Set up your notebook. You will need it at the end of class.
Copy these. Leave space under each one for a definition.
- bivariate
- evidence
- limitation
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?
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?
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.
C. The passage is blunt about it. All forty good sleepers could be among the sixty exercisers, or none of them could be, and the two counts look exactly the same either way. That is why they cannot tell the two situations apart.
B. This is the part worth being precise about. The information was collected. Every respondent answered both items on the same form. Counting is where it got thrown away, which means it can be recovered by going back and counting pairs instead.
C. And because a person made that connection, a reader can dispute it. The passage says a number can be entirely accurate and still be poor evidence for the claim it is attached to.
B. The passage adds the flip side, which is the part students will feel. A claim presented as though the evidence answers everything invites a reader to find the first thing it does not answer and throw out the whole argument.
A. And the reason it matters is the sentence right after it. The two counts are identical under both scenarios, which is exactly why they cannot tell the two situations apart.
B. That is the whole move. Instead of adding up an item’s answers without regard to who gave them, you go back to the individual responses and count pairs.
C. The passage calls that the most useful property bivariate work has. Two items can each look reassuring alone and reveal a problem the moment they are paired.
B. This is why the passage says a study executed perfectly still has them. Limitations are not errors, and treating them as errors is exactly what makes writers want to hide them.
A. And the passage puts the sting in the second half of that sentence: whatever it never asked is invisible in the results, no matter how important it turns out to be.
B. Each part is checkable by someone who disagrees, which the passage says is the entire reason for assembling an argument that way. An argument that cannot be checked is an assertion with numbers attached.
- Never10
- Once or twice44
- About weekly12
- Almost daily12
- Skipped1
- 04
- 10
- 22
- 31
- 41
- 56
- 61
- 76
- 89
- 98
- 1040
- Skipped1
- Not at all common4
- Not too common6
- Somewhat common20
- Very common48
- Skipped1
- Much less24
- Somewhat less40
- About the same12
- Somewhat more or much more2
- Skipped1
- ChatGPT70
- Gemini36
- Grok7
- Copilot6
- None of these4
- Claude2
- Perplexity1
- DeepSeek1
Document C is back up, both displays. We left this open yesterday.
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.
28 people in this room said both of those things.
That number is not on either display. You cannot get to it by reading A20 or A21, however carefully — it only exists once you go back and count pairs.
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.
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.
Partner work first. Then quiet work time.
- No cellphones
- No sleeping
- No non-academic use of Chromebooks
- 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