## What is a diffusion index?

A diffusion index is a measure used to show the dispersion of change from a reference point, and a data series can demonstrate whether there are upward or downward trends.

Diffusion indices are commonly used to highlight the results of a survey. The answers are in the form of values and based on these values a base number is designated. Many indicators use a baseline of 0, 50, or 100. A data series shows how far the results are from the baseline. While a data point not far from the base number would indicate little change, a data point far from the base could suggest significant change.

In economics, the diffusion index is used in the formulation of indicators, such as the purchasing managers indices and the Richmond Manufacturing Index. Unlike economic indicators, in which data is based on prices or units, those that use a diffusion index are based on surveys. And depending on the wording of the survey questions, the Diffusion Index can be used as a predictive tool, similar to how the PMI is considered a leading economic indicator.

## How to Calculate a Diffusion Index

There are different ways to calculate a diffusion index, and the formula can be in long or short form.

### Federal Reserve Formula

The Federal Reserve uses the basic formula to calculate a diffusion index. This formula is used in the calculation of indices for many indicators among the 12 regional Fed banks, including the Richmond and Kansas City Fed surveys.

Diffusion index = [100 * (I − D)] / (I+N+D)

I = Number of respondents reporting increases

N = Number of respondents reporting no change

D = Number of respondents reporting declines

### IHS Markit formula

IHS Markit, a research group that publishes purchasing managers’ indices in the United States and other countries, has its own formula, different from the Fed’s.

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## TheStreet Dictionary Terms

IHS Markit Diffusion Index = (% reporting ‘High’) + [0.5 * (% Reporting ‘the Same’)] + [0.0 * (% Reporting ‘Down’)]

This can be expressed in abbreviated form as follows:

Index = percentage of positive responses + 0.5 (percentage of neutral responses)

## Example of diffusion index

For example, for a sample survey question on whether the economy will soon enter a recession, the results showed that 70% of respondents answered there was a high probability, 20% answered that there was no probability and 10% answered that there was a low probability.

If the results were entered into the Fed’s formula for the Diffusion Index, it would be calculated as:

[100 * (0.70 − 0.10)] / (0.70 + 0.20 + 0.10) = 60 / 1 = 60

If calculated using the IHS Markit formula, the answer would be:

0.70 + (0.5 * 0.20) + (0.0 * 0.10) = 0.70 + 0.10 + 0.00 = 0.80

The results differ for one or the other depending on the formula used. Assigning a baseline of 0 or 100 would be ideal in this example because the answer could be manipulated to double digits.

## How to interpret a diffusion index

A data series could show the momentum and reveal if there are uptrends and downtrends. Data above the baseline would indicate expansion, while data below would indicate contraction. Data near or close to the baseline would mean little or no change.

An example chart below illustrates a data series showing expansion and contraction. The farther the data is from the baseline, the greater the likelihood of expansion or contraction over a given period.

## What are the limits of a diffusion index?

A diffusion index can represent a one-sided view. Thus, comparing the Diffusion Index to other data sets can provide additional confirmation or refute a conclusion reached using a Diffusion Index. Using other measures, such as the correlation coefficient, can show whether a diffusion index is a reliable prediction tool.