Insignificant coefficient close to zero: to round or not to round?

[Parul Gupta]

Some of my regression coefficients are quite small and significant. For example, one is -0.00003. Should I:

1. round it to zero?
2. leave it as it is?
3. write is as -0?

My other coefficients have 2 or 3 decimal places, so in the interest of uniformity in presentation, should I format all of them with the same number of decimals?

[Dirk Enzmann]

Your question cannot be answered without in-depth knowledge of the substance matter (i.e., your question is, if anything, only secondarily a statistical question): What does the model predict and in what unit? Dollar amounts, distances in kilometers, times in milliseconds, averages of 5-point Likert scale items, percentages, proportions, “unitless” z-scores? And the same question must also be answered for the predictors.

Take as an exercise mean values of 5-point Likert scale items as predictors: Experiment with different scalings/transformations: (1) the original mean values of the items, (2) percent of maximum possible scores (POMP) (Cohen et al. 1999), in the range from 0 to 100, (3) proportion of maximum possible scores in the range from 0 to 1, (4) z-scores (mean = 0, standard deviation = 1), and (5) z-scores divided by 2 standard deviations (mean = 0, standard deviation = 0.5), and compare the results. You can repeat this exercise with different scaling/transformations of the outcome variables.

Have a look at Cohen et al. (1999).

Reference:
Cohen, P., Cohen, J., Aiken, L. S., & West, S. G. (1999). The problem of units and the circumstance for POMP. Multivariate Behavioral Research, 34, 315–346.

[Richard Williams]

You might want to consider rescaling some variables. For example, if you have income in dollars, you can divide income by 1000 and have income in thousands of dollars. The coefficients will get multiplied by 1,000 and likely be easier to read and more interpretable.

[Richard Williams]

The post title says insignificant but the first post says significant. I’d definitely want variables I considered significant and important to be reported to enough decimal places so as to get a good feel for their effects. A reported coefficient of .000000 that is statistically significant at the .01 level is pretty enigmatic!

[Parul Gupta]

Sorry, there is a typo in the post. Some of the coefficients are "small but insignificant".

The variables with these small coefficients are scores on a quality index, so they are unitless.

[Joseph Coveney]

Some of my regression coefficients are quite small and [not statistically] significant. For example, one is -0.00003. Should I:

1. round it to zero?
2. leave it as it is?
3. write is as -0?

[Added:]The variables with these small coefficients are scores on a quality index, so they are unitless.

If you cannot scale the predictor, as Dirk and Richard have suggested, and still have your audience will understand its regression coefficient, then leave the coefficietn as-is. Regardless, append the coefficient's standard error demarcated by a plus-minus sign, e.g., -0.00003 ± 0.00006

My other coefficients have 2 or 3 decimal places, so in the interest of uniformity in presentation, should I format all of them with the same number of decimals?

No. It would look amateurish. I've seen rules of thumb that suggest using, say, one-third its standard error for choosing the number of decimal places for a given regression coefficient.

You can get uniformity in presentation by justification. Again, append each coefficient's standard error after a plus-minus sign and justify the coefficients on that sign for uniformity of presentation.

[Parul Gupta]

Thanl you Joseph.