Comparing Samples and Activities for Collecting Bi-variate Data

We wrapped up uni-variate data exploration. Students shared graphs and discussed their analysis and conclusions. This was a good discussion. I emphasized that any comparison of distributions should discuss the shapes (modes, symmetry/skewness, and outliers/major gaps), center (mean or median), and spread (standard deviation or IQR). I also told students that the conclusion they draw must be supported by the analysis they perform. They will often see data that has no clear-cut answer and they must communicate what they are using to draw a conclusion. This aspect of statistics typically makes students uncomfortable. They are used to coming up with an answer and it is either right or wrong. They'll get over this.

The second half of the class was focused on collecting bi-variate data to use in regression analysis. The class will meet in the computer lab next time, so this was an opportunity to generate data that we can use. We ended up generating 4 different data  sets to work with.

We had time to discuss graphing the data using a scatter plot. I then had students focus on the direction of the relationship (positive or negative), the strength of the relationship (concentrated or dispersed), and the form of the relationship (linear, curved, or shapeless). We'll use these ideas as a foundation for exploring linear correlation.

Below is the outline I followed today, along with italicized comments in square brackets, [like this].

o   Complete river sampling comparison

§  Share and discuss

·         Population versus samples

o   Populations have a mean and standard deviation, we just typically don’t know what they are

o   Designate these using Greek letters mu and sigma

§  When calculating population standard deviation, divide by n

o   Samples are drawn from a population

o   Designate sample means and standard deviations using Latin letters and bar

o   We try to gauge the value of the population mean and standard deviation from the sample data we draw

o   Every sample varies slightly, so we’ll need to understand and account for this sample variation

o   Larger samples should more closely reflect the population values

Day 4—Regression and Correlation

·         Associations

o   Orbit package delivery – part 1

§  Look for association between drop height and distance from target [delivery vehicle is a crumpled piece of paper; target is a coin on the floor; students gather at least 6 drops.]

o   Collect  additional data and use in the computer lab

§  Knotted ropes [how do the number of knots tied in a rope affect its length]

§  Height and arm span (ref. Da Vinci’s Vitruvian man)

§  Pass the Buck [hand-to-hand passing of slip of paper; start with 3 students and continue adding groups of 3 to the end of the line; response variable is time to pass the buck from one end to the other.]

o   Is there an association

§  Scatterplots

§  Direction of association

§  Shape of association

§  Strength of association

o   Work with other data sets as needed [none need, four data sets should be plenty]