Question

Explain weighted factor analysis using concrete examples of weighted factor analysis from an unrelated topic useful if this concept is not familiar to you (the student). For example, what factors are considered when buying a new car? How much weight is each factor given?

Answer 1

`Hey,

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A statistical weight is an amount given to increase or decreased the importance of an item. For example, weights are commonly given for tests and exams in class. For example, a final exam might count for double the points (double the “weight”) of an in-class test.

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 weighted mean formula uses a weighting factor, w_i.

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.

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