In this experiment you will be briefly shown a display with airplane images. On each trial you will be asked to estimate the number of airplanes in the image. Being able to quickly make judgments of this type is important for some occupations, such as an air traffic controller.
At the end of the experiment you will compute a confidence interval of the errors you make. The confidence interval provides an estimate of whether you overestimate or underestimate the number of airplanes (on average). If your estimates balance out above and below the true value, your mean would be zero. We are also interested in the spread of the confidence interval, since an air traffic controller needs to be accurate on essentially every trial (and not just on average).
What methods did we employ in this experiment? On each trial, you briey saw a set of planes on the screen. Your task was to estimate how many planes were on each screen. Because the actual number of planes varies from trial to trial, we are interested in analyzing the errors you make across the trials. If you were accurate on a trial, the error would be zero. If you overestimate the number of planes, the error will be a negative number. If you underestimate the number of planes, the error will be a positive number. Thus, the closer your error is to zero, the better your average performance. In the analysis below, you will compute a mean of your error scores across the trials. We have to be careful about interpreting the value of a mean error. You could have a mean value close to zero in many different ways. It could be that on every trial your error is almost zero, so the mean is also close to zero. This would indicate that you are quite good at estimating the number of planes. However, a mean near zero could also occur by having some trials where you substantially overestimate the number of planes and other trials where you substantially underestimate the number of planes. In the calculation of the mean, these terms would produce a value near zero. This case would indicate that you are not very good at estimating the number of planes and that you are equally prone to overestimating and to underestimating the number. Clearly, the mean by itself is not sufcient to identify whether or not someone is good at estimating the number of planes or not. A better approach is to calculate a condence interval. This identies the range of values where one can have condence that the true ability of the person exists. In our case, an air trafc controller should have a small condence interval, Willi a lower limit close to the upper limit, which is centered on zero. A poor estimator might have a mean of zero, but a larger condence interval, which would indicate that the person is sometimes far from accurate on some trials. Fon'nulas To calculate the condence interval you need to rst calculate the mean: standard deviation (this is the raw score formula): and standard error of the mean: Next, you need to identify the I'm, critical value. This is most easily done with an online calculator, using df=n'l. Finally, compute the lower and upper limits of the condence interval: (Y tar-3f, f + tans?) . Use the trial-by-trial data to answer these questions. Question Answer Status Mean estimate for the difference scores: (The difference between your answer and the correct value must be less than 0.01.) -1.4 Check answer Hint Incorrect Standard deviation of estimate for difference scores: (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Standard error. (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Degrees of freedom: 19 Hint Correct (Your answer must exactly equal the correct value.) Check answer t critical value for a 95% confidence interval: (The difference between your answer and the correct value must be less than 0.01.) 2.09302 Check answer Hint Correct Lower limit of the 95% confidence interval: (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Upper limit of the 95% confidence interval: (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Hint: Compute the mean (average) of the difference scores. The answer may be a negative number.On each trial, you estimated the number of shown airplanes. The actual number of planes varied across trials. The nal column gives the difference between the actual number of planes and your estimate. Trial Actual number of planes Esmated number of planes Difference between actual and estimated number of planes 1 8.0 9.0 1.0 2 24.0 20.0 4.0 3 8.0 8.0 0.0 4 14.0 15.0 1.0 5 18.0 20.0 2.0 6 20.0 23.0 3.0 i" 21.0 20.0 1.0 8 12.0 10.0 2.0 9 13.0 10.0 3.0 10 18.0 16.0 2.0 11 15.0 14.0 1.0 12 22.0 20.0 2.0 13 15.0 15.0 0.0 14 23.0 20.0 3.0 15 8.0 8.0 0.0 16 9.0 10.0 1.0 1? 21.0 18.0 3.0 18 15.0 10.0 5.0 19 22.0 20.0 2.0 20 20.0 20.0 0.0

Question

In this experiment you will be briefly shown a display with airplane images. On each trial you will be asked to estimate the number of airplanes in the image. Being able to quickly make judgments of this type is important for some occupations, such as an air traffic controller.

