Intergalactic Time Travel: Estimation Pilot Study

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<br><br><br><br><br>
# Intergalactic Time Travel: Estimation Pilot Study
## ISU Graphics Group
## February 17, 2022
## Emily Robinson

---
class:primary
# Estimation Pilot Study

📏 Take 15 minutes to participate in the pilot study at [https://shiny.srvanderplas.com/estimation/](https://shiny.srvanderplas.com/estimation/).

💬 Please share any feedback or comments you have during the study.

💬 We will also go through the questions from the study afterwards.

.center[
<img src="images/ewok-tribble.jpg" width="75%"/>
]

---
class:primary
# Intergalactic Populations: Tribbles

[YouTube: Star Trek The Trouble With Tribbles Clip](https://www.youtube.com/watch?v=p4wM5KvUGEc)

Hi, we're Tribbles! We were taken from our native planet, Iota Germinorum IV, and brought abroad Starfleet in stardate 4500. A Starfleet scientist, Edward Larkin, genetically engineered us to increase our reproductive rate in an attempt to solve a planetary food shortage. 
<br> <br> 
The Tribble population on Starfleet over the next 50 Stardates (equivalent to 1 week universe time) is illustrated in the graph. We need your help answering a few questions regarding the population of Tribbles.

.center[
<img src="images/tribble.jpg" width="75%"/>
]

---
class:primary
# Intergalactic Populations: Ewoks

Hi, we're Ewoks! We are native to the forest moon of Endor. After the Galactic Civil War, some Ewoks traveled offworld to help Rebel veterens as 'therapy Ewoks' and began to repopulate. 
<br> <br> 
The Ewok population After the Battle of Yavin (ABY) is illustrated in the graph. We need your help answering a few questions regarding the population of Ewoks offworld.

.center[
<img src="images/ewok.jpg" width="75%"/>
]

---
class:primary
# Time Travel

Original data were simulated from `\(x \in (3000, 3050)\)`.

**[Tribbles from Startrek](https://trekguide.com/Stardates.htm)**

+ Trouble with Tribbles occured on stardate 4523.3 (universe year = Fri Jan 11 2267 21:58:18)
+ 1 week span: Jan 11, 2267 (4516.69) to Jan 18, 2267 (4567.19) = 50.5 stardates
+ 4516.69 stardate - 3000 date of simulated data (+ 1516.69)
+ Conversion: round to 4500 (+ 1500)

**[Ewoks from Star Wars](https://starwars.fandom.com/wiki/Timeline_of_galactic_history)**

+ The Galactic Civil War occurred in 0 - 5 After the Battle of Yavin (ABY)
+ Conversion: start at 0 ABY (- 3000)

---
class:primary
# Data Plots
<br>
.center[
<img src="images/simulated-data-plot.jpg" width="100%"/>
]

---
class:primary
# Graph Comprehension

Questioning is an important aspect of comprehension ([Friel et al., 2001](https://www.jstor.org/stable/pdf/749671.pdf?casa_token=P-xvzvhOuUUAAAAA:tFasUO-_wxPaHjDnFatHnKLQEe1TzdPppsvp9z5XKTgJxxJKBa389bSFABKQCEnFLrS0GBcDSAheJdobK0TvynryBtalanSSziriK0JhWimnOF_9UA)). Three levels of graph comprehension have emerged:

1. Elementary level 
  + translation 
  + literal reading of the data

2. Intermediate level 
  + interpretation 
  + reading between the data

3. Advanced level 
  + extrapolation / interploation 
  + reading beyond the data

???
National Council of Teachers of Mathematics

Comprehension of information in written or symbolic form involves three kinds of behaviors (Jolliffe, 1991; Wood, 1968) that seem to be related to graph comprehension: (1) translation, (2) interpretation, and (3) extrapolation/interpolation.

Researchers have proposed that question-asking is a fundamental component of cognition and plays a central role in the comprehension of text (Graesser et al. 1996).

