Reducing accuracy based on audience requirements

For some calculations, a fraction value may be more intuitively meaningful than a floating point value. This is part of presenting statistical results in a way that an audience can understand and take action on.

For example, the chi-squared test generally involves computing the  comparison between actual values and expected values. We can then subject this comparison value to a test against the  cumulative distribution function. When the expected and actual values have no particular relationship (we can call this a null relationship) the variation will be random;  the value tends to be small. When we accept the null hypothesis, then we'll look elsewhere for a relationship. When the actual values are significantly different from the expected values, we may reject the null hypothesis. By rejecting the null hypothesis, we can explore further to determine the precise nature of the relationship.

The decision is often based on the table of the  Cumulative Distribution Function (CDF) for selected  values and given degrees of freedom. While the tabulated CDF values are mostly irrational values, we don't usually use more than two or three decimal places. This is merely a decision-making tool, there's no practical difference in meaning between 0.049 and 0.05.

A widely used probability is 0.05 for rejecting the null hypothesis. This is a Fraction object less than 1/20. When presenting data to an audience, it sometimes helps to characterize results as fractions. A value like 0.05 is hard to visualize. Describing a relationship as having 1 chance in 20 can help people visualize the likelihood of a correlation.

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