## The IFoA long qualification process: some evidence that it is slightly longer for women (by about half a year)

by Patrick Lee on 01 May 2023 in categories actuarial with tags ifoa lifelong learning mathsHere are the results split by sex in table form:

Distribution of Fellowship Travel Time by Sex

and graphically, first via histograms:

Histograms of Fellowship travel time by sex

and secondly by Box Whisker charts (the blue shaded boxes show the interquartile range, **which really ought to be what the IFoA mentions when it says "most people qualify within"**):

Box & Whisker charts of Fellowship travel time by sex

Note that the medians and means for women are slightly higher (6.58 and 7.74 years), than those for men, (6.17 and 7.21 years), so by about half a year.

The question is whether this difference is statistically significant. The IFoA should provide an analysis of the full dataset.

In the meantime, one way of looking at this is to take the male distribution and simulate it 10,000 times for the female sample size of 112. That gives us 10,000 populations of 112 each. For each of these we can calculate the median qualification time.

That then gives us 10,000 medians from a population size of 112, which we can sort in order.

We can then look to see where the current female median of 6.58 years fits in that sorted list.

**I did that, and 6.58 appears at around the 89% percentile.**

In other words, the difference is statistically significant at the 11% level, but not at a 5% level.

**My conclusion is that the difference is not large enough to be clearly statistically significant, but the 11% level is large enough to warrant more investigation.** **I urge the IFoA once again to publish the full data, which has much larger samples**.