LESSON PLAN Justin Erdley April 19, 005 Today s Lesson: An Introduction to Pearson s Correlation Coefficient Unit Topic: Patterns of Association Tenth Grade Geometry NYS Mathematics, Science, and Technology Learning Standards Addressed Standard 1: Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions. Standard 3: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry. Standard 6: Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning. Standard 7: Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions. Objectives Materials Anticipatory Set Students will be able to utilize and interpret Pearson s Correlation Coefficient, calculate the coefficient, and be able to draw conclusions based on Pearson s Correlation Coefficient. (Comprehension/Analysis) TI-83 Plus Calculator (each student should already have one) PowerPoint Presentation entitled: Pearson s Correlation Coefficient 1-Page worksheet entitled: Computing Pearson s Correlation Coefficient Each student should have a notebook (that they ve been using throughout the course) to additional notes. TI-Presenter Homework sheet entitled: The elementary 40 yard dash The first slide of the PowerPoint will be shown on the screen (with Pearson s formula for calculating Pearson s Correlation Coefficient on it). What does the symbol S stand for in Pearson s formula? The students should be familiar with this symbol from Spearman s Rank Correlation Coefficient. What does the bar over the x and y mean? Students should be familiar with this idea from previous units. What are the differences between Spearman s formula and Pearson s formula? Students should note that Spearman s formula is used for determining the relationship
between two ranked items, while Pearson s formula can be used for any two variables. Lesson Body Advancing to the next slide of the PowerPoint, the teacher will ask how do we use Pearson s formula? The teacher should tell the students that they will need to construct a table to calculate Pearson s correlation coefficient? What information will we need in the table? Students will discuss aloud as a class what type of information will be needed in the table. Advancing to the next slide, students will be able to see what information needs to be included in the table. Then the teacher should handout the Computing Pearson s Correlation Coefficient worksheet. The teacher should ask why the columns labeled ( x x) and ( in the table for calculating Pearson s formula are needed. They are necessary to calculate the values in other columns (i.e. ( x x), ( and ( x x)( ). The teacher will now instruct the students to fill in the table on the worksheet. They will be allowed and expected to work with the person they are seated next to in order to complete the table. During this time, the teacher will walk around the room to make sure the groups understand how to complete the table, assisting as necessary, and that the students are staying on task. After all groups have completed the table, students will be shown the next slide of the PowerPoint. They should check their results with those on the PowerPoint. If there are any questions or clarifications, the teacher will address them at this point. The teacher will not advance further until all questions have been addressed. What entries from this table do we need to calculate Pearson s Correlation Coefficient? Students will be given a few minutes to discuss this question with the person they are seated next to. Then volunteers will say which entries they feel are needed. (Students should recognized that the entries S= 330, S= 95.6, and S= 170 are needed to calculate Pearson s Correlation coefficient. They should also recognize that these entries correspond to the columns labeled ( x x), (, and ( x x)(. Now that the students know which entries are needed to calculate Pearson s Correlation Coefficient, the teacher will instruct them to calculate it. This should take just a few minutes and when everyone has an answer, the teacher will ask several students what their results were. Once everyone has agreed upon the correct value (r= 0.9571 approximately). What does this value tell us about the relationship between x and y? Students should be able to determine that there is a strong positive
association between the two variables. (They should already know how to describe the relationship from previous work with Spearman s Rank Correlation Coefficient.) Closure Using your calculator, construct a scatter plot of x and y. The teacher will also ask for a volunteer to use the TI-Presenter so that the scatter plot can be seen by all students on the screen. Do the conclusions we made based upon Pearson s Correlation Coefficient agree with what we see in the scatter plot? Accommodations for IEP Homework/Assessment The PowerPoint was incorporated into the lesson to help a student with hearing difficulties. By seeing the notes clearly written in front of him, this student did not need to focus as much on the verbal language barrier. Students will be given the The elementary 40 yard dash for homework. This will further enhance their understanding of Pearson s Correlation Coefficient. It will also continue with their description of the relationships between two variables that were discussed earlier in the unit. Extensions If the class finishes early, the students will be instructed to work on their homework. This will be done in case they need further clarification with how to use tables to calculate Pearson s Correlation Coefficient.
Name: Computing Pearson s Correlation Coefficient Date: Pearson s Correlation Coefficient is: r = ( x ( x x)( x) ( In order to calculate Pearson s Correlation Coefficient, we need to construct the following table: Fill in the table for using the following values for x and y: x 4 6 8 10 1 14 16 18 0 y 1 3 3 5 4 6 8 9 11 Using the values needed from the table, compute Pearson s Correlation Coefficient. What does the value for Pearson s Correlation Coefficient indicate about the relationship between x and y?
Name: Homework: The elementary 40 yard dash Date: A study was conducted to determine whether there was a relationship between height and running speed among elementary school children. A random sample of eight students, from a local elementary school, was selected. Each child was measured for height in inches and was timed in the 40-yard dash in seconds. The results are listed in the table below. Child Height Running Speed 1 60 8 55 11 3 56 10 4 5 1 5 48 14 6 44 16 7 47 13 8 5 1 Calculate Pearson s correlation coefficient between the height and running speed of each child. Does there appear to be a relationship between the two? If so, what kind of relationship is there?