STAT 200 – Introductory Statistics
December 19, 2025
After today’s lecture, you should:
In 1936, Democratic President Franklin Delano Roosevelt was running for his second term against the Republican governor of Kansas, Alf Landon. The Literary Digest, one of the most respected and popular publications of the day, decided on an ambitious plan: one of the largest and most expensive polls ever conducted to predict the winner. They surveyed around 2.4 million people, which accounted for over 5% of the total turnout, chosen from subscriber lists, telephone directories and other available lists, and predicted that Landon would win in a landslide, 57% to Roosevelt’s 43%. Meanwhile, George Gallup ran a focused poll of only 50,000 voters.
Roosevelt went on to win 63% of the vote in what is one of the largest landslide elections in American history, a result George Gallup predicted. Roosevelt won the second highest percentage of votes in a contested election, behind only LBJ in 1968, and the second highest electoral vote total, behind only Reagan in 1984.
The Gallup Organization is now one of the most respected names in polling.
If those two polls came out about the a House race this year, how could you determine which to trust?
When thinking about a scientific study reported in the mainstream press, consider the following factors:
As you listen to sound bites on the radio or television spouting off statistics from studies, you should ask yourself pertinent questions:
Briefly stated, the Gell-Mann Amnesia effect is as follows. You open the newspaper to an article on some subject you know well. In Murray’s case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward—reversing cause and effect. I call these the “wet streets cause rain” stories. Paper’s full of them.
In any case, you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read. You turn the page, and forget what you know.
— Michael Crichton
Have you ever read a headline like “America’s 100 Best Companies to Work For” or “Top 10 Things to Make You Happy”? You should read the fine print of the study to find out by what criteria “best” is defined or whose standard of “happy” they are talking about.
Headlines like these can mean very different things to different people.
In addition to considering what the variable of the study is measuring, we also need to think about those variables not directly being measured – ones which may have an effect of the results. (Did anyone have to watch Super Size Me in school?)
A well-constructed study will make a point to identify and account for reasonable confounding variables.
Suppose I want to study the effectiveness of various methods of quitting smoking. The easier option would be to go to a smoking support group and tracking the progess of the people involved who have chosen their own methods. The more expensive and time-consuming method would be to get subjects and assign them different methods randomly myself.
What confounding variables might I introduce to my study opting for the first study over the second?
In the end, it is the conclusions of the study that we should be most aware of:
Why does this matter to you as a scientist/scholar?
There are two main types of study validity:
External validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can be generalized to and across other situations, people, stimuli, and times.
Internal validity is the validity of conclusions drawn within the context of a particular study.
Both are important.
Internal validity concerns whether the drawn conclusions are appropriate, given the data.
External validity concerns whether these findings can be extended to other conclusions.
Because general conclusions are almost always a goal in research, external validity is an important property of any study. Mathematical analysis of external validity concerns a determination of whether generalization across heterogeneous populations is feasible, and devising statistical and computational methods that produce valid generalizations.
In the context of a study’s structure, bias refers to the how of unrepresentative the sample is of the population. There are several sources of bias in a study, broadly divided into researcher-based or respondent-based.
Note that no study is perfect. No sample will perfectly represent the population. Bias is only important when it is sufficiently severe to cause the researcher to draw incorrect conclusions.
Typical sources (and names) of bias include:
Selection bias occurs when the selection of individuals for analysis (or groups or data) is done in such a way that proper randomization is not achieved.
Researcher bias occurs when a researcher influences the results of a study, whether purposely or not.
Response bias occurs when a researcher’s behavior (or existence) causes a participant to alter his or her response or when a participant gives an inaccurate response.
Consider the responses to these questions, all ostensibly asking the same thing, particularly from the perspective of someone undecided on the topic, or on the edge?
Beyond conscious biases, there are several that do not arise from planning errors. They arise from the actions of the participants. These include:
Participation bias occurs when there is a problem with the participation — or lack thereof — of those chosen for the study.
As an example, nonresponse bias occurs when there is a lack of participation in a self-selected sample from certain segments of a population, when a person refuses to participate in a survey, or when a respondent omits questions when answering a survey.
Beyond conscious biases, there are several that do not arise from planning errors. They arise from the actions of the participants. These include:
Voluntary response bias arises when you ask for participants to chose to participate in your study. Generally only those with strong opinions will chose to participate.
Another example concerns respondents who do not report the truth.
Dropouts are participants who begin a study but fail to complete it.
Nonadherents are participants who remain in the study until the end but stray from the protocol (directions given).
Finally, there are simple errors in the study. These tend to occur in the transcribing of the data into a form that the program can handle.
Processing errors are errors that occur simply from the data being processed, such as typos when data are being entered.
The National Institutes of Health (NIH) is the primary agency of the United States government responsible for biomedical and public health research. As such, they focus on proper experimental procedures. Their extensive website contains a lot of information about sampling: https://www.ncbi.nlm.nih.gov/books/NBK253184/table/background.t1
If you will be performing biomedical research, bookmarking this site might be a good idea.
Other research organs of the US government have their own websites aimed at ensuring good research is done, such as the National Institute of Standards and Technology (NIST). https://www.nist.gov/itl