---
class:primary
# Graph Comprehension

**Elementary level:** focused on extracting data from a graph (literal reading of the data)

+ What does this graph tell you?
+ How tall was xxx?
+ What was the value of Stock X on June 15th?
+ How many boxes of raisins have 30 raisins in them?
+ What is the projected food production in 1985 for the developed countries?
+ What was petroleum use in 1980?
+ What is the value of B?

???

**Elementary level:** focused on extracting data from a graph (literal reading of the data)

+ requiring a literal reading of the data, title, or axis label
    + What does this graph tell you?
    + How tall was xxx?

---
class:primary
# Graph Comprehension

**Intermediate level:** characterized by interpolating and finding relationships in the data as shown on the graph (reading between the data)

+ Who was the tallest?
+ How much taller was x than y?
+ Over the first five days, how did the value of Stock X change?
+ How many boxes of raisins have more than 34 raisins in them?
+ Considering the two curves of the graph only as marks on a piece of paper, how do the changes in these two curves compare?
+ Given your understanding of the relationship between changes in the two curves and given your understanding of what each curve represents, what interpreation can be made about the relationship between the two curves?
+ Between 1970 and 1985 how has the use of petroleum changed?
+ Is D greater than C?
+ Is A + B equal to C + D?

???

**Intermediate level:** characterized by interpolating and finding relationships in the data as shown on the graph (reading between the data)

+ requiring comparisons and the use of mathematical concepts and skills to “read between the data
    + Who was the tallest?
    + How much taller was x than y?

---
class:primary
# Graph Comprehension

**Advanced level:** requires extrapolating from the data and analyzing the relationships implicit in the graph (reading beyond the data)

+ If x grows 5 centimeters and y grows 10 centimeters by Sept. 1981, who will be taller, and by how much?
+ If z is 5 years old, which of the following is a correct statement?
+ For the period of June 15 to June 30, what was the trend for the value of Stock X?
+ If students opened one more box of raisins, how many raisins might they expect to find?
+ If this graph was offered as a piece of evidence to prove true the statement ‘Storks bring babies,’ how would you describe the connection between the graph and attempt to prove the statement true?
+ Which fuel is predicted to show the most dramatic increase in use?
+ Which fuels show the same pattern of growth?
+ Is the variability of the data points large?

???

**Advanced level:** requires extrapolating from the data and analyzing the relationships implicit in the graph (reading beyond the data)

+ requiring an extension, prediction, or inference to “read beyond the data”
    + If x grows 5 centimeters and y grows 10 centimeters by Sept. 1981, who will be taller, and by how much?
    + If z is 5 years old, which of the following is a correct statement?

---
class:primary
# Graph Comprehension

**Other considerations**
+ The scale on the vertical axis is commonly misread. When only alternate lines were numbered, the unnumbered lines were read as halves (Beeby and Taylor, 1973).

+ Shape of graph changes depending on scale, may create a "conceptual demand" ([Leinhardt et al. 1990](https://journals.sagepub.com/doi/pdf/10.3102/00346543060001001?casa_token=6_GCTxqLgVYAAAAA:rzAcgHFUXQz0jC-lmKyJ1VU26HaCqUq0xgKNOdD4wp7QhJwpIKfsN-xZQYkAxkMkDpZxqsFUifg)).

+ Participants round to multiples of 5 or 10 in pen-ended estimation tasks ([Becker et al. 2019](https://scholar.google.com/scholar_url?url=https://www.tandfonline.com/doi/pdf/10.1080/10618600.2019.1585259&hl=en&sa=T&oi=gsb-gga&ct=res&cd=0&d=9960771689545072655&ei=MMXlYfu9ArqO6rQPo5uBoAU&scisig=AAGBfm0k6Vr_ethV-AsN0Qx60C56PS0lKw))

???

**Other considerations**
+ Beeby and Taylor 1973 (cited in MacDonald-Ross, 1973) found that in reading data from line graphs, people persistently misread the scale on the vertical axis; when only alternate lines were numbered, the unnumbered lines were read as halves.
+ Leinhardt, Zaslavsky, and Stein (1990) noted that the shape of a graph changes depending on the scale; this change may create a “conceptual demand” (p.17) that affects the mental image a graph user is able to construct.
+ Open-ended estimation tasks elicit certain well-known biases such as the tendency to round to multiples of 5 or 10.
+ Long-term interaction with a complex graph or chart showing multiple layers of data is generally not ideal within this paradigm, which requires a fixed set of numerical assessments that do not accurately represent how we explore a new, complex graphic.

