Working with StatCrunch One-Way Analysis of Variance (ANOVA) Video Lecture

Hi my name's Bart Poulson and in this tutorial
I wanna show you how to use the online statistics
application, StatCrunch, to compare the means
of several different groups on a single quantitative,
uh, outcome. Um, for this particular comparison,
we're gonna be using a one-way analysis of
variance. Um, if you have just two groups,
you can use a t-test, but when you have more
than two, you usually need to go to an analysis
of variance also called an ANOVA [ah-nova]
for analysis of variance or ANOVA [uh-nova]
depending on however you want to pronounce
it. For this, I'm gonna be using a data set
in StatCrunch that I put there. It's called
"Seating Choice versus GPA," uh, and then
I have a couple of versions of it. This one's
"For 3 rows, with Text and Indicator Columns."
You can get it by going to "Explore," uh,
"Data" and then typing this in. It'll come
up. It's pretty easy and it's got this little
picture right over here. But, um, before I
do the analysis, uh, something I tell my students
all the time is you gotta do the graphics
first, and I have done that. I'm gonna show
you a few charts I've done. Uh, first off
I did a bar chart to show that there are 10
people in each of three different rows. That's
pretty easy. In fact, lemmie just show ya.
The way the data were set up originally in
this is they had 10 scores— these are
GPAs for students in the front row, middle
row, and back row. However, for some of these
analyses, they need to be set up differently,
so I have another video where I've showed
how to stack the data so it creates a single,
um, two columns — one which says what
row they're in, another one with their actual
score. Anyhow, I also did a boxplot. Whenever
you're using a quantitative variable, this
is a good way to check for the shape for the
distribution and for the, uh, presence of
outliers which can cause real problems. Anyhow,
from this, you see that the people in the
front row generally have a higher, uh, distribution
of scores. This is the median, 50% are above
or below; this is the 25th percentile and
the 75th percentile, or actually, this is
the 75th and this is — uh, whatever.
This is the middle 50% of the scorers, uh,
and it's higher than the middle 50% and these
lines, which are called whiskers, go to the
highest and lowest non-outlying scores. Uh,
I have similar thing down here. This is Means
Plot. Now this one's based on percentiles,
and that's about the 50th percentile. This
is the mean and you notice it— it can
be slightly different. If the distributions
are symmetrical, they'll be the same, but
if they deviate from that at all, then—
then they're different. Anyhow, this is the
mean for the people in the front where you
can see it's much higher than the mean for
the people in the middle or the back row which
are basically the same. These lines are called
95% confidence intervals which indicate the
reasonable range of variation for the, uh,
numbers, that if you were to get another sample,
another similar sample for instance, people
in the front row— their mean could
be as high as this or could be as low as this.
Um, but it rarely overlaps with this one.
Anyhow, uh, I'm gonna show you now how to
do a one-way analysis variance which get the
numbers to back up our little conclusion here
that this group is much higher and these groups
are lower, but the same as each other. What
I'm gonna do then is I'm gonna go back to
here and I'm gonna go to "Stat", "ANOVA",
or analysis of variance. And I'm gonna do
a "one-way" because I only have one factor—
the, the row that they're sitting in. So I
click that. And, uh, there're two different
ways to do it. One is, if you have your data
in the separate columns the way that it originally
came, you can do it that way. I click that
and then I Shift-Click to get all three. And
just hit "Calculate." Alright. And what this
tells me— I'm gonna bring up the charts
again— is this gives me the means for
each of the groups. So, the front row has
a mean of 3.44 and that makes sense. You can
see that about right— reduce it to
like two decimals. Uh, this table here is
the actual inferential statistics, the analysis
of variance table, and this has to do with
how spread out things are. This has to do
with — a little bit like the standard
deviation. Uh, this one right here, the F-statistic,
I believe the F comes from Fisher, the guy
who, uh, created this test. But, um, anyhow,
we have a number here and the one you're probably
most interested in is the last one right here,
the P-value, which gives the probability level
or the significance level for the result,
and you're usually looking for a number that
is under, less than, .05. Um, because .05
represents a 5% chance of getting a result
that big as a false positive if it is true
that there is no difference between the groups.
