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X(10212) = X(5)-of-OaObOc; X(10212) lies on the Euler line of ABC. (Antreas Hatzipolakis and Angel Montesdeoca, 24189 ).

X(10212) lies on these lines: {2,3} (more pending)

X(10212) = midpoint of X(3) and X(5498)

In the plane of a triangle ABC, let O = circumcenter, X(3) N = nine-point center, X(5) Na = N-of-OBC, and define Nb and Nc cyclically Aa = orthogonal projection of Na on OA, and define Ab and Ac cyclically Ba = orthogonal projection of Nb on OA, and define OB and OC cyclically Ca = orthogonal projection of Nc on OA, and define OB and OC cyclically Ea = Euler line of AaAbAc, and define Eb and Ec cyclically A' = Eb∩Ec, and define B' and C' cyclically

Then ABC and A'B'C' are parallelogic, and X(10213) = (A'B'C',ABC)-parallelogic center X(1141) = (ABC,A'B'C')-parallelogic center.

(Antreas Hatzipolakis and Angel Montesdeoca, 24183 ).

X(10213) lies on these lines: (pending)

In the plane of a triangle ABC, let A'B'C' = orthic triangle Na = nine-point center of AB'C', and define Nb and Nc cyclically X(10214) = NaNbNc-to-A'B'C' cyclologic center X(125) = A'B'C'-to-NaNbNc cyclologic center.

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X(10214) lies on these lines: {4,7730}, {25,8157}, {571,2079}, {933,3518}

X(10214) = X(5620)-of-orthic-triangle if ABC is acute

In the plane of a triangle ABC, let IaIbIc = excentral triangle Ja = incenter of IaBC X(10215) = JaJbJc-to-ABC cyclologic center, on the circumcircle of JaJbJc X(3659) = ABC-to-JaJbJc cyclologic center, on the circumcircle of ABC.

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Let Aa be the Ia-excenter of IaBC, and define Bb and Cc cyclically. The lines IaAa, IbBb, IcCc concur in X(164), and the lines AAa, BBb, CCc concur in X(10215).

X(10215) lies on these lines: {1, 6724}, {10, 188}, {80, 1128}, {177, 1130}, {505, 8078}, {1488, 8241}

X(10215) = isogonal conjugate of X(10231)

In the plane of a triangle ABC, let P be a point. Let Ba = orthogonal projection of B on AP, and define Cb and Ac cyclically Ca = orthogonal projection of C on AP, and define Ab and Bc cyclically Ra = radical axis of the nine-point-circles of ABaC and ACaB, and define Rb and Rc cyclically Sa = radical axis of the nine-point-circles of ABaB and AcaC

The locus of P for which the lines Ra, Rb, Rc concur is the Gibert quintic Q038, which passes through X(i) for i = 1, 4, 5 80, 1113, 1114, 1263, 2009, 2010.

The locus of P for which the lines Ra, Rb, Rc concur is the Gibert quintic Q066, which passes through X(i) for i = 1, 2,4,254, 1113, 1114, 1138, 2184, 3223, 3346, 3459, 8049, 9510.

For P = X(5) the point of concurrence of Ra, Rb, Rc is X(10216). For details on points of concurrence and for other choices of P, see 24453 .

X(10216) lies on these lines: {4,250}, {137,143} (more pending)

A further point to note is that even if you have enough participants, you need to make sure that they’re classified correctly, and put into the right experimental group. Carrying out a study on bilinguals and monolinguals would of course be hampered if it came to light that some participants spoke one more (or less) languages than their grouping would suggest.

classified

This is particularly pertinent in studies examining different mental disorders, in which the grouping definition could be unclear. For example, studies of anxiety may need to differentiate between participants who have been diagnosed with generalized anxiety disorder, or those who suffer from panic attacks, and even if participants exhibit subclinical / prodromal symptoms.

Ensuring that the sample is well-defined, and well characterized, before beginning the study will therefore ensure that the findings are relevant to the group of interest.

Picking cherries, dredging data

While most of the selection biases occur before the data has been collected, there are several steps that occur post-hoc which are open to erroneous distortion. These steps instead to relate to how the data, rather than the sample, is selected.

Cherry-picking is undoubtedly a good way to prepare a pie, but is also the phrase given to the act of only selecting data that conforms with what the experimenter is expecting, or hoping, to see.

Cherry-picking

This can occur due to malpractice , or perhaps wishful thinking on behalf of the investigator. Ultimately though, this leads to bad science either way. The investigator must remain open-minded to the contents of the data, and question how they are interpreting things. It may also help if several people (ideally independent) check the data of the study.

Similar to the above, data-dredging (also known as fishing for data, or p-hacking ) is the practice of only considering the data that is significant after the experiment, and inventing post-hoc conclusions for why that emerged. This usually arises when a large number of variables investigated, and spurious results can appear significant.

data-dredging

By taking only significant variables from a dataset, this is essentially the same as running the same experiment multiple times, and publishing the one occurrence in which significant differences were found.

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Trick splits

Finally, in a similar way to misclassifying the participants before the experiment, their data can be misclassified after the fact. Incorrect partitioning of data is a way of dividing, or not using, certain parts of the data based on false assumptions.

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