Introduction and measurement

# Introduction and measurement

**Topic 1 · Tuesday, January 5**

]

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# Plan for today

.box-1.medium.sp-after-half[Welcome!]

.box-6.medium.sp-after-half[What statistics is for]

.box-3.medium.sp-after-half[Measurement]

???

Three blocks of about 20 minutes. Each ends with students doing something: play, predict, try.

---

# Welcome!

---

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# Please call me Andy

[Student hours on Calendly](https://calendly.com/de-barros/student-hours-andy-de-barros)

[adb@uci.edu](mailto:adb@uci.edu)
]
]

Drop-in student hours

[prithas@uci.edu](mailto:prithas@uci.edu)
]
]

---

# Shout out to all those here who find this place a bit strange

.map-left[
.picture[![World map with the United States, Guatemala, Chile, France, Germany and India shaded](img/andy-map.png)]
]

.map-right[
<table class="deck-table tight">
 <thead>
  <tr>
   <th style="text-align:left;"> Where </th>
   <th style="text-align:left;"> What </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Germany </td>
   <td style="text-align:left;"> BA and MA in Political Science, and teacher training, at Konstanz University </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Guatemala </td>
   <td style="text-align:left;"> An education NGO in Ciudad de Guatemala </td>
  </tr>
  <tr>
   <td style="text-align:left;"> France </td>
   <td style="text-align:left;"> International education policy at UNESCO </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Chile, India and the US </td>
   <td style="text-align:left;"> Education research at J-PAL and at MIT </td>
  </tr>
  <tr>
   <td style="text-align:left;"> US </td>
   <td style="text-align:left;"> PhD in Education at Harvard University </td>
  </tr>
</tbody>
</table>
]

???

The personal note. Say this your own way: nobody here should feel they have to already belong.

---

# My work promotes large-scale research-practice partnerships, particularly in Sub-Saharan Africa and South Asia

.box-inv-1.tiny-box[Educational technology]

<table class="deck-table tight work">
 <thead>
  <tr>
   <th style="text-align:left;"> Size </th>
   <th style="text-align:left;"> Partners </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 240 government schools </td>
   <td style="text-align:left;"> State Government of Haryana, Avanti Fellows, USAID DIV </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 250 early-childhood centers </td>
   <td style="text-align:left;"> State Government of Uttarakhand, Dost Education, The Agency Fund </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 30 government schools </td>
   <td style="text-align:left;"> State Government of Rajasthan, Educational Initiatives, Douglas B. Marshall Foundation </td>
  </tr>
</tbody>
</table>

.box-inv-1.tiny-box[Assisting teachers in adjusting and improving their instruction]

<table class="deck-table tight work">
 <thead>
  <tr>
   <th style="text-align:left;"> Size </th>
   <th style="text-align:left;"> Partners </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 292 government schools </td>
   <td style="text-align:left;"> State Government of Karnataka, Akshara Foundation, Omidyar </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 209 government schools </td>
   <td style="text-align:left;"> Cambodia Ministry of Education, Youth and Sport, The World Bank </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 273 government schools </td>
   <td style="text-align:left;"> Zambia Ministry of Education, TaRL Africa, VVOB, KIX </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 500+ government schools </td>
   <td style="text-align:left;"> Morocco Ministry of National Education, Pratham, J-PAL, Harvard </td>
  </tr>
</tbody>
</table>

---

# What you'll take from this course

.box-1.medium.sp-after-half[Read and explain statistics in education research]

.box-inv-1.medium.sp-after-half[Describe and define the key ideas]

.box-inv-1.medium.sp-after-half[Do the calculations]

.box-1.small[We build intuition first: you'll run simulations, and always ask what's the truth and what's only our estimate]

???

Every week comes back to the same question: is this number a fact about the population, or our estimate of it?

