A Statistical Analysis of Human Body Temperature
Part II
BY:
Dhanalakshmi Pantangi
Praneetha Mukhatira
Yaping Sun
General Body Temperature
35
We made a histogram of all
30
temperatures (130 readings) 25
obtained from public records
20
(Allen L. Shoemaker 1996) of 15
both females and males, we
10
found that the number of people 5
who had temperatures between
98 and 98.5 were the highest.
97
98
99
100
101
The mean (Total [list]/Length [list]) of all the temperatures was 98.2
The median (gives the center element in the sorted version of list) was 98.3
The mode was 98.
The variance was 0.54.
The quartiles (lower, middle and upper quartile refers to values below the
25th, 50th and the 75th percentile) are 97.8, 98.3, and 98.7.
It appears that the normal temperature of 98.6 is not the true
population mean.
We investigated further to check if this temperature does indeed
fall in the interval that has the greatest frequency.
x z
2
98.25
n
1.96
0.7332
130
, 98.25
1.96
0.7332
98.123, 98.375
130
A confidence interval is an interval in which a
measurement or trial falls corresponding to a given
probability .Here we find a 95% confidence interval
which gives us [98.123, 98.375].
98.6 did not fall in the confidence interval for body
temperature. Therefore, we concluded that 98.6 degrees
is not the population mean.
Gender and Body Temperature
Research from Dr. Han Kim of the University Of Utah School Of Medicine:
Kim and his colleagues used an infrared tympanic thermometer, which
determines core body temperature by measuring the infrared radiation
given off by the ear drum. In all, 219 people, ranging in age from infants to
84 years, were studied, 78 of them male and 141 female.
Women were found to have a higher average core temperature than
men,women had a mean core temperature of 97.6 degrees Fahrenheit
compared with 97 for men.
The mean hand temperature for women was 87.2, while men recorded 90.0
degrees.
Researchers found that menstrual status affects women's body
temperatures. Postmenstrual women over 50 had lower hand and core
readings than premenstrual girls under age 13. Further, women within the
first 14 days of their menstrual cycles were more likely to have lower core
temperatures than women in the last 14 days.
Women have a higher ratio of surface to volume than men and thus
shed heat faster.
Men have more heat-generating muscle mass.
Women have a higher vasoconstriction threshold temperature.
We wanted to find out if gender affects body temperature. We looked at
our data set, isolating the female and male body temperatures (each 65
readings) from each other, and we found the average body temperature
for males and females.The mean body temperature of human males was
found to be 98.1 and 98.39 for females.
We also looked at a box-whisker plot of the two data sets, male and
female. (The male is on the left and the female is on the right.) From
both of these, we observed that females have a higher average body
temperature than males
100
99
98
97
Male
Female
This is a plot for female and male temperature. Clearly, female
temperature is higher.
Temperature
Graph
for
males
and
females
100
Temp
99
98
97
0
10
20
30
40
Number of people
* Box-male, Star-female
50
60
If we make a bar chart of the male frequencies, we see that the
highest frequencies are around 98 and 98.6.
Frequency Male
96.396.796.9 97. 97.197.297.397.497.597.697.797.897.9 98. 98.198.298.398.498.598.698.798.898.9 99. 99.199.299.399.499.5
6
5
Num of people
4
3
2
1
0
96.396.796.9 97. 97.197.297.397.497.597.697.797.897.9 98. 98.198.298.398.498.598.698.798.898.9 99. 99.199.299.399.499.5
Temp
Female Frequency
96.496.796.897.297.497.697.797.897.9 98. 98.198.298.398.498.598.698.798.898.9 99. 99.199.299.399.499.9100.100.8
7
6
Num of people
5
4
3
2
1
0
96.496.796.897.297.497.697.797.897.9 98. 98.198.298.398.498.598.698.798.898.9 99. 99.199.299.399.499.9100.100.8
Temp
If we make a bar chart of female frequencies, the highest frequencies are
around 98.8.We also see the higher temperatures have higher frequencies
in females.
We wanted to find out with what confidence we could make this claim
statistically. In order to do this, we calculated the p-value. P-value is the
probability that a variate would assume a value greater than or equal to the
observed value strictly by chance. To calculate the p-value where X was the
male body temperature and Y was the female body temperature, we had the
following hypotheses and test statistic:
Null Hypotheses: H0=µx-µy.
This tests whether the difference between the means of the two populations is 0.
Z
y
Sx2 n
z
x
Sy 2
98.39
0.488 65
m
98.10
0.553
2.292
65
Mathematica gives us the p-value of 0.011 when we use the
“MeanDifferenceTest” function.
