"Student's" t Test – Interactive tutorial


Answers and discussion

For Quercus rubra the mean height was 10.6 ± 2.9 cm and for Quercus alba we have 8.2 ± 2.0 cm. Now why was it important to round the numbers?

Precision error is another contributor to uncertainty in determining an experimental outcome. Precision error refers simply to the imprecision inherent in any measurement. For example, you can use a wooden yardstick to accurately measure the width of a cabinet to the nearest inch, but probably not to the nearest tenth of an inch. We must round quantities to represent the imprecision in the measurements that were used to obtain them. For example, we must not report the width of the cabinet to the nearest tenth of an inch, because someone might count on that level of precision. The same goes for derived quantities, such as a sample mean.

Data distributions

What if the investigator had measured the first two plants only? What conclusion would she have reached? Obviously when data are subject to random error one needs some minimum number of data points in order to draw a conclusion. How does one decide what that minimum will be? Let's use a tool called a histogram or frequency distribution plot to pursue this question.

Here is where Excel is a royal pain in the neck. The graphing tool does include a histogram function, but you have to load up their Data Analysis add-in to get to it, and even then it is extremely awkward to use. Instead, let's simply set up a plot on a piece of graph paper. Any paper with grid lines will do. Label the x-axis "plant height (cm)" and label the y-axis "frequency of observation." This plot will be of the column type. Make the x-axis categories "3 to 5," "5 to 7," "7 to 9," "9 to 11," "11 to 13," "13 to 15," and "15 to 17," in that order. The y-axis values should start at zero and go up to 5.

Your plot area should look like this.

Now convert your data into categories so that you can use this plot to visualize their distribution. For example, the first data point for Quercus rubra is between 5 and 7 cm, so replace "6.4" with "5 to 7" (or just 5-7 for convenience).

Quercus rubra 
Quercus alba

Data table:

Quercus rubra  6.4 7.4 10.4 8.5 9.2 9.5 11.8 11.8 9.3 12.5 13.7 17
Quercus alba 11.4 9.5 5.8 9.2 11.8 7.9 7.9 7.8 5.3 7.5 7.1 6.6