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On the surface it might appear that this topic does not have a lot to do with statistics and science. This however changes when you take a closer look. It has a lot to do with food science and human nutrition, although hydration is still part of psychological research. Therefore I encourage you to carry on reading.

The water makes up to 60% of the human body weight (Guyto ,1976). Therefore it is extremely important to keep the fluid level in the body at a right level. Only 1% of dehydration (1), can cause performance to drop by even 10%. This includes decreased physical and mental performance, decreased concentration, headaches, increased heart rate, increase/ decrease of body temperature and discomfort. People who exercise while dehydrated put themselves at risk of different kinds of injuries.

Other than general well being water also have some long term impact on human body’s. The most obvious is that it filtrates the body, especially the kidneys. It is a perfect way for the organism to get rid of wastes and bacteria that can cause different diseases. It has been shown that regular consumption of water helps to prevent cancers (2). On top of this water plays a key role in the digestion system. Keeping the right level of fluid in the organism will make the digestion system to work better, will decrease the feeling of hunger (which will result in eating less undesirable food), and

There is also a downside to drinking water. One of them is having to visit toilet frequently (which is a real pain because I need to make a brake every 20 minutes when writing this blog after I had 5 liters of water so far today…), and the other one is a condition called hyponatremia. It is a result of drinking too much water, which causes the sodium in the body to become diluted, and causes the cells to start swelling.

In their study, Ciab et. al, tested 8 healthy endurance trained men. Their conditions were: euhydrated (normal state of body water content), dehydrated (up to a weight loss of 2.8%), and hyperhydrated (with a solution containing glycerol having ingested volume equal to 21.4 ml/kg of body weight). The subjects were assigned to a pedaling exercise and were administered psychological testing of psycho-motor skill, perceptive discrimination, fatigue, memory and mood. The dehydration conditions impaired cognitive abilities. After an arm crank exercise, further effects of dehydration were identified for tracking performance. Also long term memory was impaired in hydration and control situations, but no decrement in performance in hyperhydration group.

There are countless benefits of drinking water however I am a little restricted by time, and the number of words I put in this blog, as nobody would probably read it. The simplest conclusion for this topic therefore is: Want to feel better? Drink 2 to 3 liters of water a day.


Guyton, Arthur C. (1976). Textbook of Medical Physiology (5th ed.). Philadelphia: W.B. Saunders. p. 424.

‘Foods, Nutrition and Sports Performance,’ ed. C. Williams and J.T. Devlin (1994), pp 147-178

‘Clinical Sports Nutrition,’ ed. L. Burke and V. Deakin (1994), pp 333-364

E.F. Coyle (1994). ‘Fluid and carbohydrate replacement during exercise: how much and why?.’ Sports Science Exchange, 50, vol. 7, no. 3

Maughan, Leiper & Shirreffs (1996). ‘Rehydration and recovery after exercise.’ Sports Science Exchange, 62, vol. 9, no. 3

C. Cian., N. Koulmann., P. Barraud., C. Raphel., C. Jimenez., B. Melin,. (2000)., Influences of variations in body hydration on cognitive function: Effect of hyperhydration, heat stress, and exercise-induced dehydration. Journal of Psychophysiology, Vol 14(1), 2000, 29-36. doi: 10.1027//0269-8803.14.1.29








The Simpson’s Paradox

This statistical paradox has been introduced by E.H. Simpson in 1951. This apparently impossible effect can be very often observed in social and medical research. The idea is that the effect of several groups seems reversed when the groups are combined.

As a real world example of this paradox, it is worth looking at the example proposed by Morrel (1999)[ http://www.amstat.org/publications/jse/secure/v7n3/datasets.morrell.cfm%5D, or Charig, Webb, Payne, and Wickham (1986). In this medical study they compared success rates on two different treatments for kidney stones. 

The following table shows the success rates and the number of treatments involving both large and small kidney stones. Treatment A includes all the open surgery procedures, and treatment B percutaneous nephrolithotomy.


Treatment A:

Treatment B:

Small Stones:

Group 1

93% (81/87)

Group 2

87% (234/270)

Large Stones:

Group 3

73% (192/263)

Group 4

69% (55/80)


78% (273/350)

83% (289/350)


As a conclusion it is clear that the treatment A is more effective than the treatment B on Small stones as well as on the Large stones. However when both sizes are compared at the same time, the treatment B seems to be more effective.