And so this one, you say, if these three groups
actually have the same mean, the probability
can make a difference this big through random
error is .0026. Now that's a proportion and
it needs to be, uh, you need to turn it into
percentage. .1 is 10%. .01 is 1%. .0026 is
a quarter of 1%. It's a very low chance. And,
if th — if there's very strong convention
that anything less than 5% is taken as statistically
significant. So, what we have here is a statistically
significant difference between these three
groups. Now, even though it's pretty obvious
what's going on right here, that these two
are down low next to each other and this one's
up high, there is, um, room for ambiguity
sometimes in the analysis of variance. And
so, because the analysis of variance doesn't
actually tell you which group is higher, simply
that the means are different or in some combination
there is difference, uh, you often do what's
called a post-hoc test. That means after the
fact, and, uh, StatCrunch gives you one option.
I'm gonna go back to "Options" and "Edit".
This is where I set things up in the first
place, right? I'm gonna come down here and
click this one. The "Tukey", that's for John
Tukey, wonderful statistician, the guy who
gave us the boxplots that are— that
are up here. "HSD" is for "Honestly Significant
Difference." It's kind of a funny way to put
it, but anyhow, there it is. And, when I click
that, the table over here is gonna change
a little bit. You'll see it. It's gonna add
some stuff at the bottom. Ok, now, StatCrunch
does the confident, the post-hoc in a kind
of a funny way. It does with confidence intervals.
Uh, kind of wish they didn't do it that way,
but anyhow, all this stuff up here is exactly
the same as it was before, and this down here
says this is the difference between the GPA
of the people in the front row, uh, and the
people in the middle row. The people in the
middle row have a GPA that's, on average,
.977 GPA points lower than the people in the
front row. That's the difference between this
and this. It's about 1 point. Um, I'm sorry,
this is a confidence interval so that is gonna
go from .97 to .099. It could be small, it
could be big, but the point here is these
are both negative. Uh, that the front, people
in front, always have a higher GPA than the
people in the middle and similarly, the back,
you see that they're negative both times?
Again, the people in the front always have
a higher GPA than the people in the back.
On the other hand, when you compare the people
in the middle and the back, sometimes it's
negative, sometimes it's positive. Uh, which
means there's no reliable difference here.
So anyhow, what this one tells us is that
it— it is in fact the people in the
front who have the reliably higher score and
that these two are similar to each other.
Fine. I wanna show you one other way of, um,
doing the analysis of variance because you
saw over here that I had the— the data
set up as either three different columns,
which is how I got it from another data set,
or I stacked the columns to make one column
that said whether they're in the front row,
or the middle row, or the back row and the
GPA is right next. Uh, this stuff comes up
in another video I'm gonna make so we can
ignore it for now. But this is split columns
and this is stacked columns and I wanna show
you that you can do the same analysis really
easily. Whoops! Sorry. You can do the same
analysis really easily with the split columns
as well, I'm sorry, with the stacked columns.
In fact, if we go to "Options", and go back
here, you see here it says "Compare selected
columns," and I did that. Well now I'm just
gonna do "Compare values in a single column."
In this case, the vol— the responses,
of the outcome variable is GPA, so I just
drop down and select that. And this one, the
row, is the factor, that's the thing that
separates the groups one from another. So
I go right here to "Row." And, uh, and you
know what? It comes out. It's exactly the
same. The only difference is right up here,
is this time instead of saying they were in
different columns, it says responses are stored
in "GPA" and factors are stored in "Row."
And I get the exact same conclusion again
that the people in the front row have, um,
on average, a significantly higher GPA than
the people in the middle or the back row.
And the P-value is .0026 which means there's
less than — there's a quarter of a
percent of a chance of something like this
happening through random sampling if in fact
the groups are different. Anyhow, so that's
it for right now and I hope that's been helpful.
Thank you.