My name is Brittany Alexander and I am a college student currently studying Mathematics at Texas Tech University. My passion is statistics and how it affects the world around us. Currently I am researching methods of predicting elections in the United States. What I have learned in my research is that people may not understand statistics and the role they play in our lives. My goal is to educate people about basic statistical concepts like margin of error, correlation vs. causation, and why an average isn’t always the best way of finding the middle of a data set. Data is everywhere, from what TV shows we watch, to how many steps our fitness tracker records. I want to help you understand the world around you by explaining how you can use statistics in your daily life.
I was rechecking my error calculations after I received a comment about the error calculations from a reviewer of my paper. An example calculation was incorrect. This was a minor error, but a further examination led to the discovery of a error in the 2-Party error of my model in 2012. The error was approximately half of what it was supposed to be. This mistake made my model falsely appear more accurate than the Five Thirty Model do to this underestimation. All of the error calculations are currently being reexamined for possible errors. I have already recalculated all the errors but I want to check them a couple of more times to be safe. A corrected table will be posted once it is checked again.
No other major errors were found in the re-checking process. All calculations have been checked three times post the discovery of the error of the 2012 2-Party error for my model.
Below is the updated table to replace the former tables used in both the ESR Virtual Poster and the USPROC Paper:
|Tested Model RMSE||Tested Model RMSE Swing States||RCP RMSE Swing State||538 RMSE||538 RMSE Swing State|
|2008 All Candidates||3.51475||3.14788||4.23389||3.19332||1.66958|
|2008 -2 Party||2.86716||2.57051||3.63513||3.0305||1.47846|
|2012 All Candidates||3.25139||1.94492||2.33511||2.38019||1.2979|
|2016 All Candidates||6.82013||3.95985||3.32952||5.37952||3.56511|
|All Candidate Average||4.52876||3.01755||3.299507||3.65101||2.17753|
|2-Party Average Compared to 538||0.95633||0.68727||0.64923|
|2-Party Compared to RCP||1.05859|
On May 3rd, 2017, I was released from the hospital following an overnight stay for the treatment of a pulmonary embolism. I am now almost fully recovered. I think this experience is a great opportunity to teach statistics through a real-life example. I learned three things from this experience.
Vastly different fields can have the same underlying statistical processes
So far I have worked almost exclusively with political science data. My research is about how to estimate a proportion from a sample and how to compare it to other proportions. When my doctor told me I might have a pulmonary embolism, I wanted to see the data for myself. So I read the journal articles, FDA case reports, and any data I could find to try to get an estimate for the chance I had a pulmonary embolism. What I quickly realized is that the data about adverse drug reactions had similarities with the political science data I was familiar working with. The data had issues with nonresponse bias and limitations due to unideal sample sizes. Although political science and pharmacology are very different fields the share similar kinds of statistical problems.
Bayesian statistics is a powerful tool in many fields
Through this process, I saw how Bayesian statistics could help solve a difficult and important problem. My doctor came by and saw me during my brief hospital stay. She talked about how while she knew that it was unlikely any random woman in her twenties would have a pulmonary embolism, but the details of my case suggested that the probability I had a pulmonary embolism was significant. In short, the Bayesian mindset is about incorporating your prior beliefs and adapting them in the presence of additional information. I don’t think my doctor used Bayes Theorem (the formal formula for estimating a probability given prior information), but she used Bayesian reasoning. She had initial beliefs about the cause of my symptoms, and she updated her beliefs when she got new information (like lab results). This is probably normal reasoning for a doctor trying to diagnose a patient, but it showed me how Bayesian statistics could be applied to other fields. A more formal use of Bayesian statistics would provide even better information to estimate probabilities. I always knew Bayesian statistics could be useful in other cases besides politics, but this experience showed me a new area I am interested in researching.
I am interested in other fields to apply statistics to besides politics
I wish I could have discovered my interest in biostatistics without a life-threating medical event, but I am glad. I was exposed to a problem that is important and would use some of the same techniques I was exposed to during my work on political science. While I still love political science statistics, I feel like I have now answered the question on what I can research in years where is no major election. I enjoyed reading clinical trials and studies and analyzing their statistics. Maybe someday I can even study how to improve statistical methods to prevent and diagnosis pulmonary embolisms like mine.
