Lecture 7,8 - Body Temperature and Statistics

8/3/2019 Lecture 7,8 - Body Temperature and Statistics

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The fed state

The fed state

glycogentriacyglycerol

glucose triac l l cerol

protein

triacylglycerol in

glucose

in VLDL

amino acids

glycogenglycogen

amino acids

proteinprotein


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The fasting state

The fasting state

glucose

hormone-sensitive

lipase

protein

ketone bodies

glycerolamino acids

glycogenglycogen fatty acidsfatty acids


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Metabolism


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Metabolic Processes: Reversible

Glycogenesis (glucose to glycogen)

Glycogenolysis (glycogen to glucose)

Gluconeo enesis amino acids to lucose

Lipogenesis (glucose or FAAs to fats)


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Oxidation of glucose

CC66HH1212OO66 + 6 O+ 6 O22 ----> 6 CO> 6 CO22 + 6 H+ 6 H22O + 2816 kJ/molO + 2816 kJ/mol

Open airOpen air : 2816 kJ released as heat: 2816 kJ released as heat

MetabolismMetabolism : 36 mol ATP (33kJ/mol): 36 mol ATP (33kJ/mol)1188 kJ trapped in ATP1188 kJ trapped in ATP

1628 kJ released as heat1628 kJ released as heat

Efficiency : 42%Efficiency : 42%


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Energy Balance: About 50% used for

Body Heat


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Body Temperature Balance:

Homeothermic Metabolic heat production usually required to

Cells cannot use this energy to do work, but

Warms the tissues and blood Helps maintain the homeostatic body

temperature

ows me a o c reac ons o occur e c en y Balance is very narrow range, usually higher

than environment


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Homeothermic


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Homeothermic Conduction- transfers heat from one tissue to the next until

reaching the shell. It can be conducted to clothing/air (skincontact).

Convection -transfers heat from the body by motion of a gasor li uid. The faster water or air is in motion the reatercooling effect. (cold water or sauna).

Radiation -transfers heat from the body in many different.

environment is warmer. Primary pathway during rest.

Evaporation -transfers heat from the body by the evaporation

o sweat on t e s n. s sweat reac es t e s n, t sconverted to a vapor. It is the primary avenue for heat lossduring exercise. 80% active/20% rest.


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Thermoregulation:

Peripheral and body core receptors senses

Hypothalamic thermoregulatory center

Shivering, non-shivering thermogenesis,

vasoconstriction


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Thermoregulation:Homeostatic Balancing of Body Temperature


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Thermoregulation: Prevention of

Vasodilation of cutaneous vessels transportseat rom core

Behavior: activity, exposure to heat


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Thermoregulation: Prevention of


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Thermoregulation: Pathologies

Hyperthermia: body temperature too high

ever: pyrogens g pa ogens

Heat exhaustion (1020F)

eat stro e 106 eat

Malignant hyperthermia defective Ca++re ease

Hypothermia: body temperature too low

Metabolism slows loss of consciousness,death

Surgical applications: heart surgery


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Metabolic Rate

Rate of energy output (expressed per hour) equal to thetotal heat produced by:

All the chemical reactions in the body

The mechanical work of the body

easure rec y w a ca or me er or n rec y w arespirometer

Basal metabolic rate BMR

Reflects the energy the body needs to perform itsmost essential activities

Total metabolic rate (TMR) Total rate of kilocalorie consumption to fuel all


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Bod tem erature balance between heatproduction and heat loss

At rest, the liver, heart, brain, and endocrine

During vigorous exercise, heat production from

skeletal muscles can increase 3040 times Normal body temperature is 36.2C (98.2F);

optimal enzyme activity occurs at thistem erature

Temperature spikes above this range denatureproteins and depress neurons


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Direct Calorimetry


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Direct Calorimetry


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Direct Calorimetry

Measures the heat emitted b the bod over a iven

period of time Room calorimeter

Water cooled suit

Very expensive


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Indirect Calorimetry


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More practical than direct calorimetry

Based on fact that as foods are oxidised to produce energy,

proportion to the heat generated i.e. from a knowledge ofoxygen consumed, the heat production (i.e. energyexpended) can be calculated

,oxygen (O2) is required and carbon dioxide (CO2) is exhaled.By measuring either the amount of O2 consumed or the

amount of CO2 produced, it is possible to estimate theamount of energy being produced for the body to use.

gases


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The calculation of energy expended depends upon the ratio

The usual ratio that applies to humans is 0.85

.been used OR

Every litre of CO2 produced indicates 5.75 kcals have beenused


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Non-calorimetric methods

Measurement of heart rate has been used to estimate energy

expenditure over longer periods

and energy expenditure in individual subjects by

simultaneous heart-rate monitoring and indirect calorimetry Inexpensive and non-restrictive

