A Statistical Analysis of Human Body Temperature

Part II

BY: Dhanalakshmi Pantangi Praneetha Mukhatira Yaping Sun

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The mean (Total [list]/Length [list]) of all the temperatures was 98.2The 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.

General Body Temperature

We made a histogram of all temperatures (130 readings) obtained from public records (Allen L. Shoemaker 1996) of both females and males, we found that the number of people who had temperatures between 98 and 98.5 were the highest.

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.

We investigated further to check if this temperature does indeed fall in the interval that has the greatest frequency.

xz2 n98.25 1.960.7332

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0.733213098.123, 98.375

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.

Male Female

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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

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Temperature Graph for males and females

This is a plot for female and male temperature. Clearly, female temperature is higher.

* Box-male, Star-female

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. 99.199.299.399.499.5Temp

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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. 99.199.299.399.499.5Frequency Male

If we make a bar chart of the male frequencies, we see that the highest frequencies are around 98 and 98.6.

96.496.796.897.297.497.697.797.897.9 98. 98.198.298.398.498.598.698.798.898.9 99. 99.199.299.399.499.9100.100.8Temp

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elpoep96.496.796.897.297.497.697.797.897.9 98. 98.198.298.398.498.598.698.798.898.9 99. 99.199.299.399.499.9100.100.8

Female Frequency

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.

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.

Zy xSx2n Sy2m

z 98.39 98.10

0.48865 0.55365 2.292

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.

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TemperatureAndHeart Rate

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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. * Box-male, Star-female

From this box-whisker plot, we see that heart rate affects body temperature.

**Box1-4 show as following:1. Male temperature2. Female temperature3. Male heart rate4. Female heart rate

Heart rate and Body TemperatureRegression 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.

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The histogram of male heart beat rate 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.

MaleSkin FemaleSkin MaleCore FemaleCore

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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.

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 predictionThe 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.

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.

BBT ChartingUntil 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.

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Ovulation cycle of a lady

We plotted the graph of 6 different ladies. The menstrual cycle of women also affects their temperature rhythm, with the post-ovulatory temperature rise increasing the overall mean. We also see that the cycle length varies from 24 to 40.

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ConclusionsThrough 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.