Six months after returning home from the hospital, I am grateful that God has found a way to use my PE for good.
I am entering my third and final year of my undergraduate degree. I have been doing research since almost day 1, and I wanted to share what my experience was like. As a statistician, I feel like I have to mention this is from a sample size of 1 and may not reflect all undergraduate research experiences.
First, I want to give a little background. The summer before my senior year of high school, I was chosen to participate in an NSF (National Science Foundation) funded REU (Research Experience for Undergraduates) at Texas Tech. There I was exposed to what research was like. We had a series of workshops each led by different researchers over a two week period. I loved the Texas Tech math department and decided to attend Texas Tech for my undergraduate degree. I meet my current research advisor Dr. Ellingson at the REU.
Right after classes started during my freshman year, I decided to email Dr. Ellingson and see if could do research with him. I started work on image analysis (Dr. Ellingson’s specialty). I was also following the GOP nomination because it was interesting to me. I had an idea to predict the nomination using Bayesian statistics, similar to how Five Thirty Eight predicts elections. I had talked with Dr. Ellingson about political science statistics before and how there was a need for a statistically sound open source academic model. He agreed to help guide me through the process of building a model to predict the GOP nomination process.
At the time of the GOP nomination my math background was pretty limited, so I decided to just use Baye’s theorem and used the normal distribution to estimate likelihood. I did all the calculations in excel and I downloaded csv files from Huffington Post Pollster with the poll data. I used previous voting results from similar states as the prior in my model. More info about my model can be found here. What I found the most challenging was making a lot decisions about how I was going to predict the election. I also struggled with making the decisions about the delegate assignments which often involved breaking the results down by congressional districts, even when the poll data was state wide. After the first Super Tuesday (March 1st) I began to realize that how difficult it is to find a good prior state and reassign support of candidates who dropped out of the race. The nomination process taught me that failure is inevitable in research, especially in statistics, where everything is at least slightly uncertain.
In the summer of 2016, I started gearing up for the general election. I decided to use Scipy (a python package for science and stats) to make my predictions. Making the programs was incredibly difficult. I had over a dozen variations to match different combinations of poll data. I had the programs up and running by early October, but I discovered a couple of bugs that invalidated my early test predictions. The original plan was to run the model on the swing states two or three times before the real election. In the middle of October I discovered a bug in one of my programs. I had to then fix the bug in every program. I then finally did some manual calculations to confirm the programs worked. It was difficult to have to admit that my early predictions were totally off, but I am glad I found it before the election. Research isn’t like a homework assignment with answers in a solution manual. You don’t know what is exactly going to happen and it is easy to make mistakes.
I ended up writing a paper on my 2016 general election model. Writing an paper on your research is very different than writing a paper on other peoples research. My paper was 14 pages (and over 6500 words) long, and only about one or two pages were about what other people’s research on the topic. It took a very long time to write, and I had 17 drafts. I hated writing the paper at first, but when I finished it felt amazing. It was definitely worth the effort.
Undergraduate research is difficult, but I loved the entire process. I got to work with real data to solve a real problem. I learned how to read a research paper, and eventually I got to write my own. I got to give presentations to both general audiences and mathematicians and statisticians. I got to use my research to inform others about statistics. If you are thinking about doing undergraduate research, you definitely should.
Last semester I took a research ethics class. I wrote a paper on preregistration and data sharing in academic research. I decided to modify the paper into two blog posts. Here is the first part on data sharing.
Statistics is the study of uncertainty. Any research study not involving the entire population of group will not be able to provide a definite conclusion with 100% certainty. Conclusions can be made with a high degree of certainty (95-99%) but false positives and false negatives are inevitable in any large statistical analysis. This means that studies can fail to make the right call, and after multiple replications the original conclusion may be overturned.
