In our last video, we learn to explore
categorical data; both ordered categories
called "ordinal", and unordered categories,
called "nominal". But what about continuous
data like interval and ratio? We are
going to dive deeper into exploring and
summarizing scale level data with SPSS.
After you import your data, but before
you run your hypothesis tests, you should
EXPLORE your data. Interval and ratio
data are both called "scale" data in SPSS.
Both interval and ratio data are ordered
values, but the distance between the
values in the scale is always the same.
In other words, a centimeter is exactly
the same size anywhere along that tape
measure. An income of $70,000 is more than
an income of $50,000, and the distance
between those values is exactly $20,000.
An income of $90,000 is the exact same
$20,000 higher than an income of $70,000.
Scale data are also called "quantitative
data" or "continuous data". The difference
between interval and ratio data is that
ratio level data have a meaningful zero
point, and interval level data do not
have a meaningful zero point; meaning
that interval level data CAN have
negative values, whereas ratio level
cannot. Other than that, the analyses that
we run with these two types of data are
the same, because what matters most is
not the 0, but the scale; hence, "scale data."
We will still be using the demo.sav data
set supplied by IBM with your IBM SPSS
Statistics software. You can follow the
links in the description for a video
about where to find and how to open this
data set. When we have scale level data,
we want to know different things about
those data than we do with categorical
data. With scale level data - data that are
measuring something - we want to know the
most representative value of our data,
and how spread out the data are. We will
report measures of central tendency -
specifically the mean - and a measure of
dispersion - typically the standard
deviation. When we create a chart, we will
use a histogram. We have more options for
how to explore scale level data. As with
categorical variables, we could use the
Frequencies command. Go to Analyze ->
-> Descriptive statistics -> Frequencies...
We are going to use the scale level
variables "age" and "years at current
address". Now, under statistics we could
ask for measures of central tendency
like the mean, the median, and the mode,
as well as measures of dispersion, like the
standard deviation. We could still get
the minimum, and the maximum. We could ask
for quartiles, so that we can do a
five-number-summary, or we could get measures
of skewness and kurtosis. Click Continue.
For a Chart, we want a histogram, but this
time, because we have scale-level data, we
should add the normal curve, so that we
can see how closely our data match
normality. Click Continue. Frequency
tables are big and they are not very
useful with scale level data, so we will
turn those off. With those settings, click "OK".
Before we do anything else, scroll
down to the charts. We see the age is
fairly normally distributed. We have
"censored data" on the left end where
children were not surveyed, but there was
no upper boundary for age. But "years at
current address" has this tail pulled out
to the right, or the positive end of the
curve: a condition that we call "positive skewness".
People tend to move around.
Very few people have lived at the same home
address for many many years. For "Age",
the normally distributed variable, the mean,
median, and mode, are all very similar .
But for the variable about "years at current
address", notice how the mean (11.5 years) has
been pulled out to the right of the
median (9)? We can see that the value for
skewness is positive 1; whereas the
skewness for Age is close to 0. You can
divide the skewness by the standard
error of the skewness to get a z-score
that tells you approximately how badly
skewed the distribution is. Another chart
with which we can examine the normality
of a distribution is the P-P Plot.
The "P-P Plot" is not a Russian presidential scandal,
but rather the "P-P" stands for
"Percentile-Percentile" Plot.
Go to Analyze -> Descriptive statistics -> P-P Plots...
As before, we are going to use the
scale level variables Age and Years at
current address. We're going to compare
our two distributions to a normal
distribution, but I should point out that
you could choose from among a number of
options to compare your data.
We can determine if the distribution of Age
matches a Laplace distribution, or a
Chi-squared distribution, or Student's t-distribution.
I'm not sure what a
Laplace distribution is, but now that I
mentioned it, I'll need to figure it out...
and probably make a video about it.
But for now, let's compare to a normal
distribution. Click OK.
This is a percentile-percentile plot.
If a distribution is normally distributed,
the dots will all line up on a 45-degree line.
Now you can see what happens with a
roughly normally distributed
distribution and a severely positively
skewed distribution. For Age, the dots are
mostly right on the line. For years at
current address, the dots veer off the line,
particularly on the positive end.
This helps to illustrate the interaction
between the histogram and the P-P plot,
and how both of them represent normality.
Another way to examine scale level
variables is by using the Descriptives command.
With this command, many of the
most common analyses are set by default,
so there is less clicking. Go to Analyze ->
-> Descriptive statistics -> Descriptives...
Move over our variables Age and Years at
current address... and now click OK.
This is the quick and easy way to examine a
scale variable. We don't get a lot of
output, but we get the most important
output for scale level data. We get the
most important descriptive statistics in
a single table. We get mean and standard
deviation, minimum, and maximum... all with a
single click. We did not get any charts
or plots, however... very minimalist.
Go back to Descriptives. We can choose other
output if we want more. Although we are
limited in what we can choose to show,
this is a very fast way to examine
scale variables.