Paired Data: Testing a Claim about a Mean Difference (Lesson 10.6)
Chapter 10 - Day 8
Chapter 10
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
All Chapters
Learning Targets
-
Use the four-step process to perform a significance test about a mean difference.
-
Determine whether you should use two-sample t procedures for inference about μ1 −μ2 or paired t procedures for inference about μdiff in a given setting.
Experience First
In this lesson, we will be using the same relevant context from the previous lesson: climate change. This lesson was also co-developed with Dash from Skew The Script.
With the data for this lesson, you have the option to edit the Word document to include the actual data that was collected from your class in the previous lesson or you can use the data already included in the activity (thanks to our 3rd hour students!).
The 4-step significance test done in this lesson is exactly the same as the one sample t test for a mean that students learned back in Lesson 9.6 (but this time using differences as the data set!). Students will use the One sample t test for a mean applet (part of the Traditional Inference applets at www.statsmedic.com/applets) for the calculation of the interval.
Formalize Later
When debriefing the activity, here are a few items to highlight:
-
When defining the parameter, it is important to include the word "mean difference" or "mean of the differences".
-
Don't forget about the interpretation of the P-value (after all it is the holy grail). Students don't need to write this down, but it will help them to better understand the conclusion:"Assuming the null hypothesis is true (there is no climate change), there is an approximately 0 probability of getting a mean difference of temperatures of 0.35 degrees Celsius or greater purely by chance."
Because we skipped the calculation and allowed students to use the applet to get the t test statistic and P-value, the discussion about degrees of freedom is not needed (df = n - 1).
To help decide between one sample (μdiff) and two sample (μ1- μ2) t procedures, students should ask themselves:
-
How many samples do I have?
-
0ne. μdiff
-
Two. μ1- μ2 (usually) Watch out for two samples that pair individuals.
-
-
If it is an experiment, are there two treatment groups?
-
Yes. μ1- μ2
-
No. Each individual gets two treatments (matched pairs). μdiff
-
-
Do they reference pairing the data?
-
Yes. μdiff
-
No. μ1- μ2
-