Do Now · Lab Notebook · 10 minutes

Set up your notebook. You will need it at the end of class.

Terminology and Concepts to look out for

Copy these. Leave space under each one for a definition.

  • bivariate
  • evidence
  • limitation
Relevance to Me

Think about these. Nothing to write.

  • Has anyone ever proved you wrong with one fact?
  • When you are not sure about something, do you say so?
Question of the Day

Copy this into your Lab Notebook and leave room under it. You will answer it at the end of class.

What can you learn from two answers by the same person that you cannot learn from one?

What Two Answers From One Person Can Show
Day 3 · I Do passage

There is a kind of question that no amount of counting one item at a time will ever answer. It comes up constantly, and the reason it cannot be answered that way is worth understanding precisely, because the failure is not a shortage of data. The data is already there. It is the method that discards it.

Consider a survey with two items. The first asks whether a person exercises regularly and finds that sixty out of a hundred say yes. The second asks whether a person sleeps well and finds that forty out of a hundred say yes. Both results are solid. Both rest on the same hundred people. Now ask whether the people who exercise are the same people who sleep well.

Nothing in either result can answer that. The first count says sixty people said yes to one question. The second says forty people said yes to another. Neither count records which sixty or which forty. It is entirely possible that all forty good sleepers are among the sixty exercisers, and equally possible that none of them are. The two counts are identical under both scenarios, which is exactly why they cannot distinguish between them.

Counting one item at a time is univariate work, and this is its boundary. The moment a question involves a relationship between two things, univariate counting has already thrown away what the question needs. The information was collected. Each respondent answered both items on the same form. The counting stage is where the connection was lost, because counting an item means adding up its answers without regard to who gave them.

The alternative is to go back to the individual responses and count pairs instead of answers. Of the sixty people who said they exercise, how many also said they sleep well? That single number, produced by looking at what each person said to both items at once, is bivariate. The root means two variables, and the defining feature is that both answers come from the same respondent.

A bivariate result is not a stronger version of a univariate one. It is a different kind of fact, and it can contradict what the separate counts appear to suggest. Two items can each look reassuring alone and reveal a problem the moment they are paired. This is the most useful property bivariate work has, and it is why the pairing is worth the extra step.

Once such a number exists, it becomes evidence, meaning a specific finding brought forward to support a specific claim. Evidence is not the same thing as information. A fact sitting in a table is information. The same fact, named and pointed at a claim it supports, is evidence. What converts one into the other is the person doing the pointing, which means the connection between a finding and a claim is itself something a reader can dispute. A number can be entirely accurate and still be poor evidence for the claim it is attached to.

The last piece is the one most often skipped. Every claim built from survey evidence has a limitation, meaning something the evidence cannot tell you no matter how carefully it was collected. Limitations are not mistakes. A study that was executed perfectly still has them, because they come from what the survey asked rather than from how well it asked it.

Some limitations come from coverage. A survey given to one group cannot describe a different group, however many people answered. Some come from timing, since answers describe a moment and moments pass. Some come from the items themselves, because a survey can only report on what it thought to ask about, and whatever it never asked is invisible in the results no matter how important it turns out to be.

Stating a limitation is not an admission of weakness, and this is the part that runs against instinct. A claim that arrives with its limits named is more trustworthy than one that arrives without them, because the writer has shown they know where the edges are. A claim presented as though the evidence answers everything invites a reader to find the first thing it does not answer and discard the whole argument.

That is the full shape of an argument built on data. A claim, the specific evidence behind it, and an honest account of what that evidence cannot reach. Each part is checkable by someone who disagrees, which is the entire reason for assembling it this way. An argument that cannot be checked is not an argument. It is an assertion with numbers attached.

Work these together
10 questions on the passage. Pick an answer, then check it. Nothing here is collected.
Question 1 of 10the passage
The passage describes a survey where 60 out of 100 people say they exercise and 40 out of 100 say they sleep well. Why can those two results not tell you whether the exercisers are the same people as the good sleepers?
Question 2 of 10the passage
According to the passage, where does the connection between two answers get lost?
Question 3 of 10the passage
The passage says a fact sitting in a table is information, and the same fact pointed at a claim is evidence. What turns one into the other?
Question 4 of 10the passage
Why does the passage say a claim that names its limitations is more trustworthy than one that does not?
Question 5 of 10the passage
In the passage’s example, 60 of 100 people say they exercise and 40 of 100 say they sleep well. What does the passage say is possible?
Question 6 of 10the passage
According to the passage, what is the defining feature of a bivariate result?
Question 7 of 10the passage
How does the passage describe the relationship between a bivariate result and a univariate one?
Question 8 of 10the passage
According to the passage, where do the limitations on a claim come from?
Question 9 of 10the passage
Which of these does the passage name as a source of limitation?
Question 10 of 10the passage
The passage closes by describing the full shape of an argument built on data. What are its three parts?
From Our Class Survey
Your answers, collected August 11. 79 respondents. Selected items from the full topline.
A06 · Schoolwork FrequencyDocument A
How often do you use AI for schoolwork?
  • Never10
  • Once or twice44
  • About weekly12
  • Almost daily12
n = 79
A17 · Peer EstimateDocument B
Out of 10 students in this class, how many use AI without permission?
  • 04
  • 10
  • 22
  • 31
  • 41
  • 56
  • 61
  • 76
  • 89
  • 98
  • 1040
n = 79
A20 · How CommonDocument C
How common is AI use in this class?
  • Not at all common4
  • Not too common6
  • Somewhat common20
  • Very common48
n = 79
A21 · Compared to OthersDocument C
Compared to other students in this class, how much do you use AI?
  • Much less24
  • Somewhat less40
  • About the same12
  • Somewhat more or much more2
n = 79
New today: Of the 48 respondents who said AI use here is very common, 28 of them also said they personally use it somewhat less than others.
A01 · Chatbots and AssistantsDocument D
Which of these chatbots or assistants have you used?
  • ChatGPT70
  • Gemini36
  • Grok7
  • Copilot6
  • None of these4
  • Claude2
  • Perplexity1
  • DeepSeek1
79 respondents answered. You could pick more than one, so these do not add to 79.
All 29 survey items →
The work
Answer the checkable ones together. The discussion questions have no answer today.
Class discussionno answer today
Who is doing all the using?

Document C is back up, both displays. We left this open yesterday.

Why neither display can settle it

A20 counted one item. A21 counted one item.

Neither one tells you what a single person said to both questions. The information was collected — everyone answered both on the same form. Counting is where it got thrown away.

The reveal
Of the 48 respondents who said AI use here is very common, how many also said they personally use it somewhat less than others?
Naming it

That is bivariate. Two variables, and both answers come from the same respondent.

It is not a stronger univariate. It is a different kind of fact, and it can contradict what the separate counts appeared to suggest.

Notebook: bivariate
Class discussionno answer today
Where does A21 go?

It asks about you and about other people in the same sentence. There is no right answer to this one, and you are not getting one.

The rest of the block

Partner work first. Then quiet work time.

The three rules
  • No cellphones
  • No sleeping
  • No non-academic use of Chromebooks
What you get
  • A quiet room and music
  • No interruptions from the teacher
  • If you are caught up on this course's work, you may work on anything legitimate for another class
If you are picking, pick reading or writing.
Everything we build in this class, we build with words. The tools take writing as input. How well you write is the ceiling on what you can make them do.
Open this now: muggsofcompsci.net/decks/cs1-miniq-day3-wedo