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So now we are going to review one way between subjects ANOVA so we can then use some of
the same subjects to introduce a one way repeated measures or within subjects ANOVA. So take
good notes on this and make sure you get the concepts because it will help you when we
go on to the repeated measures design. Hopefully the following will be familiar to you when
you do a between subjects ANOVA, also known as independent groups ANOVA. Now we are not
talking about an IV or independent variable, this is the name of the design of the study,
which it is too bad it has some of the same words in it. The reason they call them independent
groups is each group is completely different and they don't really share anything except
the fact that they are all in the same study and your going to treat everybody identically
except for the treatment. So, lets say, like the example we did in class, some people sip
cola. And they say how much they like it on a zero to ten scale. Some people sip grapefruit
juice and again they rate that, and other people sip cod liver oil. The reason they
call it a between subjects, or independent groups design, is that each person is in each
group only once and nobody gets more than one treatment. So, we have a monkey, an alien
and a pirate and they sipped cola and rated it. But it is completely different people
who sipped grapefruit juice. We had a tiger, a knight and unicorn, let's say. And then
the people who sipped cod lover oil, let's just say we had a cat, a frog and a zebra.
Completely different individuals and these groups really don't share anything except
we put them all in the same study and kept everything as similar as we could across groups
except for one thing and that's the independent variable. Which was completely different between
groups. This will not be the case when we move on to a repeated measures design. But
for now, different people are in different groups, each person got a different treatment.
And then we asked them rate how much they liked things. So, let's just say, for example,
that the alien has taste buds that don't match with cola and he said , ehh, it's awful, it's
a zero. Monkeys had a sweet tooth and loved it and said it was a ten. And the pirate only
likes rum because he has been drinking nothing but that for years on the ship, so he rates
it a two, right? And let's just say that the way these guys rated it for grapefruit juice
we have a six, a seven and an eight. And actually we started in our example in class with water
for the third group and it got kind of medium ratings as you might expect, let's just say
four, five, six. Now the two kids of variability that I want
you to think about. Let's start with between groups variability. If for each of these groups
you compute a group mean, now hopefully you know how to do that, you add up the scores
in the group, divide by how many were in the groups. So, ten plus zero plus two divided
by three would be the group mean for this group and you could similarly get a group
mean for that and a group mean for that. Between groups variability is how far apart were the
groups. We measure that by seeing how far they were from the grand mean which is the
center of the whole study. You know how to get the grand mean, you take absolutely all
the data, add it up and divide by how many. In this case you would divide by nine. We
get deviation scores with a between groups, by taking group mean, minus grand mean for
this guy, group mean minus grand mean for this guy, happens to be the same because they
are in the same group. Group mean minus grand for that guy. Group minus grand for this guy,
this guy and this guy. We are making deviation scores. Group minus grand for this guy, this
guy and this guy. We square them, we sum them up or add them to make a sum of squares between
groups. Then we make them into an average because we don't want the number of observations
blow the data off scale, so we make into an average. And we are using degrees of freedom
to divide by so it is a tweaked average, we don't quite divide by how many scores as degrees
of freedom. And at any rate we now have a measure of how far a part are the groups.
And we hope that our treatment was extreme enough that these distances will be big, so
that mean squares between is big. Why? Well if you recall from our lecture on power, the
following. In our lecture on power, we saw that we want to get our "F" obtained as big
as possible. We want to move it this way. Because this is small and these are larger
scores over here. We want it over this way so it will exceed, "F" crit, fall in the rejection
region, let us claim an effect and publish our study. We will have more statistical power
if we can design our experiment in such a way as to maximize mean squares between. Write
that down if you don't yet have that engrained on your memory banks. So we redid the study
in our class example and we replaced the water group. We reran the study. And this was only
a thought experiment, obviously. But we replaced it with cod liver oil and guess what happened?
Scores fell so I am just going to arbitrarily put in low scores here. I am going to put,
um, cats like fish so I am going to put a one instead of a zero. Frogs might hate fish
and zebras might hate fish. Group mean would be small, right? Now I want you to pause the
video, write down the answer to the following question and see if you can get it right,
conceptually. When this group mean moved in this way. This
group mean got smaller when the scores dropped. What happens to this distance here? Pause
it see if you get the right answer. And the right answer is, this group mean fell and
it is getting more extreme, it's getting farther away from the middle, so this distance grows,
so between groups variance grows, so "F" obtained grows. We have more statistical power. Good
Thing. Let's make a little smiley face here because we want these distances to be big.
If our treatment is very effective they will be big. Or if our treatment is wimpy there
may still be some distances here but they will be small, they will be just on the magnitude
of what chance creates in terms of differences. Now let's leave the topic of between group
variability, we are not now talking about differences between groups. We are now going
to talk about differences within groups and by now you know how to get those. So, if you
take the monkey's score of ten minus the group mean. This dudes score minus his group's mean,
this dudes score minus his group's mean. The lion's score minus his group's mean, the knights
score minus his group mean, right? For each person you take their score minus the mean
for their group. You get these deviations within groups. Then you can square them to
make squares. Then you can sum them up to make sum of squares within. Then you can make
an average of them or mean squares within. When you do that you are using degrees of
freedom to divide by so it's kind of a funny average but it is an average, pretty much.
Now, we want mean squares within to be small. We do not like this kind of variability. Why?
Well again from our lecture on power, when mean squares within gets smaller and smaller,
"F" obtained gets bigger. More likely to fall over in our rejection region, enabling us
to claim an effect and publish our study. So how can we minimize mean squares within?