Significant Testing - beginner help

[brupstar]

Hello, I'm not from a particularly statistical background - so my question may be quite basic and/or badly phrased!

I've been asked to calculate how many women are in our company UK office and compare it to the most recent UK census data. The figures below are just for example purposes:

UK - My company:
400 women / 800 men; 33.34% of company are women.

UK - Census (working population):
33,000,000 women / 34,000,000 men; 49.25% of uk working population are women.

I now want to know if my company is significantly underrepresented by women compared to the census data, or not. E.g. if my company had 48% women then I would assume this finding isn't significant and down to natural variation in distribution. However, if it was 10%, then that would presumably be a significant finding.

So my question is - what's the method to use for determining at what % the difference becomes significant or not?

I think I have to use a t-test or something, but I haven't done that in ages, so could someone please walk me through the calculation and any assumptions using the above example data?

Thank you

 

[Miner]

I recommend a 2-sample proportion test.

 

[fed2]

there are some famous examples of 'simpsons paradox' related to gender bias issues aren't there? https://en.wikipedia.org/wiki/Simpson's_paradox

 

[hlsmith]

Both nice comments above. As for @Miner - I always forget if in this scenario they have the population and a sample so z-tests are needed??? I never remember these rules since I never have pop level data/estimates.

@fed2 comment would likely bring up the Berkeley scenario with admissions, but I would also like to comment that your workforce represents a certain subsection of the population. Those with a certain age, education and physical ability to work. With broad comparisons to pop may reveal a spurious association in disproportions.

 

[Karabiner]

I now want to know if my company is significantly underrepresented by women compared to the census data, or not. E.g. if my company had 48% women then I would assume this finding isn't significant and down to natural variation in distribution. However, if it was 10%, then that would presumably be a significant finding.

It seems like there could be a confusion between significant ("relevant, important, impressive...") and
statistically significant?

A statistical test of significance will do nothing more than answer the question whether to reject the hypothesis
that the proportion of women in the population from which your sample was drawn is exactely 0.492500. It will
never answer the question of whether any difference beween your sample and the UK is relevant or important.

If you think that more than 10% is an important difference between your company and the UK, then you have
your answer already.

You could consider a statistical test of signficance if you have a question about a population in mind and if you
therefore want to treat your n=1200 employees as a sample from that population.

With kind regards

Karabiner