Free-living conditions


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Non-calorimetric methods

Provides information on total energy expenditure of a non-

Subject takes oral dose of water containing stable (non-radioactive isoto es of both h dro en 2H and ox en 18O

As energy is expended, carbon dioxide and water are

produced Difference in rates of loss of the 2 isotopes is used to

calculate the CO2 production of the subject which in turnused to calculate ener ex enditure

Major advantage is free-living subject

Major disadvantage is cost


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A branch of mathematics dealing with thecollection, analysis, interpretation and

presentation of masses of numerical data


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Measures of Central Tendency: Mean, Mode, Median

Measures of Variability:

Range, Variance, Standard Deviation

Perform Statistical Tests to analyze the data:

Is there an effect of your factor on the dependent variableversus control?


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Statistics

Mode the most common valueIn statistics, the mode of a list of data is the element that has the largest

number of occurances in that list, namely the most frequent valuewithin the list. For example, the mode of {1, 3, 6, 6, 6, 7, 7, 12, 12,17} is 6.

Median sort from low to hi h, locate the middlevalue (if there are an even number of data pointsthen average the two middle numbers)

Mean the arithmetic mean (average) xx


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Statistics

, ,

40, 55, 30, 30, 40, 55, 70, 70, 55, 55, 60


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Measures of Variability

minus the smallest measure

Variance: the sum of the squared differences

from the mean divided by n 1

1

)( 22

n

xxs

Standard deviation: the square root of the

variance

1

n

xxs


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Normal (Gaussian) distribution

Many kinds of data follow this symmetrical, bell-shaped curve, oftencalled a Normal Distribution.

Normal distributions have statistical properties that allow us to predictthe robabilit of ettin a certain observation b chance.

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0. . . . . . . . .


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Statistics


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When sampling a variable, you are most likely to

68% within 1 SD

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0. . . .


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Note that a couple values are outside the 95th (2 SD) interval

These are im robable

The essence of hypothesis testing:

If an observation appears in one of the tails of a distribution, there.

- . - . - . - . . . . . .

2.0 1.0 0 1.0 2.0


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Significant Differences

A difference is considered significant if thepro a y o ge ng a erence yrandom chance is very small.

P value:

The probability of making an error by chance Historically we use p < 0.05


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The probability of detecting a significant

A big difference is more likely to be significant


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The probability of detecting a significant

If the Standard Deviation is low, it will be easier


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Hypothesis testing

Hypothesis:

Null hypothesis HO:There is no difference H0:

1 = 2

Alternative hypothesis (HA):

There is a difference

HA: 1 2 ,

hypothesis

If the null hypothesis is false, it is likely that our alternative

ypot es s s trueFalse there is only a small probability that the resultswe observed could have occurred b chance


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Common probability levels

Alpha Reject Null

P > 0.05 Not No

P < 0.05 1 in 20 Significant Yes

P


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Common statistical tests

Question Test

Does a single observation belong to a population

of values?Z-test

re wo or more popu a ons o num erdifferent?

T-testF-test (ANOVA)

Is there a relationship between x and y Regression

Is there a trend in the data (special case of above Regression


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The z distribution: Standard normal

The Z-distribution is a Normal Distribution, with special properties:

Mean = 0 Variance = 1

Z = (observed value mean)/standard error

Standard error = standard deviation / sqrt(n)

The Z distribution

S


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Statistics


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Mean and Standard Deviation of the mean

es ma es rom a popu a on

Just as we calculated the mean of a sample, we can also calculate

the mean of means. (sum them up and divide by the number of

.

The standard deviation of the mean estimates is called thestandard error, and is given by:

NSE


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xx


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Are two populations different: The t test


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Are two populations different: The t-test

Also called Students t-test. Student was asynonym for a statistician that worked forGuinness brewery

Useful for small samples (


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the

difference

w n

the means

same in all

ree.

But, the three situations don't look the same-- the two groups that appear most different ordistinct is the bottom or low-variability case


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This leads us to a ver im ortantconclusion:

differences between scores fortwo rou s, are evaluated basedon

the difference between their

means relative to the spread or

variability of their scores.

e - es oes us s.


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-

e ormu a or e - es s a ra o

The top part of the ratio is just the

difference between the two means oraverages

The bottom part is a measure of thevariability or dispersion of the scores.


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STUDENT'S T TEST


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STUDENT'S T-TEST

General Procedure

First calculate the t-test statistic-

value located in the t-table for the

The t-distribution is tabled with several differentprobability levels as columns and degrees of.


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'o ca cu ate your t-va ue, you nee to rst

calculate the mean (x bar) and the standarderror of EACH of our sam les.

The standard error of a sample meanis the

square root of the sample size


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-critical t-value

or a g ven , your -va ue s arger anthe value found in the table.

the null h othesis of no difference between

the means should be rejected.

