3.7 Confidence intervals

Our models predict that there are 1.35 more DNMs for additional every year of paternal age, and 0.38 more DNMs for every additional year of maternal age. Does this mean that sperm and oocytes accumulate DNMs at different rates?

The maternal and paternal slopes look different, but we need statistical evidence that they actually are. (For example, what if there’s a lot of variability in the maternal DNM data, and the true maternal coefficient could be anywhere between -1 and 10?)

To do this, we compare the confidence intervals of our slope estimates.

What is a confidence interval?

We use confidence intervals when estimating a value – in this case, the Mother_age and Father_age slope parameters.

A confidence interval (CI) is a random interval that has a 95% probability of falling on the parameter we are estimating. So, a 95% CI contains the true value of the slope 95% of the time.

Keep in mind that the definition above (95% of random intervals fall on the true value) is not the same as saying there is a 95% chance that the true value falls within our interval. This latter statement is not accurate.

In R, we get the confidence interval of a parameter from a linear model with the confint function.

?confint

confint requires three arguments:

A fitted linear model (our fit_pat variable)
The parameter we want a CI for (Father_age)
The CI’s probability (typically 95%)