Analyzing Paired Data: Estimating a Mean Difference
Chapter 9 - Day 8 - Lesson 9.5
Use a graph to analyze the distribution of differences in a paired data set.
Calculate the mean and standard deviation of the differences in a paired data set, and interpret the mean difference in context.
Use the four-step process to construct and interpret a confidence interval for the true mean difference.
Activity: Does memory training help?
The last type of analysis we will be doing this chapter is matched pairs. Students often have trouble differentiating between matched pairs and two sample means. It’s important to really focus on how with matched pairs there is only one sample but each individual is yielding two pieces of data as opposed to two samples with each individual yielding only one piece of data.
Matched pairs is often used with experiments so we are going to conduct an experiment with the students. We’re going to investigate whether particular memory strategies will help students to remember more words.
To setup the activity you will need copies of both the memory strategy instructions and both lists of words for each student. Randomly assign half the students to receive memory strategy A first. The other half will get memory strategy B (quizzing). You can also randomly assign the Random Word Lists if you’d like. The word lists should be equally challenging to remember. Make sure you explain to students that they can only use the strategy they were given.
Give the students 3 minutes to study the list of words using their memory strategy. Then students should write down as many of the words as they can remember. Then repeat the process with the other strategy. Students need to subtract the number of words they memorized, and add their data to the table on the board. Make sure that students keep straight which strategy is which.
Enter the class data into the applet and copy the dotplot. Make sure to spend some time with students looking at both the positive and negative sides of the dotplot and discussing what the dot represent.
The good news is that once the data has been converted to the differences, we now are working with a 1 sample mean difference which is the same as what we did in chapter 8. Encourage students to work through the rest of the activity in their groups from memory, but if necessary they could look through their old notes. After students calculate the confidence interval, they need to think about what it tells them about the strategies. Does the interval contain zero? If not, which strategy helped students to remember more words?