One way to improve the statistical integrity of research is to have a database of the data from non-published studies. Ideally, this database would be accessible to all academic researchers. A research would then be able to see the data from other similar studies. The research would then be able to compare his data with the data from the other studies. At a significance level of .05, approximately 1 in 20 studies that were statistically significant were a false positive. This number applies to theoretically perfect studies that meet all the statistically assumptions used. Any modelling error increases that rate. With each external replication of a study the probability of a false positive or a false negative greatly decreases. Grants from the National Science Foundation1, and the National Institute of Health2 currently require that data from the funded studies be made available to the public after the study was completed. But not all grants and funding sources require this disclosure. Without an universal requirement for data disclosure, it can be difficult to confirm that the study and the results are legitimate.
Advocates of open data say that data sharing saves time and reduces false positives and false negatives. A research can look at previously conducted studies and try to replicate the results. The results of the data can then be recalculated by another research to confirm accuracy. In a large study with lots of data it is very easy to make a few mistakes. These mistakes could cause the results to be misinterpreted. Open data can even help discover fraudulent studies. There are methods to estimate the probability the data is fraudulent by looking at the relative frequency of the digits. The distributions of the digits should be pretty uniform and in one case the data didn’t look quite right. In 2009, Strategic Vision (a polling company) came under fire from potentially falsifying polls, after a Five Thirty Eight analysis3 discovered that something didn’t look quite right. This isn’t an academic example, but open access data could prevent fraudulent studies from being accepted as fact as in the infamous vaccines cause autism study. The statistical analysis of the randomness isn’t definite, but they can raise questions that prompt further investigations of the data. Open data makes replication easier. False positives and false negatives can cause harm in some cases. Easier replication can help confirm findings quicker.
 Public Access To the Results of NSF-Funded Research. (n.d.). Retrieved April 28, 2017, from https://www.nsf.gov/news/special_reports/public_access/
 NIH’s Commitment to Public Accountability. (n.d.). Retrieved April 28, 2017, from https://grants.nih.gov/grants/public_accountability/
 Silver, N. (2014, May 07). Strategic Vision Polls Exhibit Unusual Patterns, Possibly Indicating Fraud. Retrieved April 28, 2017, from https://fivethirtyeight.com/features/strategic-vision-polls-exhibit-unusual/
Update 09/23/17: I am switching to two proportion Z tests. I am setting the population proportion to .5 to prevent an underestimation of variance.
This is a bit of a technical post, I will have a better explanation later.
Post election, I have been working on a paper and thinking about what to do next. I am really interested in breaking down voter behavior in the swing states. I have collected exit poll data from the 11 swing states. I want to test if voter behavior across the swing states was consistent with the national vote or the swing state average.
For phase 1 of this experiment, I will run Chi-Square Test of Homogeneity between a swing state compared to the average of the other swing state and the national vote. I will look at each category four different ways: Trump vs. not Trump, Clinton vs. not Clinton, Other vs Clinton and Turmp, and overall. This will probably be around 1500 tests. I will have an initial alpha level of 0.05. I will then run a two proportion z-tests on the tests were the p value was less than 0.05. I will do the z-tests on the direction that matches the data.
For phase 2, I will collect data from 2008 and 2012 in states that have a statistically significant portion of significant tests. Then I will compare voting behavior with Chi-Square Test of Homogeneity on: 2008 vs 2012, 2008 vs 2016, and 2012 vs 2016. Then significant results will be tested using a two proportion z-test.
I am going with the Chi-Square test first for two reasons. The Chi-Square test is not subject to errors in the direction of an effect, and the Chi-Square test is less sensitive than a two proportion z-test. I have to be very careful in my interpretation of the results since an analysis this large means that there is a big potential for false positives and false negatives. This analysis will probably take me most of next year. I’ll give an update on my progress in December.
I thought I would provide my perspective on the special election that occurred last week in Kansas, and the upcoming special house election in Georgia.
For full disclosure, I am a republican who is against some of the President’s policies on immigration, and health care.
I do not think Trump’s performance will have a major affect the voting behavior of people with strong party ties. Republicans vote Republican most of the time, and Democrats vote Democrat most of the time. Independents and moderates are more of a wild card. Independents may not vote the same as they did in 2016.
The districts in question are in no way representative of the whole country. They Any result from these elections cannot be applied to the whole country or “predict” the entire midterm election outcome. You could maybe use the results to for certain districts, but certainly not the entire country. For statistical analysis to work properly, the samples need to be reasonably representative.
