Thank you once again very much for taking part! You will receive a lump-sum payment of {{ ShowUpFee }} for completing the study, conditional on approval. In addition, you will have the chance to earn a bonus of up to {{ Prize }} based on your performance. Please read the following instructions carefully.
Please keep in mind that a pocket calculator may come in very handy for you. You could also use a calculator app installed on your computer.
It is also important for you to know that the guesstimation tasks you will be asked to work on relate to statistics from German-speaking countries (Germany, Austria, Switzerland). Speaking German fluently is not a requirement, however.
Today, we will ask you to work on so-called "guesstimation tasks". In such a task you are asked to provide a number or statistic that you (probably) won't know. For example:
In a typical year, how many children aged between 10 and 14 years old are enrolled in a public music school in Germany?
If you don't have this particular piece of information, giving a satisfactory answer to such a question may seem extremely difficult at first glance. However, after some careful and structured thinking, it is actually possible to get reasonably close to the right answer. You could call this process "making an educated guess".
To illustrate the process of coming to an educated guess, consider another example question:
How many streets and squares in Berlin have the letter x, y or z in their name?
Unless you are a Berlin taxi driver, you will not be able to answer this question right away. The best strategy to tackle such a problem is breaking it into pieces that can be dealt with. One way to approach the issue in this particular case is to think about the following more basic questions:
If you are able to come up with some estimates for these questions, then you can make an educated guess about the correct answer to the main question.
The answer to this question seems like something we might find on the internet. Indeed, a quick Google search gives the answer: 9.473. But beware, there may be different answers to be found, and it is always advisable to check whether the magnitude makes sense and to verify the reliability of the information found.
You can also find this information on the internet. z has an approximate likelihood of 1.2%, x and y roughly 0.05% each - thus, the latter two are quite rare. Putting them together, we get 1.3% for an x, y or z.
Since we know how likely a single letter is equal to an x, y, or z, we need to adjust for the average length of the street name. Let us estimate that street names are between 8 and 20 letters long. One possibility for your educated guess would be to just use the average: (8+20)/2 = 14.
Now we are able to calculate the fraction of street names containing the letter x, y or z as: 14 * 0.013 = 0.182. Multiplying by the total number of streets, 9,473, we get 1,724 as our estimate for the number of streets that contain x, y or z.
We have inserted this step just as an attention check. In the following you will see a selection of European cities. Your task is to click on Hamburg. This has nothing to do with the actual study.
The German name for a square, “Platz”, contains a z. Also, many street names start with “Zur”, “Zum”, “Zu den”. This implies we might adjust our guesstimate a bit upwards, since the statistical likelihood may not hold exactly in our sample of street names. Maybe we feel a correction of 100 extra streets is appropriate, so that our final educated guess is 1,824.
Typically, there are different ways to approach a guesstimation problem. In the street example, searching online briefly shows that there are street lists of Berlin organized by the street names' starting letters (one page with a list of street names beginning with the letter "A", another with a list of names beginning with "B" and so on). While counting all the streets with certain characteristics by opening all of these pages is infeasible (there will be a time limit!), we could proceed by taking a closer look at a sample of these pages:
First, we can easily check that 1, 3, and 164 streets start with an x, y, and z, respectively, a total of 168.
Second, we can check some other lists, say those for streets starting with an "A", "B", or "C". Using the browser's "find in page" function, we can check how commonplace the letters x, y, and z are. We get:
Now we extrapolate. There are 26 letters in the alphabet. We have covered those that begin with x, y, and z. This leaves 23 more letters, 3 of which we have sampled, which is about 1/7. However, we might feel that "A" and "B" are particularly popular letters. Thus, perhaps "A", "B", and "C" together account for approximately 1/6 of the total number of streets.
We would then get (10+7+2)*6 = 114 streets with an x, (4+24+9)*6 = 222 streets with a y, and (111+107+24)*6 = 1,452 streets with a z. Taking the sum, we have 114 + 222 + 1,452 = 1,788. When we include the 168 streets that start with x, y, or z, we obtain 1,956 as our educated guess.