---

# Your week has a routine

<table class="deck-table">
 <thead>
  <tr>
   <th style="text-align:left;"> When </th>
   <th style="text-align:left;"> What </th>
   <th style="text-align:left;"> Where </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Before class </td>
   <td style="text-align:left;"> Do the reading </td>
   <td style="text-align:left;"> The book, through MindTap </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Tue and Thu, 12:30–1:50 PM </td>
   <td style="text-align:left;"> Lecture: 20 minutes of talk, then you do something, three times </td>
   <td style="text-align:left;"> EDUC 2009 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Fri, 12:00–12:50 PM </td>
   <td style="text-align:left;"> Lab A1 </td>
   <td style="text-align:left;"> EDUC 2009 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Fri, 1:00–1:50 PM </td>
   <td style="text-align:left;"> Lab A2 </td>
   <td style="text-align:left;"> EDUC 2001 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Sun, 6 PM </td>
   <td style="text-align:left;"> MindTap homework is due </td>
   <td style="text-align:left;"> Canvas </td>
  </tr>
</tbody>
</table>

.box-1.small[Go to all classes. Go to your own lab. Lecture activities aren't scored]

???

Andy: confirm rooms and times on WebSOC.

---

# Fridays: regular labs and quiz days

The same idea on real data, in a spreadsheet or the simulator

One written sentence on what it means
]
]

Labs 6 and 10 also review for the exams

We'll explain the format in class
]
]

.box-inv-1.small[Labs 2 and 8 start with a 15-minute individual check. Use Google Sheets or Excel]

???

Three quizzes plus the checks in Labs 2 and 8 make the five Friday events. Go to your own lab. No R for students.

---

# It adds up to 350 points

<table class="deck-table tight">
 <thead>
  <tr>
   <th style="text-align:left;"> What </th>
   <th style="text-align:center;"> Points </th>
   <th style="text-align:left;"> How it counts </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Quizzes </td>
   <td style="text-align:center;"> 40 </td>
   <td style="text-align:left;"> Best 4 of 5 Friday events, 10 points each </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Labs </td>
   <td style="text-align:center;"> 21 </td>
   <td style="text-align:left;"> Best 7 of 10 labs, 3 points each </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mastery Training </td>
   <td style="text-align:center;"> 40 </td>
   <td style="text-align:left;"> Best 8 of 9, 5 points each </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Problem Sets </td>
   <td style="text-align:center;"> 40 </td>
   <td style="text-align:left;"> Best 8 of 9, 5 points each </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Midterm </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:left;"> In person </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Final </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:left;"> In person, cumulative </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Course evaluation </td>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:left;"> For completing it </td>
  </tr>
</tbody>
</table>

.box-1.small[You earn 261 of the 350 points in person. Lecture attendance isn't graded]

???

A lab's 3 points are for being there and handing in a real attempt at the sentence, not for being correct. Quiz days earn them for being there.

---

# Two exams, both in person

80 minutes, Chapters 1 to 9
]
]

Cumulative
]
]

.box-inv-1.small.sp-after-half[Each is 100 points of free response, built on the Mindspark data]

.box-inv-1.small.sp-after-half[Open book: bring any print materials, and your own notes]

.box-inv-1.small.sp-after-half[A calculator is the only device. We attach tables and a formula sheet]

.box-inv-1.small[You can ask for a translated exam, in any language]

???

Exams use an outcome students haven't seen in class. Andy: add the final's date once WebSOC has it, and the date to ask for a translation by.

---

# Homework is due Sundays at 6 PM

.small.center[
Unlimited attempts
]
]

.small.center[
3 attempts, full credit at 75%
]
]

.box-inv-1.small.sp-after-half[Chapters 5 to 12 and 14. The first set is due Sunday, January 17]

.box-inv-1.small.sp-after-half[An automatic one-day extension, to Monday at 6 PM]

.box-inv-1.small.sp-after-half[Your lowest score of each type drops]

.box-1.small[Get access to Cengage MindTap now, through Canvas]

???

There are 9 of each type. No other extensions, and no need to email. Chapters 1 to 4 are open as ungraded practice. MindTap is practice: the Friday lab's by-hand problem is what looks like the exams.