I am sure many of you can instantly see a big problem with this design. The group sizes are not equal. Also the size of the stone was a confounding variable. The inequality between the two ratios (success/ total), needs to be considered to determine which treatment is more successful.

When the confounding variable is ignored, the group means differ a lot. The severe cases (large stones) were more likely to receive the better treatment (A), and milder cases (small stones) the other treatment. So the totals were dominated by bigger groups 1, and 3, rather than smaller 2, and 4. 

Severity of the case, influenced the success rate more than the choice of the treatment. This means that the group of patients with small stones (group 2) will do still do worse when administered the inferior treatment (B), than patients with large stones (group 3) when administered the better treatment.

According to Pavlides and Perlman (2009), the probability of occurrence of the Simpson’s Paradox just by chance in a 2x2x2 table is 1/60.

The Simpson’s Paradox points out how important it is to include data about possible confounding variables, when calculating causal relations. Pearl (2000, 2009), gives a precise criteria for selecting confounding variables when using causal graphs.

In conclusion this is another very interesting probability paradox. The researchers need to be very careful, and try to avoid such confounding variables. Not just to avoid getting involved with the paradox itself but also to avoid making Type 1 and Type 2 errors which are often results of confounding variables. However it might be a good idea to explore this topic further for the next blog. Thanks for reading!

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The Monty Hall paradox

This paradox is named after Monty Hall, the host of the famous American Television game ‘Let’s make a deal’. This problem is based on the probability theory.

In the original game, the player is asked to stand in front of three sets of doors. There is a prize hidden behind one of them (assigned completely randomly by the computer system, and only the TV host knows where it is).  When the player picks one of the doors, the presenter then opens one of the other two doors highlighting that the prize is not there. Then the player is asked to either stick with their original choice or to switch to the other door. Mueser and Granberg (1999), found that when first presented with the Monty Hall problem, majority of people concluded that it does not matter whether you stick or switch.

According to intuition it does not matter whether the player sticks or switches. However it turns out to be completely different. By choosing to stick with the original choice, the probability of winning is 1/3, however the probability of winning when choosing to switch is 2/3.

This means that it is better to switch the doors, as it doubles your chances of winning. The paradox is a result of a common misunderstanding, and underestimation. The host by opening one of the empty doors tries to trick the players, to think that they have 50/50 chance of winning (since there are only two doors left). The show is cleverly designed, and they know that most of the people will choose to stick with their original choice (in their study, Granberg and Brown, (1995), found that only 13% out of 228 subjects in the study, chose to switch. In the experiment carried out by ’Mythbusters’ (see the video clip attached) all of their 20 participants decided to stick with their original choice), whereas switching doubles your chances of winning.

Another words by opening an ‘empty’ door, the host decreases the number of ‘empty’ doors, and therefore decreases the probability of losing from 2/3 to 1/3. Therefore the ’remaining’ probability of winning needs to be 2/3.

One of the strategies that the host of the show uses is the endowment effect (Kahneman et al., 1991). The idea behind this effect is that people tend to overestimate the probability of winning of the door, they have already chosen. Also because of the ‘status quo bias’ (Samuelson and Zeckhauser, 1988), which states that people are more likely to stick to the choice they have already made. However the research of Morone and Fiore (2007), shows that this bias does not depend on the probability intuition.

Picture taken from: http://en.wikipedia.org/wiki/Monty_Hall_problem

In the popular show ‘Mythbusters’ (see the video clip attached) were asked by the audience to investigate the Monty Hall Paradox. This clip summarizes the problem very well and I believe it is a very good introduction to the topic. Therefore feel free to have a look.

To conclude this is a very interesting topic, which requires people to look at the problem without any sentiments. Clive Thompson (http://www.wired.com/magazine/2010/04/st_thompson_statistics/) suggested that students shouldn’t leave education unless they complete statistics course, and this would not be a bad idea, as it would make people realize that sticking with their original choice has half the winning probability as switching.

Clip By ‘Mythbusters’:


Clip by ‘stedwick’:








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