We can summarize our (first) answer in the following table.
| How many streets and squares in Berlin have the letter x, y, or z in their name? | ||
|---|---|---|
| Step | Reasoning | Number and/or calculation |
| 1 | How many streets and places are there in Berlin in total? | 9,473 (source: https://de.wikipedia.org/wiki/Straßen_und_Plätze_in_Berlin) |
| 2 | How likely are the letters x, y, and z in the German language? | “z“: 1.2%. “x”+”y” = 0.1%. Total: 1.3% (source: https://www.sttmedia.com/characterfrequency-german#letters) |
| 3 | How long is a street name on average? | (8 + 20) / 2 = 14 letters |
| 4 | Number of streets containing the letters x,y, or z. | 14 * 0.013 * 9,473 = 1,724 |
| 5 | Upward correction “Platz” etc. | 1,724 + 100 = 1,824. |
| Our guesstimate: 1,824 | ||
When you work on a guesstimation task, you can enter the steps behind your reasoning directly into a form similar to the table shown on the previous page.
You can try it out here. Just click on the field below the "Please describe your reasoning" heading and write a few words. You can move to the next field ("Relevant number / calculation") by pressing the "Tab" key on your keyboard or by directly clicking on it.
To add a step or insert a step, just click on the relevant button. Up to 10 steps are allowed. You can remove a step by clicking on the relevant close button in the top right corner (marked by an "X"). The only exception is Step 1 which cannot be removed.
It is very important for us that you document your reasoning in the actual guesstimation tasks.
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When you have arrived at a guesstimate answer, you can enter your number in a special field as seen below. To ensure that the computer understands your input correctly:
You can try it out the guesstimate field below. Just click on the field and enter a random number. Hit the tab key on your keyboard to see how the computer interprets your number.
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In this session you will be asked to work on TWO different guesstimation tasks yourself. At the end of the session the computer will randomly pick ONE of these and will determine your bonus payment based on your performance in the selected guesstimation task.
The prize for the task will be {{ Prize }}. Your payment will depend on how accurate your guesstimate is. Specifically, you will receive ...
If you feel very uncertain about your guesstimate, it is often advisable to stay below your initial hunch. The reason is that there are simply more ways of 'getting it wrong' by overestimating than by underestimating. Take our streets of Berlin example, and suppose that our guesstimate of 1,824 is really the correct answer. If you had submitted 450, a number that vastly underestimates the true value - by a factor of 4 -, you would still receive {{ P20 }} because your answer would be in the +/-80% range. But overestimating by a factor of just 2 (e.g. 3,500) would imply a payment of zero because your guess would be off by more than +80%.
Please describe your reasoning and write down the relevant numbers or calculations for each step. We may reduce payments if an answer is not well enough documented. Most importantly, of course, put your final guesstimate into the "Your guesstimate" box at the bottom of the screen. You will be given {{ TimeLimit }} to work on each guesstimation problem. A timer will be shown throughout.
Please submit a final guesstimate in any case - even if you realize that you will run out of time, and even if you are very unhappy with your guess.
In case you complete the task early, you will receive an (admittedly small) additional reward of 1p for every block of 5 seconds that you finish early, e.g. 23 seconds early = 4p. Just like the bonus payment for accuracy (see previous page), this extra reward is paid out only for the task that the computer picks randomly at the end of the session.
You are allowed to search for relevant background information on the internet, as also explained in the example. Sometimes, that will help. However, it is also possible that it wastes more of your time than it does help you. To our knowledge the actual final answers to our guesstimation questions cannot be found online. Please document the source of the information you use on your answer sheet (e.g., copy and paste the url).
As you will be paid according your performance in a guesstimation task under time pressure, it is very important that you start the main part of this study only when you feel really ready to begin. If possible, please go to a place where you will not be disturbed. Once the timer starts it cannot be stopped, and you cannot take a break. Remember that there will be two tasks each of which takes up to {{ TimeLimit }}. There will also be (very short!) questionnaire at the end. In addition, it is very important to us that all participants read the instructions carefully. The sole purpose of the slider below is to test whether this is the case for you. Please ignore the instructions below regarding how relaxed you are at the moment. Instead, just set the slider to a value of twenty-three. This is very important because choosing any other value may lead to you being excluded from this study.
Are you relaxed and comfortable?
On a scale of 0 to 100, which number have you been asked to select?
This completes our instructions. Before you begin your first guesstimation task, please check again that you have understood the instructions.
Also, make sure that you have your pocket calculator in reach (or have started your calculator app). Depending on your approach, you may need it.
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