label this
axis for the means with numbers
in the correct order. And then you drop scores in piles
in the right places to tell you how the scores distribute or how they fall.
How frequently each what happened. That's all a frequency distribution is.
Let's talk about how we're going to use them in statistics class.
Let's take a frequency distribution of a statistic. You could do one for
a T statistic, a chi-squared, or an
F statistic. This is going to be for an F statistic we use in ANOVA.
Well you'd list all the possible Fs on one axis.
Put the numbers for all the possible Fs. They'll range from 0 up to ...
above 4, but for this we'll do 4.
These are gonna be F statistics happening by chance. these are not the F statistics
you're actually computing from your study.
These instead are going to be 100 studies. And each one has a dot.
Those 100 studies come from data where there is no treatment effect.
Because we want to know how often
each F ratio would happen by chance. First study
came out with the 1 for the F. Then a 2, then a 0, then a 1.5
Then we had a study with 1.5 and then a 2.
et cetera so basically I'm running a hundred studies.
This is what some people call a Monte Carlo simulation.
to figure out, out of a hundred studies where there's no effect, I'm
literally computing an F ratio, like you're aware of, it's a mean square
over a mean square, right?
I'm just piling them them up and seeing how often each one occurs by chance.
Why would we do this? The reason is
we wanna know which
F ratio occurs by chance very rarely.
only five percent of the time. So we could draw an F curve
and once I had 100 scores, let's just say these were 100 scores, I could
then count the top five. That would be the top five percent
of scores, wouldn't it? I could say
"Beyond this point, which is about a three,
it looks like that is a rare F ratio. That
F ratio does occur by chance, but only five percent of the time.
We call this F critical. This is our cutoff beyond which we say
"this is a rare F." If we have a doubt level of .05 and
only want 5 a percent chance of being wrong claiming an effect,
a p of .05, or an alpha of .05 is the way we would say that.
We need to figure out
which F the top 5 percent of
scores will fall beyond just by chance when there's no effect.
Then we come along and we do OUR study.
That's what this red dot represents. This is our F obtained
from our study. We're gonna drop it where it belongs. And see in the
scheme of things where it goes If it falls over here
it's not in the rejection region. We can't reject the null.
we would not claim in effect. if however
our F obtained falls somewhere over here in the rejection region,
we reject the null. why? because this F ratio occurs very rarely by chance.
So it's probably, ninety-five percent, probably not due to chance.