# Determining Height From Bone Length

Determining Height from Bone Length

In some cases all that police recover is a bone or bones from a victim. There may be little more to go on in the way of clues. It is possible to get an estimate of the height of the person based on the length of just one bone. A better estimate of the height can be made if the gender and ethnic background of the person is known. Usually, it is possible to make a establish the gender of the person the bone came from and in some cases a guess can be made regarding the race.

In this activity we will focus on separating the data based on the gender. Several different bones can be used with varying degrees of success. We will be working with two bones located in the arm, the radius and humerus, and two of the bones located in the leg, the tibia and femur.

Materials

Meter stick

Tables to record data

Activity 1

Let’s start with the arm. In the lower section of the arm are two bones, the ulna and the radius. The radius is the bone that ends closest to the thumb. In the x-ray you can see both the ulna and the radius. The radius is the bone on the bottom.

To measure the length of the radius take a meter stick and find the length from the base of the wrist to the fold in your elbow. Record the length in the appropriate table provided below.

Next you will need to measure the length of the humerus. This is the bone in the upper arm and extends from the shoulder to the elbow. Measure the distance from the top of the shoulder socket to the just above the elbow hinge to determine the humerus length. Record the length of this bone in the table provided.

Results from males:

|Name |Radius (cm) |Humerus (cm) |Height (cm) |

| | | | |

| | | | |

| | | | |

| | | | |

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Results from females:

|Name |Radius (cm) |Humerus (cm) |Height (cm) |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

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Analyzing the Data

You will need to be careful to work with either the data from the males or females. Once a regression equation is obtained it can be recorded and the next set of data analyzed.

What is the equation for each bone for the males?

The equation for the radius to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

The equation for the humerus to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

What is the equation for each bone for the females?

The equation for the radius to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

The equation for the humerus to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

Activity 2

There are two leg bones we are going to consider for use in predicting height; they are the femur and the tibia. The femur is the large bone in the upper leg and the tibia is the shinbone. As with the arm bones, there are differences in the relationship between the bone length and height for men and women so we will need to keep the data separate.

Let’s start with the tibia. To measure the length, determine the distance from just below the knee cap to the ankle. Record this length in the table provided below.

The length of the femur is found by measuring from the top of the hip socket to the knee cap. Record this length.

Results from males:

|Name |Tibia (cm) |Femur (cm) |Height (cm) |

| | | | |

| | | | |

| | | | |

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Results from females:

|Name |Tibia (cm) |Femur (cm) |Height (cm) |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

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| | | | |

| | | | |

| | | | |

Analyzing the Data

You will need to be careful to work with either the data from the males or females. Once a regression equation is obtained it can be recorded and the next set of data analyzed.

What is the equation for each bone for the males?

The equation for the tibia to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

The equation for the femur to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

What is the equation for each bone for the females?

The equation for the tibia to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

The equation for the femur to height is with

an r2 value of .

Would you want to use this as your first predictor of height? Why or why not?

Improving Your Prediction

Is it possible to improve your ability to predict height if you have information on two of the bones? For example, suppose that you have recovered both the tibia and the femur. Do two pieces of evidence help in forecasting the victim’s height?

To determine if it is of help, let’s add the length of the tibia and femur together for each individual person and try the regression again.

Results from the males

|Name |Tibia + Femur (cm) |Height (cm) |

| | | |

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| | | |

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Results from the females

|Name |Tibia + Femur (cm) |Height (cm) |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

Analyzing the Data

You will need to be careful to work with either the data from the males or females. Once a regression equation is obtained it can be recorded and the next set of data analyzed.

What is the equation for the combined length on the males?

The equation for the combined length to height is

with an r2 value of .

Would you want to use this as your predictor of height? Why or why not?

What is the equation for the combined length on the females?

The equation for the combined length to height is

with an r2 value of .

Would you want to use this as your predictor of height? Why or why not?

Conclusions

In some cases all that a forensics team has to go on is a bone. What are your conclusions regarding the level of accuracy you can obtain in predicting height based on one or two bones?

If you were working on a forensics team, which bone or bones would you prefer to

recover?

Explain why you would prefer this set of evidence.

What ideas do you have to improve the accuracy if you have several bones available?

What limitation(s) do you see in using the techniques we used today?

An investigation team finds a radius from a woman. The bone is 24 cm long. Estimate the height of the woman.

You are called into court to testify as an expert witness regarding the woman’s height. How confident are you of the height estimate?

Explain why your level of confidence is as stated.

Teacher Notes

There are a number of useful websites that look at relationships between bone length and height. The PBS website

suggests the following relationship between radius and humerus bone length and the person’s height.

MALES (height in inches)

o Height equals (length of radius x 3.3) plus 34

o Height equals (length of humerus x 2.9) plus 27.8

FEMALES (height in inches)

o Height equals (length of radius x 3.3) plus 32

o Height equals (length of humerus x 2.8) plus 28.1

Please note that these relationships are in inches.

Another PBS website has some useful information regarding the relationship between leg bone length and height.

The site even provides some correlations based on ethnic background. Those are provided below from the site.

|Caucasoid male |(2.42) |(tibia length in centimeters) + 81.93 |

|Caucasoid female |(2.90) |(tibia length in centimeters) + 61.53 |

|Negroid male |(2.19) |(tibia length in centimeters) + 85.36 |

|Negroid female |(2.45) |(tibia length in centimeters) + 72.56 |

|Mongoloid male |(2.39) |(tibia length in centimeters) + 81.45 |

|Mongoloid female |not available |

NOTE: Mongoloid is the major ethnic group that includes Chinese, Japanese, Eskimos, Native Americans, Siberians, Malayans, and Mongolians.

The same site also provides the following equation to relate combined leg bone lengths to height

Height = 1.31 (length of femur in centimeters + length of fibula in centimeters) + 63.05

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