---
class:primary
# Elementary Questions

**Open Ended**
+ Between stardates 4530 and 4540, how does the population of Tribbles change?
+ Between 30 ABY and 40 ABY, how does the population of Ewoks change?

**Numerical Translation**
+ What is the population of Tribbles in stardate 4510?
+ What is the population of Ewoks in 10 ABY?

+ At what stardate does the population of Tribbles reach 4,000?
+ In what ABY does the population of Ewoks reach 4,000?

.center[

<img id='imgsimulateddataplot' src='images/simulated-data-plot.jpg' alt=' ' width='55%'>

<div id='modalsimulateddataplot' class='modal'>
  
  <img class='modal-content' id='imgmodalsimulateddataplot'>
  
  <div id='captionsimulateddataplot' class='modal-caption'></div>
</div>
]

---
class:primary
# Intermediate Questions

**Additive Comparisons**

+ From 4520 to 4540, the population increases by ____ Tribbles.
+ From 20 ABY to 40 ABY, the population increases by ____ Ewoks.

**Multiplicative Comparisons**

+ How many times more Tribbles are there in 4540 than in 4520?
+ How many times more Ewoks are there in 40 ABY than in 20 ABY?

+ How long does it take for the population of Tribbles in stardate 4510 to double?
+ How long does it take for the population of Ewoks in 10 ABY to double?

.center[

<img id='imgsimulateddataplot2' src='images/simulated-data-plot2.jpg' alt=' ' width='55%'>

<div id='modalsimulateddataplot2' class='modal'>
  
  <img class='modal-content' id='imgmodalsimulateddataplot2'>
  
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---
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# Minor Breaks on Log2 Scale

.center[

<img id='imglogdefaultminorbreaks' src='images/log-default-minor-breaks.jpg' alt='Default Minor Breaks' width='18%'>

<img id='imglognominorbreaks' src='images/log-no-minor-breaks.jpg' alt='No Minor Breaks' width='18%'>

<img id='imgloghalfminorbreaks' src='images/log-half-minor-breaks.jpg' alt='Minor Breaks at 1/2' width='18%'>

<img id='imgloghalfthreequarterminorbreaks' src='images/log-half-threequarter-minor-breaks.jpg' alt='Minor Breaks at 1/2 and 3/4' width='18%'>

<img id='imglogquarterhalfthreequarterminorbreaks' src='images/log-quarter-half-threequarter-minor-breaks.jpg' alt='Minor Breaks at 1/4, 1/2, and 3/4' width='18%'>

<div id='modallogdefaultminorbreaks' class='modal'>
  
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</div>

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<div id='modalloghalfminorbreaks' class='modal'>
  
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  <div id='captionloghalfminorbreaks' class='modal-caption'></div>
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<div id='modalloghalfthreequarterminorbreaks' class='modal'>
  
  <img class='modal-content' id='imgmodalloghalfthreequarterminorbreaks'>
  
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<div id='modallogquarterhalfthreequarterminorbreaks' class='modal'>
  
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.pull-left[

Number 8 from the [Standards of Graphics](https://infowetrust.com/project/1915-standards): *When curves are drawn on logarithmic coordinates, the limiting lines of the diagram should each be at some power of ten on the logarithmic scales.*

].pull-right[

<img id='imgstandardsforgraphicslog10minorbreaks' src='images/standards-for-graphics-log10-minor-breaks.jpg' alt='Standards for Graphics Log10 Minor Breaks' width='80%'>

<div id='modalstandardsforgraphicslog10minorbreaks' class='modal'>
  
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---
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.center[
# Additional Suggestions or Considerations?
]

---
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# Group Discussion
## [International Day of Women and Girls in Science](https://www.un.org/en/observances/women-and-girls-in-science-day)

.center[
<img src="images/women-and-girls-in-science.jpg" width="80%"/>
]