# A Formula For Risk of Nightmares

As already noted in this blog post, I recently conducted a survey on sleeping which also included the topic nightmares. The strongest effects on the occurrence of nightmares come from the variables age, depression and stress. While among younger people (age 36 or lower) roughly 50 % frequently have nightmares, the same is true for only 27 % of older people. A statistical test shows that this difference has a very strong statistical significance. Depression led the nightmare risk to rise from 24 % (no tendency for depression, self-reported) to 57 % (strong tendency for depression) and stress from 21 % (low stress level, self-reported) to 50 % (high stress level). Both increases were also statistically significant.

There were other variables that also led to an increase in the nightmare risk as well, though none of them as robust as age, depression and stress. The living conditions have a noticeable effect. A busy road increases the risk by 22 %, noisy family members or roommates by 26 % and noisy neighbors by 27 %. Also noteworthy are the effects of lifestyle. Frequently drinking stimulating beverages adds 15 % to the nightmare risk, smoking adds 16 %, alcohol adds 18 %, cannabis adds 21 % and eating late roughly 13 %. At this point, even a little before that, the differences went below the threshold for statistical significance. One more thing I can say is that the variables education, income and sleeping alone do not seem to have any effect at all on the risk of nightmares.

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With all of this input I produced a predictor variable and a formula to compute the nightmare risk. Define the following variables:

Lifestyle Variable:
L = 1/5*(Stim Beverages + Smoking + Alcohol + Cannabis + Eating Late)

Circumstance Variable:
C = 1/3*(Busy Road + Noisy Family + Noisy Neighbor)

Mind Variable:
M = 1/2*(Stress + Depression)

All individual points range from 1 (no) to 5 (yes). For example, when a person never drinks stimulating beverages such as Coke or Coffee, set Stim Beverages = 1, if a person heavily consumes stimulating beverages, set Stim Beverages = 5. This way you can produce the values of L, C and M. Once these values are known for a person, one may compute the predictor P:

P = 0.6*M + 0.3*C + 0.2*L + 0.5*(90/Age)

And then insert the predictor P into this formula, that was found by regression analysis, to calculate the nightmare risk of this person:

Risk = 0.802 – 0.720 / ( 1 + (P / 4.55)^5.12 )

Where the symbol ^ means “to the power of”. To asses the accuracy of the formula, I compiled the table below. It shows the predictor range with the corresponding nightmare risk as measured in the survey and as calculated from the formula (in the bracket) for the midpoint of the predictor interval.

2.0-2.5 … 10 % (10 %)
2.5-3.0 … 19 % (13 %)
3.0-3.5 … 17 % (19 %)
3.5-4.0 … 25 % (28 %)
4.0-4.5 … 41 % (38 %)
4.5-5.0 … 45 % (48 %)
5.0-5.5 … 61 % (57 %)
5.5-6.0 … 68 % (64 %)

So while there are deviations, the formula works quite well for the most parts.

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Let me demonstrate the process of finding the nightmare risk using the formula, I’ll offer myself as the test subject. Here are my values for the variables. Remember that each variable ranges from 1, a strong no, to 5, a strong yes.

Lifestyle Variable:
L = 1/5*(Stim Beverages + Smoking + Alcohol + Cannabis + Eating Late)
L = 1/5*(4 + 5 + 2 + 1 + 4) = 3.2

Circumstance Variable:
C = 1/3*(Busy Road + Noisy Family + Noisy Neighbor)
C = 1/3*(3 + 1 + 1) = 1.7

Mind Variable:
M = 1/2*(Stress + Depression)
M = 1/2*(4 + 4) = 4

Predictor:
P = 0.6*M + 0.3*C + 0.2*L + 0.5*(90/Age)
P = 0.6*4 + 0.3*1.7 + 0.2*3.2 + 0.5*(90/32) = 5

Nightmare Risk:
Risk = 0.802 – 0.720 / ( 1 + (P / 4.55)^5.12 )
Risk = 0.802 – 0.720 / ( 1 + (5 / 4.55)^5.12 ) = 0.53 = 53 %

So roughly 50/50, not that bad actually. I would say that puts me in the risk group, but luckily not the high-risk group.