Statistics Definitions > Weighting Factor

Contents:

1. What is a Weighting Factor?
2. Use in Sampling.
3. Use in Nuclear Medicine.

1. What is a Weighting Factor?

A weighting factor is a weight given to a data point to assign it a lighter, or heavier, importance in a group. It is usually used for calculating a weighted mean, to give less (or more) importance to group members. It is also used in statistical sampling for adjusting samples and in nuclear medicine for calculating effective doses.

Simple Example

For example, let’s say you take three tests in class. The last test is much harder than the first two tests, so your professor gives it less weight. The weights for the three tests are:

• Test 1: 40 % of your grade.
• Test 2: 40 % of your grade.
• Test 3: 20 % of your grade.

The percents listed after the tests are the weighting factors. For example, test 1 has a weighting factor of 40% while test 3 has a weighting factor of 20%. Let’s say you score 80, 80, and 85 points. The weighted mean for the three tests is found by:

1. Multiplying your scores by the percentage weights:
   .4(80) = 32
   .4(80) = 32
   .2(95) = 19
2. Adding the numbers up. 32 + 32 + 19 = 83.

See more examples in Weighted Mean.

2. Use In Sampling

Weighting factors are used in sampling to make samples match the population. For example, let’s say you took a sample of the population and had 41% female and 59% male. You know from census data that females should make up 51% of the population and males 49%. In order to make sure that you have a representative sample, you could add a little more “weight” to data from females. To calculate how much weight you need, divide the known population percentage by the percent in the sample. For this example:

Known population females (51) / Sample Females (41) = 51/41 = 1.24.
Known population males (49) / Sample males (59) = 49/59 = .83.

3. Use In Nuclear Medicine

Weighting factors are used extensively in radiologic and nuclear medicine to calculative effective doses for procedures. The calculations for Tissue Weighting Factors (sometimes called Radiologic Weighting Factors) account for the fact that different parts of the body absorb radiation at different rates.

A tissue weighting factor(W_T) is assigned to body parts, with more radiosensitive parts given higher weighting factors.
Effective dose = individual organ dose values * W_T.

Tissue weighting factors (ICRP) are:

• W_T = 0.12: stomach, colon, lung, red bone marrow, breast, remainder tissues,
• W_T = 0.08: gonads,
• W_T = 0.04: urinary bladder, oesophagus, liver, thyroid,
• W_T = 0.01: bone surface, skin, brain, salivary glands.

Reference:
European Nuclear Society. Tissue Weighting Factor. Retrieved 9/20/2006 from: https://www.euronuclear.org/info/encyclopedia/t/tissue-weight-factor.htm
International Commission on Radiological Protection. The 2007 Recommendations of the International Commission on Radiological Protection. ICRP publication 103. Ann ICRP. 2007;37 (2-4): 1-33. Available from PubMed.