---

# Use AI to learn, not to get answers

Make practice problems

Help with a spreadsheet formula
]
]

.box-inv-1.small[Homework is your practice for exams and quizzes, where you'll have no AI and no devices]
]

.box-inv-1.small.sp-after-half[AI also makes mistakes in statistics, so check what it tells you]

.center.small[UCI's academic integrity rules still apply]

???

The full wording is in the syllabus. There's no take-home writing in this course, so this replaces the old Composition Program wording.

---

# Where to find things

.small.center[
[educ15.de-barros.com](https://educ15.de-barros.com)

Syllabus, schedule, slides, lab handouts
]
]

.small.center[
MindTap and the ebook

Grades, solutions, and slide files
]
]

.box-inv-1.medium[Not sure about a rule? It's in the syllabus]

---

# It's in the syllabus

.picture[![Four comic panels. Students ask a busy instructor: What did we cover in class last week? What's your late homework policy? When are your office hours? How will my grade be computed? Each time the instructor answers, It's in the syllabus, and in the last panel just holds up a sign that says so. Below: It's in the syllabus. This message brought to you by every instructor that ever lived.](img/phd-syllabus.jpg)]

.source["Piled Higher and Deeper" by Jorge Cham, [www.phdcomics.com](https://phdcomics.com/comics.php?f=1583)]

---

# Most importantly

.box-1.medium.sp-after-half[Ask for help, and tell us how you're doing]

.box-inv-1.medium.sp-after-half[Check yourself before you wreck yourself]

.center.small[(Sorry, Ice Cube)]

.box-inv-1.small[Not sure about your math? Try the Math Skills Assessment in Appendix A]

---

# Play it: Course rules

.box-inv-8.small.sp-after-half[In Jeopardy, the clue is an answer. Talk to a neighbor, then call out the question]

.options.clues[
.option[
**100** · Sunday at 6 PM
]
.option[
**200** · 7 of 10
]
.option[
**300** · A calculator, and no other device
]
.option[
**400** · Explain an idea, but not a MindTap answer
]
]

???

About 6 minutes. Nothing is scored.

---

# Play it: The questions

.options.clues[
.option[
**100** · When is homework due?
]
.option[
**200** · How many labs count?
]
.option[
**300** · What device can you use on an exam?
]
.option[
**400** · What can AI do for you?
]
]

.box-8.small[That's the rhythm of every lecture: some talk, then your turn]

---

# What statistics is for

---

# Where are we?

.box-inv-1.small[Summarize data]

.box-inv-1.small[Visualize data]

.box-inv-6.small[Forecast the future]

.box-inv-6.small[Focus is on Y]
]

.box-inv-3.small[Effect of X on Y]

.box-inv-3.small[Focus is on X]
]

???

This map opens every topic. Statistics does three jobs, and we'll work through them in this order.

---

---

# One topic, three kinds of question

<table class="deck-table">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> Description </th>
   <th style="text-align:left;"> Prediction </th>
   <th style="text-align:left;"> Explanation </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Netflix </td>
   <td style="text-align:left;"> Which movie was watched most? </td>
   <td style="text-align:left;"> What's your next show? </td>
   <td style="text-align:left;"> What's the effect of the time of day on what you pick? </td>
  </tr>
  <tr>
   <td style="text-align:left;"> SNAP </td>
   <td style="text-align:left;"> What % of students are eligible? </td>
   <td style="text-align:left;"> Who will enroll? </td>
   <td style="text-align:left;"> What's the effect of SNAP on poverty? </td>
  </tr>
</tbody>
</table>

.box-6.small[Before you pick a method, ask which of the three you're trying to do]

???

Ask students for a third row from their own lives.

---

# Prediction focuses on Y. Explanation focuses on one X

???

Left: Netflix doesn't care which X matters, as long as the guess is good. Right: poverty has many causes, and the program explains only a sliver of it. The whole job is getting that sliver right.

---

# Meet Mindspark, our running example

.box-6.small.sp-after-half[Adaptive learning software in after-school centers in Delhi, India]

.center.small[students]
]

.center.small[centers]
]

.center.small[in grades 6 to 9]
]

.box-6.small[You'll work with the real data in labs and on both exams]

???

