Human Life Tables and
Survivorship Curves
Life Tables
For today's calculations you will use data from
your cemetery and three others.
Data from all cemeteries are in an Excel spread
sheet on your university computer.
The Table
Age Class: Group of ages that will depend on the
study. We decided to use five year blocks.
X = a reference number we assigned to refer to
the different classes
The Table
dx= the number of individuals that die in the
x age class. From the data collected.
nx= total number of individuals surviving
to that age class.
nx = nx-1- dx-1
The Table
lx =Survivorship. Portion of population
that survived to the x age class
n0 = ?
nx
lx =
n0
The Table
ax = 5 year survival (since we picked 5 year
periods). This is usually an annual survival.
Given you are in the x age class what is the
probability you will live to the next age class.
ax =
n x 1
nx
The Table
qx = 5 year mortality. The probability one will
die in the x age class
d
qx = x
nx
NOTE: you either Live or Die so
ax +qx = 1
Last two columns are for the survival
curves...
1000* lx
log (1000* lx)
The Table
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You will be using Excel to do your life tables.
There are examples of life tables already done
on the spread sheet you will be using.
You will create two survivorship curves using
Excel. Following are some examples from a
previous semester.
Age Class
101-105
96-100
91-95
86-90
81-85
76-80
71-75
66-70
61-65
56-60
51-55
46-50
41-45
36-40
31-35
26-30
21-25
16-20
11-15
6-10
0-5
1000 * logSurvivoship
Pine Hill
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Females
Male
Age Class
-8
5
-8
0
-7
5
-7
0
-6
5
-6
0
-5
5
-5
0
-4
5
-4
0
-3
5
-3
0
-2
5
-2
0
-1
5
10
5
-9
91 0
-9
96 5
-1
10 00
110
5
86
81
76
71
66
61
56
51
46
41
36
31
26
21
16
11
6-
0-
1000* log survivorship
Auburn Memorial
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Males
Females
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Age Class
91
-9
5
10
110
5
81
-8
5
71
-7
5
61
-6
5
51
-5
5
41
-4
5
31
-3
5
21
-2
5
Male
Female
11
-1
5
05
1000* log survival
Rosemere
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
5
10
110
-9
5
91
-8
5
81
-7
5
71
-6
5
61
-5
5
51
-4
5
41
-3
5
31
-2
5
21
-1
5
Males
Female
11
05
1000*log Survival
Garden Hill
Age class
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Age Class
101-105
96-100
91-95
86-90
81-85
76-80
71-75
66-70
61-65
56-60
51-55
46-50
41-45
36-40
31-35
26-30
21-25
16-20
11-15
6-10
New
Old
0-5
1000*log survivorship
Old vs. New Cemetery
Life Expectancy
The amount of time one is expected to live once
age class x is achieved.
You will use Excel to calculate life expectancy, but
following is an example of how the calculations are done
for a group of males who died in or after age class 10 (46
years of age or older):
= l10 +l11 +l12 +l13 +l14 +l15 +l16 +l17 +l18
+l19 +l20 =
.844+.798+.729+.647+.522+.396+.278
+.156+.062+.02+.004 =4.46
SO:
 4.46

e10  
 0.5  * 5 =23.88
 0.844

If you are a male in this group, you can expect to live another 24
years after you reach the age of 46.
Now for the Statistical Tests
HO: The life expectancy of women is the same
as for men or less than that of men.
HA: Women have a greater life expectancy than
men.
We are investigating this hypothesis because statistics
show that men engage in riskier behaviour than
women and that they suffer health consequences from
testosterone.
Prediction1: Females have a higher life expectancy than
Males.
HO: Men do not have a greater life expectancy during
child bearing years.
HA: Men have a greater life expectancy than women
during child bearing years.
We are investigating this hypothesis because statistics show
there are risks associated with childbirth.
Prediction2: Males have higher life expectancies and
survivorship than females between the ages of 16 and 40.
HO: Human life expectancy has not
increased over the period of time during
which people were buried in our study area
cemeteries.
HA: Human life expectancy has increased
over this time period
We are investigating this hypothesis because
of the health benefits derived from advanced
medicine, nutrition, and sanitation.
Prediction: People in older cemeteries will
have a lower life expectancy than people in
newer cemeteries.
Chi Square or X2
Use a Chi Square goodness of fit test to see if the two
curves in your graphs are different. If you find a
significant result (your X2 is larger than the table value)
then the two curves are significantly different from
each other.
Use the example in the Excel spread sheet to create your own
Chi square test. The compiled data for your cemetery are in the
spread sheet.
Compare the Chi square value with the critical value on the
table (at the back of this lab section) at the .05 alpha level, and
degrees of freedom # Categories (rows) -1
If your chi square value is greater than the critical
chi square value then there is a significant
difference.
If so, you can state (for example), “There is
enough sample evidence to suggest that the life
expectancy of the newer and older cemeteries is
different.”
Now, create survival curves for your three
hypotheses and, if you haven’t done so, create life
expectancy values.
Did your tests support our predictions?
Today:
1) Create survivorship curves for your hypotheses. Hypotheses 1 and 2 will be
the same curve.
2) Calculate life expectancies for the nine categories in your spread sheet.
3) Calculate Chi square tests for your three hypotheses.
The example in the spread sheet is your best guide.
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Conclusions:
●
Which predictions were correct?
●
Hypotheses Supported?
●
What Statistical test did we do?
●
What type survivorship curve did we find with our study organism?
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First draft of this report is due June 24 and June
25.