It also rejects the null hypotheses at a significance level of 0.05.
This means that with 98.9% confidence we can reject our null hypothesis,
which assumed the means were equal. The average female body
temperature is greater than the average male body temperature;
therefore, there is a relationship between gender and average body
temperature.
Probability of male having temperature between 95.6 to 96.4 is
3%.Probability of male having temperature between 96.5 to 97.5 is
15%.Probability of male having temperature between 97.6 to 98.4 is
49%.Probability of male having temperature between 98.6 to 99.5 is
27.5%.Probability of Male having temperature between 99.6 to 100.5 is
1.5%.
Probability of female having temperature between 95.6 to 96.4 is
1.5%.Probability of female having temperature between 96.5 to 97.5 is
7.7%.Probability of female having temperature between 97.6 to 98.4 is
46%.Probability of female having temperature between 98.6 to 99.5 is
38.4%.Probability of female having temperature between 99.6 to 100.5 is
4.6%.Probability of female having temperature between 100.5 to 101.5 is
1.5%
We wanted to know if there were any abnormal temperatures in the data
set. We looked at a box-whisker plot for body temperature, the suspected
outliers, and the confirmed outliers. The plot showed 3 outliers in the
female temperatures. It can be ignored. We believe that the data was
collected and recorded accurately because there are no abnormal
temperatures.
Heart rate and Body Temperature
Regression analysis with heart rate as the dependent variable gives the
equation: Heart rate= 2.44*temperature -166.3. We looked at how heart
rate affects body temperature.
100
T emperatureAnd Heart Rate
From the scatter plot, we
concluded that there is a
correlation between heart
rate and body temperature
that as heart rate increases,
body temperature also
increases.
Heart Rate
80
60
40
20
97
98
99
100
* Box-male, Star-female
T emp
100
From this box-whisker
plot, we see that
heart rate affects
body temperature.
90
80
70
60
1
2
3
4
**Box1-4 show as following:
1. Male temperature
2. Female temperature
3. Male heart rate
4. Female heart rate
14
15
12
12.5
10
10
8
7.5
6
5
4
2.5
2
60
65
70
75
80
85
The histogram of male heart beat rate
60
65
70
75
80
85
90
The histogram of female heart beat rate
Looking at the histogram, we thought that the heart rates of females are
higher. The mean male heart beat rate is ~73.36, mean female heart beat
rate is ~74.15.But heart beats has to be a whole number. Both the numbers
rounded off to the nearest integer gives us 74 beats per minute.
We decided to analyze it statistically. The function “MeanDifferenceTest”
gave us a p value of 0.263 and failed to reject the null hypotheses at a
significance level of 0.05. We concluded that the means of X and Y are
equal. Thus, gender does not affect heart rate. The variance of the
female data (65.69) is larger than the variance of the male data (34.52),
and therefore there is a significant difference between the variances. We
found this difference interesting to note.
Skin Temperatures
We wanted to observe if the skin body temperature of females is colder than
that of men. We obtained data from Reynaud's study. We found the mean
skin temperature of female skin was much lower than the mean skin
temperature of males. The variance of temperatures was more in female data
(4.75) as compared to males (1.065). Mean of male skin temperature is 90.
Mean of Female Skin temperature is 87.2.
100
97.5
95
92.5
90
87.5
85
MaleSkin
FemaleSkin
MaleCore
FemaleCore
Basal Body temperature
Basal Body Temperature (BBT) is the body temperature at rest. Basal
body temperatures are taken each morning prior to getting out of bed to
start the day. The temperatures are charted on a special graph to follow
the rise in temperature. The rise is a small fraction of a degree, so it is
helpful to purchase a special basal body thermometer, which has 1/10oF of
a degree ranges, plus charts to monitor your menstrual cycle. Basal body
temperatures can rise for other reasons such as fever, stress, and poor
sleep, smoking and being overheated in your bed.
Ovulation: Deep body temperature shows a strong circadian rhythm. It
varies in response to a variety of behavioral and external stimuli, including
sleep, physical activity, postural changes, ambient temperature and meals.
The menstrual cycle of women also affects their temperature rhythm, with
the post-ovulatory temperature rise increasing the overall mean. The data
is arranged by three main sections: basal body temperature, progesterone
and sleep. The connection between these three factors seems essential to
the evaluation of the subject
Ovulation and Basal Body temperature
Normal ovulation, the process of development and release of an egg, is
driven by three pituitary hormones (1-3):
(1). gonadotropin-releasing hormone (GnRH)
GnRH is produced and released from hypothalamus.
A neoro-endocrine loop between the hypothalamus and pituitary Leads
to the development of the follicle.
