# Shouldn't we take absolute values when + or - sign indicates only direction, not higher or lower values?

What I am trying to do?

I want to explore the relationship between Magnetic Field and Blood Pressure in case of diabetic patients. In short, I will create a heavy magnetic field and will collect magnetic field's value on three different axes. After data collection, I want to correlate blood pressure with magnetic field's values in three different axes (e.g. magnetic field in x axis).

Then, what is the problem?

As magnetic field is a vector, values of magnetic field in each axis can be positive as well as negative. However, in case of magnetic field,

..... scientists and engineers use the terms ‘positive’ or ‘negative’ instead of ‘North’ or ‘South’. The positive pole is considered the North-seeking pole. [1]

Therefore, positive or negative magnetic field in the axes do not mean lower or higher values. Rather, positive magnetic field indicates a direction and negative magnetic field indicates the opposite direction. Consequently, if we set these negative values, I think, it will misinterpret the correlation between blood pressure and magnetic field.

Therefore, my question

Shouldn't we take absolute values when positive or negative sign indicates only direction, not higher or lower values?

Update

Sample Data (Randomly Generated)

• Can you provide some sample data? – oszkar Apr 8 '20 at 16:16
• @oszkar Thanks for your interest. Check the updated question. – Md. Sabbir Ahmed Apr 8 '20 at 16:41

It depends on your application - in this instance, it may be warranted. It seems that your hypothesis is that blood pressure is related to the strength of the magnetic field, but its directionality is irrelevant. That seems to make sense, since I don't see a compelling reason why whether the magnetic field pointing left/right or forwards/back would make much of a difference. In this case, the direction is irrelevant, so you are justified in taking the absolute value. If you do this, be aware that you are implicitly assuming that a value of X and -X should behave the same, and ignoring any possibility that they are not.

Do consider if that's the only hypothesis you want to explore, however. I could see there perhaps being a difference in the z-axis, whether the magnetic field is pointing up or down, since that axis is not symmetric in terms of forces like the x- and y- axes. But if you know for a fact that the direction of a magnetic field makes no difference in this case, you can ignore it.

In other applications, you may not be justified in taking the absolute value. In physics mechanics problems, the sign on acceleration values indicates the direction (to the right/left). Here, the direction of the vector is critical to understanding how an object moves, so you absolutely cannot just take the absolute value and ignore the directionality.

• @Md.SabbirAhmed Almost correct. An object moving to the right (positive velocity) that undergoes negative acceleration will have the magnitude of its velocity reduced. But if that object is moving to the left (negative velocity), negative acceleration will increase the magnitude of the velocity. It gets confusing when talking about adding/subtracting positive/negative numbers, it's best just to keep the signs for directionality and add everything. – Nuclear Hoagie Apr 8 '20 at 17:25
• Thanks for your valuable feedback. – Md. Sabbir Ahmed Apr 8 '20 at 17:29
• Can you please let me know, what did you want to mean by "that axis is not symmetric in terms of forces like the x- and y- axes."? – Md. Sabbir Ahmed Apr 8 '20 at 17:32
• @Md.SabbirAhmed Gravity only pulls down, not up, so there's an asymmetry in any physical problem. In most physics problems, it doesn't matter much if the projectile is fired to the left or right, or forward or back, but it makes a big difference if you fire it up or down. No constant forces exist in the horizontal plane, so effects on the body should be similar when there's forces acting to the left vs. right. But there could conceivably be differences if the forces act up or down, against or with gravity. – Nuclear Hoagie Apr 8 '20 at 17:41
• @Md.SabbirAhmed If you wanted to check somebody's apparent weight on a scale, for example, you could put them in a box accelerating to the left, right, forward, or backwards, and you'd get the exact same answer. But if you accelerate the box upward, you'll get a different answer than if you accelerate them downward, or if they're standing still. This physical asymmetry exists only on one axis due to gravity. – Nuclear Hoagie Apr 8 '20 at 17:45

This is not a statistical issue. Whether or not the polarity of the field matters depends on whether it matters in your theory that you wish to test.

I am not sure what theory you imagine that could make humans sensitive to magnetic fields, but potentially North vs South matters.