Special elections are all about who turns out. In the Kansas election, Democrats spent a lot of money and attention on the race since there are only a few races this year. The money and a lack of an incumbent is probably why the race was closer than the 2016 race. The 2017 Kansas race had about half the votes compared to the 2016 race, this big of a change can affect the outcome. In Georgia, I expect a race that is closer than usual for that district, but still with a Republican win. I doubt that a Democrat will win a majority of the votes in the primary.
These special elections need to be interpreted in context. They are two races in House districts that haven’t been competitive in years. We should not even try to extrapolate to the entire country from these races. Favorability polls are a much better indicator of political sentiment However, I think that the favorability polls like the general election polls could be underestimating Trump’s support. It has been difficult to get Republicans to respond to the polls, and this may affect the accuracy of polls. After the midterms in 2018, there will be a clearer picture of support for the Republican party. Until then we can only guess.
Statsland is a magical world that exists only in (certain) Statistics textbooks. In Statsland, statistics is easy. We can invoke Central Limit theorem and use the normal distribution when n is larger than 30. In Statsland we either know or can easily determine the correct distribution. In Statsland 95% confidence intervals have a 95% chance of containing the real value. But we don’t live in Statsland.
The point of doing statistics is that it would be too difficult (or impossible) to find the true value of a population. You aren’t likely to find the exact value, but you can be pretty close. In a statistics textbook problem, you probably have enough information to do a good job of estimating the desired value. But in applied statistics you may not have as much information. If you know the mean and standard deviation of a population you do not need to do much (if any) statistics. Any time you have to estimate or substitute information, your model will not perform as well as a theoretically perfect model.
Statistics never was and never will be an exact science. In most cases, your model will be wrong. There are no perfect answers. Your confidence intervals will rarely perform as they theoretically should. The requisite sample size to invoke Central Limit Theorem is not clear cut. Your approach should vary on the individual problem. There is no universal formula to examine data. Applied Statistics should be flexible and instead of rigid. The world is not a statistics textbook problem, and should never be treated as such.
Recently I have been writing up a draft of a research article on my general election model to submit for academic publication. But that paper is technical and requires you to have some exposure to statistical research to understand. I wanted to explain my research without going into all the technical details.
The President of the United States is elected every four years. The Electoral College decides the winner, by the votes of electors chosen by their home state. Usually the electors are chosen based on the winner of that state and they vote for the winner of that state. Nate Silver correctly predicted the winner of the 2008 election with Bayesian statistics. Silver got 49 out of 50 states correct. Silver certainly wasn’t the first person to predict the election, but he received a lot of attention for his model. Silver’s runs Five Thirty Eight which talks about statistics and current events. Bayesian statistics is a branch of statistics that uses information you already know (called a prior) and adjusts the model as more information comes in. My model like Nate Silver’s used Bayesian statistics. We do not know the details of the Silver model, besides that it used Bayesian statistics. To the best of my knowledge, my method is the first publicly available model that used poll data from other states as the prior. A prediction was made for 2016, where I correctly predicted 6 states. Then the model was applied to 2008 and 2012, where my prediction of state winners matched the prediction of Five Thirty Eight.
I took poll data from Pollster, which provided me csv files for the 2016 and 2012 election. For 2008 I had to create the csvs by hand. I had a series of computer programs in Python (a common programming language) to analyze. My model, used the normal distribution. My approach divided the 50 states into 5 regional categories: swing states, southern red states, midwestern red states, northern blue states, and western blue states. The poll data source used as the prior were National, Texas, Nebraska, New York, and California respectively. This approach is currently believed to be unique, but since multiple models are proprietary it is unknown if this has been used before. I only used polls if they were added to pollster before the Saturday before election date. For the 2016 election analysis this meant November 5th. I posted my predictions on November 5th.
I outline more of my method here.
