One major objective of this class to learn to deal with real world data. So let's start by taking a look at our class data.
Note that, as we go through these examples, we'll meet several important concepts from section 1.2 of our text whose title is Data Basics.
I've collected the results of our class survey and stored the result in a data table. There are 38 folks enrolled and the last few lines look something like so:
|Section||How old are you?||How tall are you? [Feet]||How tall are you? [Inches]||Are you left or right handed?||What is your gender (optional):||Choose your eye color||What is your major?||Where is your hometown?|
|2||18||5||8.00||Right||Female||Hazel||Mass Communication||looks like: 35.6,-82.55|
|2||21||5||11.75||Right||Male||Blue||Political Science||looks like: 35.6,-82.55|
|1||20||5||5.00||Right||Male||Blue||New Media||looks like: 35.6,-82.55|
|2||21||5||9.00||Right||Male||Brown||Computer Science||looks like: 35.6,-82.55|
|2||18||5||6.00||Right||Female||Blue||Environmental studies||looks like: 35.6,-82.55|
That's actual data, though I've set everyone's hometown to Asheville for privacy purposes.
The result of our import is called a data table or data frame.
Each row in a data table is called an observation and corresponds to a case in our study. In this particular example, each case corresponds to a student enrolled in the class.
Each column corresponds to a variable or characteristic associated with the cases.
There are two main types of data and both types can be further classified into two sub-types.
A histogram partitions the horizontal axis into intervals and places a rectangle over each interval indicating a count of values. Here's a rough histogram of the heights of folks in the class. The dashed yellow line at about 5.64 is a quantification of location called the mean.
Here's a histogram for the ages in the class. The shape is quite different and the mean is, perhaps, less meaningful.
Alernatively, we might look at box plots fore these same variables. These illustrate the so-called five-point summary of
min, 1st quartile, median, 3rd quartile, and max.
Sometimes we'll want to find if there's a relationship between two variables. In the following side-by-side boxplot, we examine how the relationship between gender and height.
Like a histogram, a bar chart represents value counts with vertical bars. Here's a bar chart for the different eye colors in the class:
A key difference between a bar chart and a histogram is that a bar chart represents categorical data. So, for example, the order of the bars doesn't really matter. Here's a bar chart for the same data, the variables are sorted in ascending order, rather than alphabetically:
Lots of people seem to love pie charts for categorical data. I only favor pie charts when comparing two values of a categorical variable. In our data - section, gender or handedness are logical choices to illustrate with a pie chart. You get a good sense of relative magnitude or proportion.
While people do love pie charts, there's really no way to tell absolute magnitude and they can be confusing for data sets of moderate size. Here's a pie chart for the majors in the class:
An better way to look at categorical data is with a bar chart, which makes it much easier to compare two values that are quite close to one another. We can also indicate magnitude with a single scale.
Geographic data is of tremendous importance and is often best illustrated on a map. Here's what the actual answers to the hometown question looks like:
One simple characterization of statistics is
the study of how to collect, analyze, and draw conclusions from data.
Note the three parts:
The images we've seen today allow us to draw rough qualitative conclusions about the data we see. Quantiative analysis is more numerical. For example, 5 out of the 38 people in the class are left handed, or about 13.9%.
This is more precise information than we could glean from a pie chart.
Ultimately, we want to draw inferences or conclusions from data. To do so, it helps to have a little terminology:
The main question is: once you've computed a statistic from a sample, what might that tell you about the corresponding parameter for the whole population?
For example, I guess that about 13.9% of our class is left handed. We could take that as an approximation to the number of left handed folks in the whole population. How accurate an approximation might we expect that to be?