(2). follicle stimulating hormone (FSH)
In the presence of GnRH, the pituitary gland in the brain produces
FSH. As increasing levels of FSH are generated, immature follicles in
the ovary begin a maturation process. Generally only one follicle
matures.
(3). lutenizing hormone (LH)
A sudden burst of LH from the pituitary gland causes the mature
follicle to rupture, releaseing the egg 28 to 32 hours later and leading to
the formation of the corpus luteum and progesterone production.
Additional two hormones:
(4). progesterone
Progesterone secretions reach a maximum at eight days following the LH
surge. Unless fertilization occurs, the corpus luteum declines 14 days after
ovulation and a period begins.
(5). estrogen
Concurrent to the above events, the uterus is primed by two hormones,
estrogen and progesterone.
The cascade of the 5 identified hormones allows for ovulation, fertilization
and implantation.
The mechanism underlying the biphasic nature of an ovulatory cycle-BBT is the
production of progesterone after ovulation. Progesterone is a thermogenic
hormone which usually causes a rise in the basal temperature of 0.4 to 1.0
degrees Fahrenheit. Thus, after ovulation, and the production of progesterone
by the corpus luteum, the basal temperature rises. The temperature rise
usually occurs two days after the LH surge. Ovulation usually occurs one
day before the temperature is elevated. The temperature usually stays elevated
for 10 days.
The Thermal Shift Rule and ovulation prediction
The length of a menstrual cycle varies between 28-35 days.
A typical woman's BBT will usually range between 97.2 degrees F and 97.6
degrees F up to 98.6 degrees F. On a Celsius scale, the reading will be
between 36.2 and 36.4 C. From just after ovulation, at mid-cycle, through the
beginning of menstruation, the BBT rises as much as one degree.
Therefore, a woman's temperature is lower during the first half of her cycle
than during the last two weeks of the same cycle.
This shift from a lower temperature to a higher temperature occurs around the
time of ovulation.
BBT charting has been used to predict ovulation.
Use the temperatures recorded on the chart for the first 10 days of the
menstrual cycle to identify the highest of the “normal, low” temperatures. Draw
a line 0.05-0.1o above the highest of these 10 temperatures. This line is called
a cover line.
The chart usually displays a mid-cycle drop and then significant temperature
rise that is maintained for almost 14 days. A chart that appears to be Biphasic
is suggestive of ovulation.
The most fertile days are 2 to 3 days before ovulation and for about 12 to 24
hours after ovulation. The infertile phase begins on the evening of the third
conseutive day that the temperature stays above the cover line.
BBT Charting
Until now, in all the data collected, we see that core temperature of females
has been higher than that of males. Female temperatures have another cycle
exclusively. This is the temperature variations that occur when ovulation
occurs.
Here is a graph of an ovulation cycle of a lady.
Ovulation
cycle
of
a
lady
98.4
Body Temp
98.2
98
97.8
97.6
97.4
97.2
0
5
10
15
20
Days
25
30
35
Biphasic the chart displays a mid-cycle drop and then significant
temperature rise that is maintained for almost 14 days. If temperature
rises above normal temperature for consecutive 3 days in a row, it
indicates that ovulation has occurred and the egg has already passed.
We plotted the graph of 6 different ladies. The menstrual cycle
of women also affects their temperature rhythm, with the postovulatory temperature rise increasing the overall mean. We
also see that the cycle length varies from 24 to 40.
98.5
98
97.5
10
20
30
40
Conclusions
Through our research and data analysis, we found that with 95% confidence the true
population mean of body temperature is not 98.6 degrees Fahrenheit. It is 98.2 or
36.8 degrees Centigrade.
We also found that the average female body temperature is greater than the
average male body temperature.
It is also true that heart rate affects body temperature. The higher the heart rate is,
the higher the body temperature is. We calculated the average heart rate to be 74
beats per minute. However, there is no relationship between gender and average heart
rate; although, the female heart rate variance is greater than the male heart rate
variance.
We see that the mean skin temperatures of females are less than the mean skin
temperatures of males. The mean skin temperature of female is 87.2 and for male
is 90. We also observe that the variance is more in mean skin temperatures of females.
We also observed that the temperature varies during a day according to the circadian
rhythm. It is lowest at around 6 in the morning and highest around 6 in the
evening. The average cycle lasts about 24.16 hours.
The ovulation cycle also affects temperature. The ovulation cycle lasts about 29 days
in most women. The variation in temperature can be used to predict ovulation
after a time series graph is constructed.
We also observed that exercise affects the body temperature more in the morning.
We also found that by examining the suspected and confirmed outliers, there did
not appear to be any problems with our data.