At the end of the experiment you will compute a confidence interval of the errors you make. The confidence interval provides an estimate of whether you overestimate or underestimate the number of airplanes (on average). If your estimates balance out above and below the true value, your mean would be zero. We are also interested in the spread of the confidence interval, since an air traffic controller needs to be accurate on essentially every trial (and not just on average).

What methods did we employ in this experiment? On each trial, you briey saw a set of planes on the screen. Your task was to estimate how many planes were on each screen. Because the actual number of planes varies from trial to trial, we are interested in analyzing the errors you make across the trials. If you were accurate on a trial, the error would be zero. If you overestimate the number of planes, the error will be a negative number. If you underestimate the number of planes, the error will be a positive number. Thus, the closer your error is to zero, the better your average performance. In the analysis below, you will compute a mean of your error scores across the trials. We have to be careful about interpreting the value of a mean error. You could have a mean value close to zero in many different ways. It could be that on every trial your error is almost zero, so the mean is also close to zero. This would indicate that you are quite good at estimating the number of planes. However, a mean near zero could also occur by having some trials where you substantially overestimate the number of planes and other trials where you substantially underestimate the number of planes. In the calculation of the mean, these terms would produce a value near zero. This case would indicate that you are not very good at estimating the number of planes and that you are equally prone to overestimating and to underestimating the number. Clearly, the mean by itself is not sufcient to identify whether or not someone is good at estimating the number of planes or not. A better approach is to calculate a condence interval. This identies the range of values where one can have condence that the true ability of the person exists. In our case, an air trafc controller should have a small condence interval, Willi a lower limit close to the upper limit, which is centered on zero. A poor estimator might have a mean of zero, but a larger condence interval, which would indicate that the person is sometimes far from accurate on some trials. Fon'nulas To calculate the condence interval you need to rst calculate the mean: standard deviation (this is the raw score formula): and standard error of the mean: Next, you need to identify the I'm, critical value. This is most easily done with an online calculator, using df=n'l. Finally, compute the lower and upper limits of the condence interval: (Y tar-3f, f + tans?) . Use the trial-by-trial data to answer these questions. Question Answer Status Mean estimate for the difference scores: (The difference between your answer and the correct value must be less than 0.01.) -1.4 Check answer Hint Incorrect Standard deviation of estimate for difference scores: (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Standard error. (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Degrees of freedom: 19 Hint Correct (Your answer must exactly equal the correct value.) Check answer t critical value for a 95% confidence interval: (The difference between your answer and the correct value must be less than 0.01.) 2.09302 Check answer Hint Correct Lower limit of the 95% confidence interval: (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Upper limit of the 95% confidence interval: (The difference between your answer and the correct value must be less than 0.01.) Check answer Hint Not yet answered correctly Hint: Compute the mean (average) of the difference scores. The answer may be a negative number.On each trial, you estimated the number of shown airplanes. The actual number of planes varied across trials. The nal column gives the difference between the actual number of planes and your estimate. Trial Actual number of planes Esmated number of planes Difference between actual and estimated number of planes 1 8.0 9.0 1.0 2 24.0 20.0 4.0 3 8.0 8.0 0.0 4 14.0 15.0 1.0 5 18.0 20.0 2.0 6 20.0 23.0 3.0 i" 21.0 20.0 1.0 8 12.0 10.0 2.0 9 13.0 10.0 3.0 10 18.0 16.0 2.0 11 15.0 14.0 1.0 12 22.0 20.0 2.0 13 15.0 15.0 0.0 14 23.0 20.0 3.0 15 8.0 8.0 0.0 16 9.0 10.0 1.0 1? 21.0 18.0 3.0 18 15.0 10.0 5.0 19 22.0 20.0 2.0 20 20.0 20.0 0.0