76% of the students are girls. Their math and Hindi were tested before the program ("baseline") and after it ("endline").

---

# A lottery decided who got it

.center.small[314 students got the program]

.box-inv-6.medium[18.68]

.center.small[average math score at endline]
]

.center.small[305 students were promised it later]

.box-inv-6.medium[15.99]

.center.small[average math score at endline]
]

.box-6.small[Is a gap of 2.69 points real, or just luck? By March, you'll be able to say]

???

Here's the hook for the quarter. This is explanation: X is the program and Y is the math score, and the lottery is why we can read it as an effect.

---

# From population to sample, and back

???

In Mindspark, the sample is the 619 students. Ask who the population might be. Delhi? Students like these? That's a real question, and the data can't settle it.

---

# We use data to estimate the truth

$$
X \;\rightarrow\; M = \frac{\sum X}{n} \;\rightarrow\; \hat{\mu} \;\overset{\text{hopefully}}{\longrightarrow}\; \mu
$$

<table class="deck-table">
 <thead>
  <tr>
   <th style="text-align:center;"> Data </th>
   <th style="text-align:center;"> Calculation </th>
   <th style="text-align:center;"> Estimate </th>
   <th style="text-align:center;"> Truth </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> The scores we saw </td>
   <td style="text-align:center;"> The mean of those scores </td>
   <td style="text-align:center;"> Our best guess about the population </td>
   <td style="text-align:center;"> The population's real mean </td>
  </tr>
</tbody>
</table>

.box-6.small[A *parameter* describes a population. A *statistic* describes a sample]

.center.small[Greek means population. A Latin letter or a hat means an estimate]

???

This chain is the course. Students should soon be able to label any number as a parameter or an estimate.

---

# Predict it: Two samples from one population

.box-inv-8.small.sp-after-half[Treat our 619 students as a population, with a mean math score of μ = 11.12]

.box-8.small.sp-after-half[Two people each draw a random sample of 25 students and find M. What happens?]

.options[
.option[
**A** Both get exactly 11.12
]
.option[
**B** They match, but miss 11.12
]
.option[
**C** They differ, and both land near 11.12
]
.option[
**D** They differ, and both land far from 11.12
]
]

???

About 6 minutes. Hands are fine. Ask two or three students why before showing the next slide.

---

# Predict it: Samples rarely agree

.box-inv-8.small.sp-after-half[The first two samples, in red, got M = 10.24 and M = 11.28. The answer is C]

.box-8.small[*Sampling error* is the chance gap between an estimate and the truth]

???

Sampling error isn't a mistake. Nobody did anything wrong. It's the reason we need the rest of this course. Topic 6 comes back to this with the simulator.

---

# Measurement

---

---

# Statisticians measure variables

.box-3.small.sp-after-half[A *variable* is a characteristic that differs from one person to the next]

<table class="deck-table tight">
 <thead>
  <tr>
   <th style="text-align:left;"> Center </th>
   <th style="text-align:center;"> Grade </th>
   <th style="text-align:center;"> Group </th>
   <th style="text-align:center;"> Math score </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Chhatarpur </td>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> Control </td>
   <td style="text-align:center;"> 12 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Govindpuri </td>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> Treatment </td>
   <td style="text-align:center;"> 14 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Tekhand </td>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> Control </td>
   <td style="text-align:center;"> 3 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Chhatarpur </td>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> Treatment </td>
   <td style="text-align:center;"> 15 </td>
  </tr>
</tbody>
</table>

.box-inv-3.small[Each row is a student. Each column is a variable]

---

# Many variables stand in for constructs

.box-3.small.sp-after-half[A *construct* is an internal attribute that we can't observe directly]

.center.small[Math ability, motivation, self-esteem]
]

.center.small[A test score, a survey answer]
]

.box-3.small[We can't see math ability. We can see how many questions a student gets right]

---

# Say what you mean, then measure it

.center.small[**What do you mean?**]

.box-inv-3.small[Math ability: which math, at what level?]
]

.center.small[**How do you measure it?**]

.box-inv-3.small[A test, scored by the number of correct answers]
]

???