• For instance on the one hand: you could think about a theory on human magneto reception and then the polarity could play a role, because magneto reception can be sensitive to polarity (think about birds with their sense of direction to North and South). Or if you think about interactions with implants like pacemakers, insulin-meters, insulin pumps or whatever could be inside a human body, then it might be that those components contain permanent feromagnetic materials and then direction, again, matters.
• On the other hand you might imagine something like interaction with isotropic paramagnetic or diamagnetic materials and in that case the polarity does not matter. (But direction might still be relevant)

So you should be more clear about your theory. We can not answer this part of the question for you. It is not statistics

But anyway. Let's assume direction matters but polarity not (the most interesting case).

If direction matters, but polarity not, then I would still treat this value as if the polarity matters (you could take just half the sphere but it is problematic at the edges of this half).

You can not simply take the absolute values of the x, y and z axis. For instance the reverse polarity of the vector 2.5 1.2 -3.2 is -2.5 -1.2 3.2 and not 2.5 1.2 3.2

If you have some theory about a certain axis, then you could parameterize the angle of the magnetic field relative to this axis and you get your vectors reduced to a single value (the angle relative to the hypothetical axis). Possibly you could have this axis determined by the data and you do not need to hypothesize the axis beforehand.

• Undoubtedly, this is a great answer. I respect your thoughts. My null hypothesis is "There is no correlation between magnetic field and blood pressure". Let's say, I have set the negative values in the correlation formula and found a significant negative correlation. As negative and positive values presents opposite directions, then, what the significant negative correlation coefficient will tell us? – Md. Sabbir Ahmed Apr 8 '20 at 20:15
• You mentioned two terms: Polarity and Direction. What is the difference between Polarity and Direction in this case? – Md. Sabbir Ahmed Apr 8 '20 at 20:25
• If polarity doesn't matter then you have point symmetry. E.g. the vector x y z and -x -y -z give the same effect. Direction is much broader and about the question whether all possible values x y z with the same magnitude are the same. – Sextus Empiricus Apr 8 '20 at 20:47
• Can you please answer the first comment which I asked you on the basis of your answer? – Md. Sabbir Ahmed Apr 9 '20 at 5:05
• Negative correlation would mean that the heart rate is low when the coordinate value is high and vice versa. It would mean that polarity could matter (but you might find correlation by chance, check the significance for that, or due to systematic errors). – Sextus Empiricus Apr 9 '20 at 7:40

I do not know if it takes you any further, but I would go with the length of the magnetic field vector: $$\sqrt{\left(\text{Magnetic Field}_{\text{X Axis}}\right)^2 + \left(\text{Magnetic Field}_{\text{Y Axis}}\right)^2 + \left(\text{Magnetic Field}_{\text{Z Axis}}\right)^2}$$ as the strength of the magnetic field. Of course this is based on the assumption that direction of the magnetic field doesn't matter, just the strength of it.

As there are three orthogonal components of the magnetic field given, the resultant magnetic field is the vectorial sum of the three components. As a vector, it has a direction, and a magnitude. The latter is the length of the resultant vector, or with other words it's absolute value (more generally it's (Euclidean) norm). If you are interested in the magnetic field's magnitude (strength), you have to use this, because this is the measure of it by definition.

If you also interested in the direction, you must go with the original components, but together with the $$\pm$$ sign, because that alters the direction.

• Thanks for your suggestion. I have already thought about this as I found this in several sites (e.g. this one) and a book. – Md. Sabbir Ahmed Apr 9 '20 at 10:32
• My question was, should we take absolute value or not? In your answer, you did not say anything about that. – Md. Sabbir Ahmed Apr 9 '20 at 17:11
• The 3 dimensional Euclidean distance is the generalisation of the absolute value. In 1 dimension they are equal. – oszkar Apr 9 '20 at 17:26
• Thank you. Basically, I wanted an insightful answer like in this data set, why do you think we should use absolute values? – Md. Sabbir Ahmed Apr 9 '20 at 17:30
• Sorry, Euclidean norm. – oszkar Apr 10 '20 at 7:20