Statistical Literacy (CoRD)
Joan Brenneman, University of Central Oklahoma
Kristi Karber, University of Central Oklahoma
These activities encourage active learning of statistics through exploration of non-routine problems. By actively learning topics such as sampling, bias, sample means, sampling variability, sampling distributions, and confidence intervals, students engage directly with the core concepts of statistical literacy. This hands-on approach brings awareness to various data-driven statistics that students encounter in their everyday lives. Not only will students be prompted to analyze and reflect upon various interpretations of data to determine their validity, but they will also collect and analyze their own data. Afterwards, they will reflect on the meaning of their results, hence enhancing their statistical literacy.
|
How to Combat the Age of Misinformation with a Healthy Dose of Skepticism
|
Students begin this activity with a pre-class assignment where they watch two videos discussing the prevalence of misinformation that circulates on the internet. They will then take a quiz based on the videos. The in-class portion of the activity includes a brief discussion on the definitions of population and sample prior to student investigation of multiple scenarios demonstrating poorly conducted studies. Students will discuss each scenario as a group and a class-wide discussion will follow. Key terminology such as ‘well-defined population’, ‘representative sample’, ‘random selection’, and ‘neutral wording’ is introduced and explored during this discussion.
|
|
Understanding the Simple Random Sample and its Limitations
|
In this activity, the instructor will start by defining a unit, a statistical variable, and a simple random sample. How the simple random sample is obtained along with its limitations will be presented. Students will then work in pairs to select simple random samples of 5, 15, and 30 countries from a population list of countries. They will research life expectancies for these countries from two assigned websites. This exercise will prompt a discussion on three biases: undercoverage, non-response, and response bias. Finally, students will brainstorm additional questions to ask when evaluating statistics online.
|
|
Sampling Error, Sampling Variability
|
This activity begins with the instructor discussing the difference between a statistic and a parameter. Students will learn the formulas for sample mean and sample standard deviation, they will calculate these manually for a small sample and use technology for larger samples from Activity 2. They will record their results for comparison, with the instructor providing the population mean for reference. Students will then analyze their findings to develop critical thinking skills. The class will explore sampling error and variability using student data and using an applet. Additional questions students should consider when reviewing online research will be addressed.
|
|
Sampling Variability Revisited through Graphics and Sampling Distributions
|
In this activity, the class will discuss the difference between population distribution and sampling distribution for the mean. Using Excel, the students will create a side-by-side boxplot of sample means calculated using sample sizes of 5, 15, and 30. Following this, students will answer reflective questions on their findings. Through a whole-class discussion, the instructor will clarify the distinctions between population and sampling distributions across different sample sizes. At the end of class, the instructor will present a brief lesson on the goal of sampling to tie together what they have learned.
|
|
The One-Sample Mean T-Confidence Intervals
|
In this activity, students will first discuss the limitations of the sample mean with the instructor. They will then explore the one-sample mean t-confidence interval as a more effective estimate of the population mean. Using technology, they will calculate various confidence intervals for the data they collected in Activity 2. Results will be recorded and discussed for further understanding. Students will also determine whether the assumptions for using the t-confidence interval are met for their computed confidence intervals.
|
|
Extending Knowledge of Confidence Intervals and Sampling Error to a Real-World Example
|
In this last assignment, students will read a news article that talks about the inaccuracy of confidence intervals used in election polls. Students will apply the knowledge they have gained throughout the CoRD activities by answering open-ended questions on this article. The questions will allow them to revisit concepts such as sampling error, margin of error, and bias in a real-world example.
|
This work is licensed under CC BY-NC-SA 4.0