Mindspark's total math score is one operationalization. A different test would give a different variable for the same construct.

---

# Two related variables get special names

.box-inv-3.small[Outcome variable]

.box-inv-3.small[Response variable]

.box-inv-3.small[Dependent variable]

.center.small[What you want to explain or predict]
]

.box-inv-3.small[Explanatory variable]

.box-inv-3.small[Predictor variable]

.box-inv-3.small[Independent variable]

.center.small[What you use to explain or predict Y]
]

---

# Find the Y and the X

.work-grid[
.option[
A study examines the effect of smoking on lung cancer
]
.option[
You want to see if taking more AP classes in high school improves college grades
]
.option[
Researchers predict genocides by looking at negative media coverage, revolutions in neighboring countries, and economic growth
]
.option[
Netflix uses your past viewing history, the day of the week, and the time of day to guess which show you want to watch next
]
]

???

One or two minutes, then show the next slide. This is a quick check inside the talk, not one of the three activities.

---

# One X to explain, many X to predict

<table class="deck-table">
 <thead>
  <tr>
   <th style="text-align:left;"> Study </th>
   <th style="text-align:left;"> Y </th>
   <th style="text-align:left;"> X </th>
   <th style="text-align:left;"> Purpose </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Smoking </td>
   <td style="text-align:left;"> Lung cancer </td>
   <td style="text-align:left;"> Smoking </td>
   <td style="text-align:left;"> Explanation </td>
  </tr>
  <tr>
   <td style="text-align:left;"> AP classes </td>
   <td style="text-align:left;"> College grades </td>
   <td style="text-align:left;"> AP classes taken </td>
   <td style="text-align:left;"> Explanation </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Genocides </td>
   <td style="text-align:left;"> Genocide </td>
   <td style="text-align:left;"> Media coverage, nearby revolutions, economic growth </td>
   <td style="text-align:left;"> Prediction </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Netflix </td>
   <td style="text-align:left;"> Next show </td>
   <td style="text-align:left;"> Viewing history, day of the week, time of day </td>
   <td style="text-align:left;"> Prediction </td>
  </tr>
</tbody>
</table>

---

# The categories we use to measure a variable make up a scale

<table class="deck-table">
 <thead>
  <tr>
   <th style="text-align:left;"> Scale </th>
   <th style="text-align:left;"> What it does </th>
   <th style="text-align:left;"> Examples </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Nominal </td>
   <td style="text-align:left;"> Labels categories. No quantities </td>
   <td style="text-align:left;"> Gender, diagnosis, experimental or control </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Ordinal </td>
   <td style="text-align:left;"> Puts categories in order of size </td>
   <td style="text-align:left;"> Rank in class, clothing sizes, Olympic medals </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Interval </td>
   <td style="text-align:left;"> Equal steps, but an arbitrary zero or none </td>
   <td style="text-align:left;"> Temperature, IQ, golf scores above or below par </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Ratio </td>
   <td style="text-align:left;"> Equal steps and an absolute zero </td>
   <td style="text-align:left;"> Number of correct answers, time to finish a task, gain in height </td>
  </tr>
</tbody>
</table>

.box-3.small[Each scale can do everything the one above it can, and a bit more]

---

# Nominal, ordinal and binary

.picture[![Three hand-drawn panels. Nominal, unordered descriptions: a turtle, a snail and a butterfly. Ordinal, ordered descriptions: three bees who are unhappy, OK and awesome. Binary, only 2 mutually exclusive outcomes: a dinosaur who says I am extinct and a shark who says I am not extinct.](img/horst-nominal-ordinal-binary.png)]

