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Human Life Tables and Survivorship Curves
PURPOSE:
Test hypotheses about human survivorship using:
1.Life tables
2. life expectancy3.Survivorship curves
Hypotheses aboutMales and Females
R.I.P.BRB
– 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.
Hypotheses aboutMales and Females
R.I.P.BRB
– 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.
Hypotheses aboutPublic Health
R.I.P.BRB
– 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
What are life tables?
• A life table contains age-specific survival and mortality rates in a population. It also contains fecundity and age distribution information.
• Life tables come in 2 varieties:– Cohort life table: Follows a group of
individuals born at the same time. – Static life table: Constructed by recording
the age at death of a large number of individuals. This is what we’ll be making.
Life Tables
Age Class x dx nx lx ax
0-5 16-10 2 x11-15 3Etc.
X = a reference number we assigned to refer to the different classes
Life Tables
Age Class x dx nx lx ax
0-5 1 x-16-10 2 x11-15 3Etc.
X = a reference number we assigned to refer to the different classes
Life Tables
Age Class x dx nx lx ax
0-5 16-10 2 x11-15 3 x+1Etc.
X = a reference number we assigned to refer to the different classes
Life Tables
Age Class x dx nx lx ax
0-5 1 66-10 2 211-15 3 0Etc.
dx= the number of individuals that die in the x age class.
Life Tables
Age Class x dx nx lx ax
0-5 1 6 How many?
6-10 2 211-15 3 0Etc. Etc.
nx= total number of individuals surviving to the x age class. nx = nx-1- dx-1
Life Tables
Age Class x dx nx lx ax
0-5 1 6 1006-10 2 2 How many?
11-15 3 0Etc. Etc.
nx= total number of individuals surviving to the x age class. nx = nx-1- dx-1
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 1006-10 2 2 94 lx =11-15 3 0 92Etc. Etc.
(lx) Survivorship: Portion of population that survived to the x age class
0n
nx
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 100 16-10 2 2 94 .94 lx =11-15 3 0 92 .92Etc. Etc.
(lx) Survivorship: Portion of population that survived to the x age class
0n
nx
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 100 16-10 2 2 94 .9411-15 3 0 92 .92 ax = Etc. Etc.
ax = Given you reach the x age class, what is the probability you live to the NEXT age class.
x
x
n
n 1
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 100 1 =94/100
6-10 2 2 94 .9411-15 3 0 92 .92 ax = Etc. Etc.
ax = Given you reach the x age class, what is the probability you live to the NEXT age class.
x
x
n
n 1
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 100 1 .946-10 2 2 94 .94 .9811-15 3 0 92 .92 qx = Etc. Etc.
qx = Given you reach the x age class, what is the probability you do NOT live to the NEXT age class.
x
x
n
d
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 100 1 .946-10 2 2 94 .94 .9811-15 3 0 92 .92 Etc.Etc. Etc.
ax + qx = 1
Life Tables
Age Class x dx nx lx ax qx
0-5 1 6 100 1 0.94 0.066-10 2 2 94 0.94 0.98 0.0211-15 3 0 92 0.92 Etc. Etc.Etc. Etc.
ax + qx = 1
Make three: Males, Females, and Totals for your group’s data
x Dx
Nx
lx ax qx 1000lx log1000lx
0-5 1 4.00 250.00 1.00 0.98 0.02 1000.00 3.00
6-10 2 0.00 246.00 0.98 1.00 0.00 984.00 2.99
11-15 3 1.00 246.00 0.98 1.00 0.00 984.00 2.99
16-20 4 3.00 245.00 0.98 0.99 0.01 980.00 2.99
21-25 5 3.00 242.00 0.97 0.99 0.01 968.00 2.99
26-30 6 0.00 239.00 0.96 1.00 0.00 956.00 2.98
31-35 7 3.00 239.00 0.96 0.99 0.01 956.00 2.98
36-40 8 2.00 236.00 0.94 0.99 0.01 944.00 2.97
41-45 9 1.00 234.00 0.94 1.00 0.00 936.00 2.97
46-50 10 12.00 233.00 0.93 0.95 0.05 932.00 2.97
Example Life Table
Life Expectancy
The amount of time one is expected to live once age class x is reached or during a specified period of time.
How can we test whether health issues influence survivorship, or if there is a difference between males and females?
Use your lab sections’ data: Compute life expectancies for all age groups and for childbearing years. Do this for Males, Females, and Totals
Compute life expectancies for the older cemetery and the younger cemetery.
You will have 8 life ex valuese
1
ll . 5x
xi
i x
Survivorship curves:
R.I.P.BRB
●Make 2: your data (Male vs. Female)previous data (Old vs. New)
Pine Hill
00.10.20.30.40.50.60.70.80.9
11.11.21.31.41.51.61.71.81.9
22.12.22.32.42.52.62.72.82.9
33.13.2
0-5
6-1
0
11
-15
16
-20
21
-25
26
-30
31
-35
36
-40
41
-45
46
-50
51
-55
56
-60
61
-65
66
-70
71
-75
76
-80
81
-85
86
-90
91
-95
96
-10
0
10
1-1
05
Age Class
10
00
* lo
gS
urv
ivo
sh
ip
FemalesMale
Auburn Memorial
00.10.20.30.40.50.60.70.80.9
11.11.21.31.41.51.61.71.81.9
22.12.22.32.42.52.62.72.82.9
33.13.2
Age Class
1000*
log
su
rviv
ors
hip
Males
Females
Rosemere
00.10.20.30.40.50.60.70.80.9
11.11.21.31.41.51.61.71.81.9
22.12.22.32.42.52.62.72.82.9
33.13.2
Age Class
10
00
* lo
g s
urv
iva
l
Male
Female
Garden Hill
00.10.20.30.40.50.60.70.80.9
11.11.21.31.41.51.61.71.81.9
22.12.22.32.42.52.62.72.82.9
33.13.2
Age class
10
00
*lo
g S
urv
iva
l
Males
Female
Old vs. New Cemetery
00.10.20.30.40.50.60.70.80.9
11.11.21.31.41.51.61.71.81.9
22.12.22.32.42.52.62.72.82.9
33.13.2
0-5
6-1
0
11
-15
16
-20
21
-25
26
-30
31
-35
36
-40
41
-45
46
-50
51
-55
56
-60
61
-65
66
-70
71
-75
76
-80
81
-85
86
-90
91
-95
96
-10
0
10
1-1
05
Age Class
10
00
*lo
g s
urv
ivo
rsh
ip
New
Old
Chi Square tests
How do we know if 2 survivorship curves differ?1) look at the graphs2) do a 2 test
We’ll use Females as our observed group and males plus females/2 as expected.
Old vs. new
Graph dx for males vs. females and old vs. new. What does this tell us?
0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 76-80 81-85 86-90 91-95 96-100
101-105
0
10
20
30
40
50
60
malesfemales
A lot of data… To leave today you need
1) Three life tables (male, female, all) using lab section’s data
2) Eight life expectancies3) Survivorship curve (M and F) (lab section data)4) Survivorship curve (Old and New) (Previous Data)5) dx graphs6) Two Chi square tests: Old vs. New (Previous data), M
vs. F (lab section’s data)
