ESP Lab

Summary:  Do you have ESP? ESP (extra-sensory perception) is the transmission of information from one person to another without any known physical means such as sound, sight, motion, and so forth. In this lab, you’ll pick a partner and use statistics to test whether one of you can receive images that the other sends.

Your partner may be a classmate or someone outside the class, even a non-student. If both of you are MATH200 students, do the experiment twice. This will give each MATH200 student a completely separate set of data to analyze and hand in.

If you don’t feel comfortable doing the experiment with a partner, see Alternative Protocol at the end of this assignment.

Preparation

Pick five distinct objects in a category — five colors, five models of car, five foods, five names of your kids, five sports teams or logos or players, five supermodels, whatever. Make sure you pick five objects that both sender and receiver can readily distinguish: if you’re a car nut but the other person never gets beyond “big and blue”, don’t use cars.

Take two sheets of paper. Write “SENDER” and the sender’s name at the top of one; write “RECEIVER” and the receiver’s name at the top of the other. Then in a row at the top of both papers write the names of the five objects or colors you chose. On the “SENDER” paper only, number the objects from 1 to 5.

On both papers, write the numbers 1 to 100, leaving space for the answers, because you are going to make 100 trials.

Turn on your TI-83, which you will use to make sure you send images in random order. In preparation, compute randInt(1,5) — to do this, press [MATH] [◄] [5] to select “randInt(”, then press [1] [,] [5] [)] [ENTER].

The Experiment

One of you will be the sender, and the other will be the receiver. (Usually the sender is a MATH200 student, but this is not mandatory.) In 100 trials, the sender will concentrate on one of the five objects or colors (in random order), and the receiver will try to get the signal. Make sure you both understand the instructions before you begin the experiment.

Instructions to both: Pick a time and place with no distractions, to make the most favorable conditions for ESP. Sit comfortably where you can’t see each other’s paper, back to back for instance. Don’t compare answers in any way during the experiment.

Instructions to receiver: Your partner will call out a trial number 1–100, and then send you a mental image of one of the five things at the top of your paper. You should concentrate and try to receive the image your partner is sending. Write it down in the numbered space, and say “Ready”. Don’t try to think about it, just write down the first one of those five images that pops into your head.

Instructions to sender: Press [ENTER] to get the next random number. Look at the top of your sheet for which object has this number, and write down the object name (not the number) in the next numbered space. Announce “sending trial” and the trial number (1–100), and concentrate on sending an image of the object or color to your partner. When he or she says “Ready”, get another random number and do the next trial, till you’ve done this 100 times.

After the 100th trial, compare papers. Using a different colored marker, mark each trial where the receiver and sender wrote down the same object name. (Do this on either the sender’s paper or the receiver’s; you don’t have to do it on both.) Count up the number of these successes and write it at the bottom of the data sheet: “___ successes out of 100”. This is the key result of your experiment.

The data sheets may be a little messy, but that’s fine. In an experiment you always save your original data sheets, and never rewrite them, because that could bring in copying errors.

Data Analysis

What hypothesis are you testing? “My partner and I have ESP.” How can you frame that in statistical terms? Remember that your hypotheses should be in this form:

(population parameter symbol) (operator like =, >, ≤) (number)

Here are three questions to help you set up your hypotheses in correct symbols:

• First, what kind of data do you have? Note that each of the trials was either a match (success) or not a match. What does that tell you? Are you testing a mean or a proportion?

• Next, what number are you testing against? In other words, what number or proportion of successes would be obtained by guessing? Think of a multiple-choice test with five answers per question. If you just guessed at random, what is the probability that you would get the first question right? What is the probability that you would get the second question right? How would you expect to do on the whole test, just by guessing? That is what you are testing against in your hypothesis.

• Finally, should you have <, ≠, or > in your hypothesis, and why? (There’s more than one correct choice, depending on how you look at the situation.) Think about what you’re trying to find out, and what <, ≠, or > would mean, then choose the one you think best fits what you’re trying to prove. In your report, you’ll explain briefly why you made your choice.

Use a significance level of 0.01. (Since people have strong opinions about ESP, you don’t want to get into it on a significance of merely 0.05.)

You may remember from week 10 that sometimes it’s appropriate to do something extra after a hypothesis test. If you do, you’ll get a couple of extra-credit points.

It may be a good idea to discuss your data analysis with your instructor or a Baker Center tutor before turning in your report, to make sure you’re on the right track.

What to Hand In

Your report may be word processed or neatly and legibly handwritten. Include the following, in order please:

• Purpose of the experiment: in a few words, what were you trying to decide?
• Population — Every hypothesis test uses a sample to test a population. What population are you testing?
• Date of the experiment, and your partner’s name. Who was sender and who was receiver?
• (Omit the customary description of how the experiment was conducted, since everyone is doing the experiment the same way.)
• Case number and description from Inferential Statistics Cases.
• Brief justification for choosing the <, ≠, or > symbol in hypothesis. (For example, if you tested ≠, why did you test ≠ and not > or <?)
• Six numbered steps of hypothesis testing — Include full TI-83 input and output screens. Show the bell curve, labeled correctly as discussed in class and shown in the Statistics Manual. State your conclusion both in Statistics and in English.

Check the grading protocol to make sure you’ve included everything you need.

Staple the report and sender’s and receiver’s original data sheets together in that order; you don’t need any kind of report cover. (Don’t hand in these instructions.)

Grading

The lab counts 50 points; maximum possible points are shown below. If an item is partially done then partial points are earned.

Alternative Protocol

TC3 Survey Guidelines state: "students may not be required ... to participate as subjects in any research project." In compliance with the spirit of that policy, if you don’t feel comfortable with the idea of ESP testing, you can simulate the experiment with your TI-83. To do that, follow the above protocol with the following changes:

• Use the five colors Blue, Green, Yellow, Orange, Red to set up data sheets for sender and receiver as described above.
• Use your name as name of sender. Working alone, use the TI-83 as described above to generate 100 random numbers and write down the appropriate colors (not numbers).
• Then set the Sender sheet aside and turn to the Receiver sheet. Use “Simulation with Random Numbers” as the receiver’s name. Use the TI-83 to generate a further 100 random numbers and write down the appropriate colors (not numbers). Don’t look at the Sender sheet during this process.
• As described above, mark where Sender and Receiver have the same color, and record the number of successes.

Proceed with Data Analysis as indicated above. When you reach a conclusion, it will be about “the simulated test subjects” rather than you and your partner.