---

# Mindspark has all four scales

<table class="deck-table">
 <thead>
  <tr>
   <th style="text-align:left;"> Variable </th>
   <th style="text-align:left;"> Its values </th>
   <th style="text-align:left;"> Scale </th>
   <th style="text-align:left;"> Why </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Center </td>
   <td style="text-align:left;"> Chhatarpur, Govindpuri, Tekhand </td>
   <td style="text-align:left;"> Nominal </td>
   <td style="text-align:left;"> Names only </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Extra math tuition </td>
   <td style="text-align:left;"> Less than 1 hour to more than 4 hours </td>
   <td style="text-align:left;"> Ordinal </td>
   <td style="text-align:left;"> The top group has no upper end </td>
  </tr>
  <tr>
   <td style="text-align:left;"> SES index </td>
   <td style="text-align:left;"> −5.6 to 4.8 </td>
   <td style="text-align:left;"> Interval </td>
   <td style="text-align:left;"> Zero is just the group's average </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Math score </td>
   <td style="text-align:left;"> 0 to 35 correct </td>
   <td style="text-align:left;"> Ratio </td>
   <td style="text-align:left;"> It counts correct answers </td>
  </tr>
</tbody>
</table>

.box-3.small[A score of zero means no correct answers. It doesn't mean no math ability]

???

SES is socioeconomic status. Treatment group is nominal too, with two categories, which is called binary.

---

# Discrete or continuous?

.small.center[Only limited values, often counts]

.box-inv-3.small[Students in a class]

.box-inv-3.small[Children in a family]
]

.small.center[Measured, so any value in a range]

.box-inv-3.small[Time to finish a test]

.box-inv-3.small[Height]
]

???

A raw test score counts correct answers, so strictly it's discrete, while the ability behind it is continuous. Bring this up if someone asks.

---

# Measured or counted?

.picture[![Two hand-drawn panels. Continuous, measured data can have infinite values within a possible range: a chick who says I am 3.1 inches tall, I weigh 34.16 grams. Discrete, observations can only exist at limited values, often counts: an octopus who says I have 8 legs and 4 spots.](img/horst-continuous-discrete.png)]

---

# Switches and sliders

.picture-medium[![Two wall controls side by side. A plain light switch on the left is labeled categorical variables. A dimmer slider on the right is labeled continuous variables.](img/switch-slider.png)]

.box-inv-3.small[Getting the program is a switch: on or off. Age is a slider]

.source[Image: Andrew Heiss, *Program Evaluation for Public Service*, [CC BY-NC 4.0](https://creativecommons.org/licenses/by-nc/4.0/).]

---

# A rounded value is really a small range

.box-inv-3.small[Recording weight to the nearest pound, 149.6 and 150.3 both become 150]

???

Real limits sit halfway between neighboring values. We bucket a continuous variable into cells like these.

---

# Try it: What scale is this?

.box-inv-8.small[
Mindspark also records a math quintile for each student, from 1 (the lowest fifth) to 5 (the highest fifth). Which scale is that?
]

.options[
.option[
**A** Nominal
]
.option[
**B** Ordinal
]
.option[
**C** Interval
]
.option[
**D** Ratio
]
]

???

About 6 minutes. Work alone, talk to a neighbor, then vote.

Andy: create this poll in Poll Everywhere, then add the `.poll-bar` button from EDUC 265's 06-01 with its presenter id.

---

# Try it: Answer

.options[
.option.wrong[
**A** Nominal
]
.option.correct[
**B** Ordinal
]
.option.wrong[
**C** Interval
]
.option.wrong[
**D** Ratio
]
]

.box-inv-8.small.sp-after-half[
Quintiles keep the order, but the steps aren't equal
]

.box-8.small[
Step by step, average scores rise 2.5, 1.2, 2.0, then 3.5 points
]

---

# What you can do now

.box-inv-8.small[Say how this course runs, and where to find things]

.box-inv-8.small[Tell description, prediction and explanation apart]

.box-inv-8.small[Label a number as a parameter or an estimate, and explain sampling error]

.box-inv-8.small[Name a study's Y and X, and a variable's scale of measurement]

---

# Next steps

Topic 2, displaying data. Read sections 2-1 to 2-3 first
]

Meet the data. Go to your own lab, and bring a calculator and a laptop
]

.box-3.small[Nothing is due this Sunday. Get MindTap through Canvas now]

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