Types of Student's t tests


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Types of Student s t tests

for Quality Control

One-Sam le

Two Independent (Unpaired) Samples

e ca cu a o o e -va ue sdifferent for each of these tests


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One-sample Student's t test

inferred from a sample with a


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(sample vs. standard)

Sample mean

minus

mean

Divided

the mean

t=(Sample Mean - Hypothetical Mean)/SEM

Many are confused about the difference between


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the standard deviation SD and standard error ofthe mean (SEM).

e quant es scatter - ow muc t e

values vary from one another. On average, theSD will sta the same as sam le size etslarger.

the true population mean. The SEM gets smalleras your samples get larger, simply because themean o a arge samp e s e y o e c oser othe true mean than is the mean of a smallsample.

Two-tailed and One-tailed


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Two tailed and One tailed

versions of these tests

Two-tailed test - evaluates whether adifference exists between 2 samples, not thedirection of the difference

One-tailed test - evaluates whether adifference exists between 2 samples, andspec ca y eva ua es e rec on o edifference (whether one sample is larger or

0 05

One-tailed: use if you know a priorith t th d t l t d i


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= 0.05that the data can only trend in one

= 0.05

rec on

Sum

= 0.05

Two-tailed: use if you do not knowa prioriwhich direction the data willtrend

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Example


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Example

t-test for a Single Sample

You are responsible for the operation of all

equipment in a prepress area. A film processor ins area s es gne o eve op m a a s an ar

temperature of 65 degrees.

A sample of twenty measurements are made overthe course of a day with a mean of 70.5 and a

.

Is your processor temperature significantly

different from the standard? Use an = 0.05


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s t-test s one as a two-ta e test at = 0.05.

0 = 1

,variance:

s = S RT s2 = S RT 121 = 11

Next, compute the standard error of the mean:

sem = s/SQRT(n) = 11/SQRT(20) = 11/4.47 = 2.46


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Compute the t-test:

t = ar - sem = 70.5 - 65 2.46 = +2.24

, = - = - =

The critical value for t at al ha = 0.05 is +2.09

Thus, it is concluded that the temperature of your

processor scored significantlyhigher than thestandard. You reject the H0.


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Table for t-Statistic

Degrees of freedom

=(n1-1) + (n2-1)

Patients were given one of two drug treatments


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-

Experiment #

Placebo Drug

(mean values)

New Drug

(mean values)

1 8.8 9.9

2 8.4 9.0

3 7.9 11.1

4 8.7 9.6

. .

6 9.6 10.4


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- Calculate the mean and S.E.M. for the control and

treatment group.

Calculate the ooled sam le estimator, s 2

Calculate the t-Statistic

Look-up the t-Statistic for = 0.05

- .

Would you conclude that there is a significant differencebetween the two groups?

Regression defined


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Regression defined

40

45

A statistical technique to define

30

35

t(oz

)the relationship between a

response variable and one ormore predictor variables

20

25

h

W

eigh Here, fish length is a predictor

variable (also called anindependent variable.

5

10Fis Fish weight is the response

variable

0

5 7 9 11 13 15

Fish Length (in)


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Identify the relationship between a predictor andresponse variables

Correlation

Estimate the degree to which two variables varytoget er

Does not express one variable as a function of the other

No distinction between de endent and inde endent variables

Do not assume that one is the cause of the other Do typically assume that the two variable are both effects of


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40

45 Assumes there is a

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35

t(oz)

straight-line relationship

between a predictor (orindependent) variable X

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25

h

W

eighan a response or

dependent) variable Y Equation for a line:

5

10Fis= +

m the slope coefficient(increase in Y per unit

0

5 7 9 11 13 15

Fish Length (in)

b the constant or YIntercept(value of Y when X=0)


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40

45 Re ression anal sis

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35

t(oz)

finds the best fit line

that describes thede endence of Y on X

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25

h

W

eigh

Outputs of regression Regression model

Y = mx + b

5

10Fis

Weight = 4.48*Length +-28.722

0

5 7 9 11 13 15

Fish Length (in)

Coefficient ofDetermination

2 .

How good is the fit? The


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45

oe c en o e erm na on

30

35

40

oz)

R2: The proportion of

the total variation that is

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25

W

eight

regression Coefficient of determination

5

10

15

Fish R2 = 0.89

Ranges from 0.00 to 1.00

0.00 No correlation

0

5 7 9 11 13 15

Fish Length (in)

1.00 Perfect correlation no scatter around line

Example coefficients of


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1.2

70

80determination

0.8

1

50

60

0.4

0.6

30

40

0

0.2

0

10

. . . .

R2 = 0.08

. . . .

R2 = 0.54

Lecture 7,8 - Body Temperature and Statistics

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Transcript of Lecture 7,8 - Body Temperature and Statistics