The Power of Historical Data: An Accurate Method in Estimation?
Faculty Advisor Name
Brian C Leventhal
Department
Department of Graduate Psychology
Description
As humans, we make hypotheses every day. We take information from our previous experiences to inform our decisions. For example, I wake up and begin to get ready for work. As I leave for work, I notice that there are storm clouds. I wonder how likely it is that it will rain given that there are storm clouds. I first consider previous environmental conditions when it has rained, such as the way the sky looks and the temperature. Then, I wonder how likely it is that there are storm clouds given that it is raining. Aside from the occasional sun shower, it has rained when there are storm clouds. I conclude that it will likely rain today and decide to bring my umbrella. This example highlights the use of prior information to make inferences and is known as Bayes theorem.
Bayes theorem can be applied to make inferences in a wide variety of situations. From predicting who will win a race to inferring the best medicine to administer to patients, Bayesian statistics can help us assign probabilities to various events. A primary advantage of Bayesian statistics is that we can assign? prior probabilities to inform our decisions. We continuously take in information and update our beliefs. Our prior experiences provide ways to make better-informed decisions that result in more accurate findings.
The more informative the prior information is, the more accurate the results that are obtained. Informative priors can be based on opinions of subject-matter experts or previous research (Ames & Smith, 2016). Another type of informative prior is the power prior (Chen, Ibrahim, & Shao, 2000; Ibrahim & Chen, 2000). The power prior is based on historical data or data from a previous study that matches data for the variable of interest in the current study (Ibrahim & Chen, 2000). The idea of power priors has seldom been applied to scoring tests. Matteucci and Veldkamp (2015) explain how to apply power priors to the context of scoring tests. In the current project, I study ways to best use prior information, specifically power priors, to determine the accuracy of results.
At James Madison University, freshman and sophomore students take a science test to determine growth in learning after completing their general education requirements. This test has been administered over multiple years. The historical data can be used to better estimate students’ test scores. Thus, as in the rain example above, using prior information can help to make better-informed decisions about students. The technique of introducing historical data to estimate students’ test scores is novel in the field of education. Through my use? Incorporation? of Bayesian statistics, I show that I can make more accurate inferences about students by incorporating information from? prior data. Through a simulation study, I also examine the effects of inaccuracies in historical data on students’ (estimated?)test scores. For example, test questions, curriculum, or students could have changed across years. This information will be helpful to faculty in making better informed decisions about students’ competencies.
The Power of Historical Data: An Accurate Method in Estimation?
As humans, we make hypotheses every day. We take information from our previous experiences to inform our decisions. For example, I wake up and begin to get ready for work. As I leave for work, I notice that there are storm clouds. I wonder how likely it is that it will rain given that there are storm clouds. I first consider previous environmental conditions when it has rained, such as the way the sky looks and the temperature. Then, I wonder how likely it is that there are storm clouds given that it is raining. Aside from the occasional sun shower, it has rained when there are storm clouds. I conclude that it will likely rain today and decide to bring my umbrella. This example highlights the use of prior information to make inferences and is known as Bayes theorem.
Bayes theorem can be applied to make inferences in a wide variety of situations. From predicting who will win a race to inferring the best medicine to administer to patients, Bayesian statistics can help us assign probabilities to various events. A primary advantage of Bayesian statistics is that we can assign? prior probabilities to inform our decisions. We continuously take in information and update our beliefs. Our prior experiences provide ways to make better-informed decisions that result in more accurate findings.
The more informative the prior information is, the more accurate the results that are obtained. Informative priors can be based on opinions of subject-matter experts or previous research (Ames & Smith, 2016). Another type of informative prior is the power prior (Chen, Ibrahim, & Shao, 2000; Ibrahim & Chen, 2000). The power prior is based on historical data or data from a previous study that matches data for the variable of interest in the current study (Ibrahim & Chen, 2000). The idea of power priors has seldom been applied to scoring tests. Matteucci and Veldkamp (2015) explain how to apply power priors to the context of scoring tests. In the current project, I study ways to best use prior information, specifically power priors, to determine the accuracy of results.
At James Madison University, freshman and sophomore students take a science test to determine growth in learning after completing their general education requirements. This test has been administered over multiple years. The historical data can be used to better estimate students’ test scores. Thus, as in the rain example above, using prior information can help to make better-informed decisions about students. The technique of introducing historical data to estimate students’ test scores is novel in the field of education. Through my use? Incorporation? of Bayesian statistics, I show that I can make more accurate inferences about students by incorporating information from? prior data. Through a simulation study, I also examine the effects of inaccuracies in historical data on students’ (estimated?)test scores. For example, test questions, curriculum, or students could have changed across years. This information will be helpful to faculty in making better informed decisions about students’ competencies.
