Wednesday, December 07, 2005

Examples of Questionable Causation

An early AP Statistics practice exam had cricket chirps per minute as the explanatory variable and temperature as the response variable. Does this mean that we might blame the chirping of crickets for global warming?

Perhaps we can investigate whether dead manatees cause powerboat registrations. The two values seem to have a strong, positive linear relationship.

I read somewhere that as teacher salaries in a state increased, so did total liquor sales. Hmmmmmmm.

Going back to global warming, it was recently pointed out that the frequency of pirate attacks is inversely associated with ocean temperatures. Could an increase in pirate attacks spell the beginning of a new ice age?

What other spurious relationships have you found?

Four Correlation Labs

Before students begin to calculate the correlation coefficients or coefficients of determination for sets of bivariate data, they need to recognize general trends and compare the strength of different relationships. Here are four simple lab investigations students can perform within a 54 minute period.

Break the class into 4 productive student groups. Start each group at a different station. This will be the relationship that they will summarize at the end of the lab.

At each station, students will follow the investigation directions and place a tiny sticky tab at the point of a graph which represent their results. Write the results on the sticky tab.

Materials needed: Balls of various sizes, measuring tapes and rulers, a bucket, a very large shoe box marked in inches inside (so the length of a foot can be measured), four posters marked with appropriate axes, one six-sided die.

(1) On a poster with x values 0-31 and y values 0-31, place your mark at the point where x equals the day of the month of your birthday and y represents the number of days left after your birthday in your birth month. Come to a consensus for the number of days in February.

(2) Select a ball from the bucket of balls. Estimate the diameter of the ball by using a ruler. Measure the circumference using the measuring tape. Record the point (estimated diameter, circumference) on the graph. DO NOT USE A CALCULATOR.

(3) Measure the distance from your wrist to your elbow. Measure the length of your foot using markings in the box. Record the ordered pair (length of forearm, length of foot) on the graph.

(4) Throw one die and observe the number of pips showing, n. Toss a ball toward a basket with your non-dominant hand n times, recording the number of baskets made. Repeat using your dominant hand, again recording the number of successes. Record the ordered pair (right hand baskets, left hand baskets) on the graph.

(1) If the class establishes that there are 28 days in February and you have leap year babies in the class it makes for an interesting graph.

(2) As long as the units used remain constant for a ball, we don't care whether you use English or metric measures. If no students bring this up, this makes for a good critical thinking prompt.

(3) I used shoe size in previous years because I didn't want to have kids measuring their feet with my nice measuring tapes, but we thought up this method this year. You might need for the box to be for size 13 shoes.

(4) This investigation underscores the difference between empirical and theoretical values. Perfect skill would result in ordered pairs (1, 1), (2, 2), (3, 3), etc. Variation is a beautiful thing.

After the students have cycled through each station, have the original group describe the relationship between x and y, determine a line of best fit through the data, and investigate the strength of the relationship. Can the proposed relationship be justified or explained?

Please let us know how these labs work out for you.