Results and Discussion
My model worked pretty well compared to other models. Below is a table of other models and their success rate at predicting the winning candidate in all 50 states plus (and Washington D.C.).
|Race||Real Clear Politics||Princeton Election Consortium||Five Thirty Eight (Polls Plus)||PredictWise (Fundamental)||Sabato’s Crystal Ball||My Model|
|2008 Winner Accuracy||0.96078||0.98039||0.98039||N/A||1||0.98039|
|2012 Winner Accuracy||0.98039||0.98039||1||0.98039||0.96078||1|
|2016 Winner Accuracy||0.92157||0.90196||0.90196||0.90196||0.90196||0.88235|
As you can see all the models do a similar job at picking the winner in each state, which predicts the electoral college. There are other ways to compare accuracy, but I don’t want to discuss this here since it gets a little technical. No one was right for every state in every election. It would probably be impossible to create a model that would consistently predict the winner in all states, because of the variability of political opinions. Election prediction is not an exact science. But there is the potential to apply polling analysis to estimate public opinion on certain issues and politicians. Right now the errors in polls are too large determine public opinion on close issues. But further research could determine ways to reduce error in polling analysis.
My research relies heavily on polls. So I understand why it is important to do polls. If I see a poll and determine it’s well written, I do it. But I think this position is rare because people don’t know the importance of polls. I want to explain why I think polls are important. Pre-election polls are commonly used to predict elections, and favorability polls are often used to judge a politician’s popularity. Polls are an important part of American politics.
I get that polls are annoying. I know it takes time and you are probably busy (like me). But doing 1 political poll a year can greatly help improve the accuracy of polls. You don’t have to always answer a poll, but increased participation in polls improves accuracy. Now there are a lot of bad polls, and it’s difficult to tell if a phone poll is good based of the phone number. Some people have “polls” that really are marketing calls. I understand if you are hesitant to do phone polls. But internet polling provides a good alternative. I think the future of polling is quality internet polls. When you do an good internet poll you know more about the quality of the poll then a poll phone call. But Internet polls from scientific polling agencies require a large base of people to create accurate samples. You can randomly call 1000 phones, but you really can’t send 1000 random internet users a poll. To combat this problem polling agencies have databases of users to send polls. Polling agencies send surveys to certain users to create a good sample. Joining a survey panel with political polls is a way to get your voice heard.
My view on participating in political polls is you can’t complain if you don’t participate. Polls need a diverse sample to be accurate. If you feel your political stance is not heard in the polls, then you should do more polls instead of less. We need all kinds of people to do good polls. Not everyone may have internet access, but enough voters do to create a good sample. What you can do is join a poll panel. My two recommendations are https://today.yougov.com/ or https://www.i-say.com/. They also do non-political polls and market research which are also important (I might do a post later on this). I recommend them because they are user friendly and statistically sound. I am not receiving anything for recommending these agencies, I just think they are good.
If you want polls to be more accurate, the best (and easiest) thing to do is participate in polls. As a statistician, I value good data. But for data to be good it needs a representative sample. Regardless of your politics, you should participate in political polls.
First, I want to be clear, that there is no universally fair way to elect a president. All methods have pros and cons, and you can have your own opinion about which way is the best.
Right now with the exception of Nebraska and Maine, the electoral college is decided by whoever has the most support in a state. The winner usually has a majority of votes, but sometimes no single candidate was a majority. This method also helps smaller states as they have a lower ratio of voters to electors than larger states.
This method makes it easy to determine the winner on election night. You don’t necessarily need all the votes to come in if you have enough information to predict the winner.
Most states have a clear winner party. So most of the attention goes to swing states who do not have a regular winner.
The popular vote method is based on the winner of the popular vote. Whoever gets the most votes wins. This method can be implemented if enough states change their laws to award their electors to the popular vote winner.
Every vote counts the same. Larger states would have more power than the current system.
Smaller states lose some electoral power compared to the current system.
Congressional District System
This system awards 2 electors to the state winner and 1 elector to the winner of every congressional district. This is the method Maine and Nebraska use.
Disclaimer: This is my personally prefered system.
It’s a compromise between the current system and the popular vote system. The electoral college would probably mimic the congressional makeup.
Like the current system, could elect a president that didn’t win the popular vote.
All of these systems have pros and cons. There isn’t necessarily a “best” way to pick the president.
Here is a Five Thirty Eight article about different methods of deciding the electoral college.