Homework 10 HT2021

HOMEWORK 10 - Statistics and scientific reproducibility

Due Wed Dec 8 at 17.00

1. Confidence intervals and statistical significance

a. An experiment that was carried out 100 times resulted in the following measured values of
a certain quantity:

9.217235 10.318129 10.129548  8.694245 10.137817  9.425283 10.623405  9.342076 10.596094  9.774860
8.574891  9.879593  9.484296  9.344638 11.595789  9.888536  8.534009 10.095894  9.727538 10.337148
11.513322 12.206648  9.835393  9.971442 11.740494 10.854234 11.598732  5.296376  9.997404  9.523829
6.931937  7.442440 10.203614  9.893644 11.493547  8.684547 10.701225  9.096643  7.403547  9.524160
8.109332 10.635259 11.017585  8.025185 10.639323 10.194740  8.547801 10.524075  9.794782  9.662731
7.679089 10.003210  9.096323  9.838539 12.397197  8.770399  9.376120  7.370233  9.570937 11.546209
12.983894 10.918312  7.947315 10.478530 11.097465  7.428212  8.378904 11.149247 10.528399  9.773401
8.077814  9.921014  6.700658  9.606119 10.412562 11.177284  9.889142  7.052527 10.233331 10.504087
13.257061 10.507389 10.405352 11.081850 10.093603  9.478749 10.430384 11.066278 10.938973  7.646291
13.077798  9.414972 10.945849 10.651533  8.235178  9.775766 12.374642 10.335392  9.919154 10.562624

How would you present the resulting experimental mean value in an article (i.e., so that both
the result and its accuracy is indicated)? Motivate your answer.

b. The same experiment was repeated by another research group, who obtained the following 100 values:

10.329801  9.663788  9.197355  6.201325 10.664198 11.154959  9.021815 11.153069  9.881691  6.578968
7.156940  6.975508  6.312702 10.660096 12.157871 10.067693  9.381362 10.262361 10.281788  9.814017
11.204465  8.792269  9.328487  8.838741 10.732438 10.834142  9.474563  7.384828  6.553554  4.691474
10.869922  8.264926  9.610700 10.103980 11.544642  8.592157 10.061099  7.096357  9.311878  6.376473
9.615128 14.317692 11.042854  9.041580  8.506643  8.420273  9.750081 10.300563 13.874328  7.863532
10.787244  9.466067  6.197738 10.246936 11.708249  8.405613 12.180735  9.300543 10.387406 10.621370
12.731710 11.075102  8.709873  7.608089 10.989466  8.872121  9.352832 11.005217  9.475105  7.786765
10.134454 10.035387  5.607347  9.450380  9.985086 11.113034  8.006207 14.915114 12.174291 12.768685
9.950252 12.066192 10.625821 10.467335  7.545005 12.081193 11.592738  9.081246 10.736805 11.393570
8.546344  8.316007 10.077501  9.142106 10.599870  9.757105  3.903690  9.126403  6.577111 11.794643

Are the results consistent with each other, or is there a statistically significant difference? Motivate your answer.

c. Consider the data from another experiment found in this file Download this file. Calculate the mean and median of the data.
Why are they different? Plot the data in a histogram that clearly illustrates the distribution of the data, and
discuss which quantity is most representative of the data.

Finally, how would you go about to calculate confidence intervals for the median value? This question may
require some information search, and a description of how this can be calculated is sufficient, but you will
learn more by actually doing the calculation.

2. Reproducibility in research

Go back to the articles listed in part 2 of Homework 5. Select one of the articles (such as the one
you have already read) and comment on the reproducibility of the results of the study.

Do the authors provide enough information for someone else to replicate the study? Consider both the article
itself and any linked supplemental online information. If not, what are the obstacles, e.g., in terms of missing information?

Handing in your solution

Please save your solution as a pdf file and hand it both in Canvas (for grading) and Peergrade (for peer review). 

Peer grading

You will be asked to review the homework of two other students in Peergrade. Your solution will also be
reviewed in this way. The peer review is a mandatory part of the course. 

Feedback from your TA

Your seminar leader will grade your submission and report the result in Canvas. This may happen before
the associated seminar, but if your seminar leader is busy it will 

Complete means you have passed the assignment.

Incomplete means you have to hand in a revised version.

Fail means that you will have to submit a new version and attend the make-up seminar.
The Fail grade will only be applied in exceptional circumstances such as plagiarized work.