# How to interpret increases in percentage with different sample groups

Apologies if this question is not worded very well - this is not really my field of expertise but I'd like to see how to correctly understand some data.

Let's say I am studying the increase in cases of a disease over the last 100 years. I am comparing two different ethnicities, to see if one of them is more susceptible to the disease. The data I have is as follows; for the purposes of the example let's assume that all other factors are equal:

1917: General population consists of 70% Ethnicity A, 30% Ethnicity B

1917: 10% of Ethnicity A contracts the disease during their lifetime

1917: 30% of Ethnicity B contracts the disease during their lifetime

2017: General population consists of 60% Ethnicity A, 40% Ethnicity B

2017: 30% of Ethnicity A contracts the disease during their lifetime

2017: 60% of Ethnicity B contracts the disease during their lifetime

I can make two observations:

1. The percentage of infection has doubled in Ethnicity B, and tripled in Ethnicity A.

2. There is a 30 percentage point increase in Ethnicity B, but only a 10 percentage point increase in Ethnicity A

To someone who has a limited grasp of statistics and data analysis (i.e. me), these two outcomes seem contradictory - observation 1 indicates that Ethnicity A is worse off than Ethnicity B with regard to the rate of increase, while observation 2 seems to indicate the reverse.

From a data analysis and statistics point of view, what is the correct approach to take to determine the significance of the respective increase in percentages?

Also, does the changing ratio of ethnicities in the general population also affect how I should interpret the results?

• Hi Welcome to Economics.SE! It seems like this question isn't focused on economics. If it is can you add some details to the question?
– EconJohn
Commented Oct 11, 2017 at 2:20
• To be honest I have no idea which section of SE this question belongs in. I figured statistics and data analysis might land under the economics umbrella, but perhaps not? If you can suggest where it might be better posted I'll happily pack up and head over there! Commented Oct 11, 2017 at 5:55
• Perhaps I misunderstand your point, but why are they contradictory statements? Is it because the decease is lethal and you'd expect a reduction in the infected population? Commented Oct 11, 2017 at 10:08
• You might try CrossValidated.SE. That's the statistics site. I'm not sure of what their standards are or how this question might fit or potentially need modifications. Commented Oct 18, 2017 at 21:34
• I'm voting to close this question as off-topic because it's not about economics Commented Oct 21, 2017 at 15:30

If you ask me your question is better suited to cross validated (stats.stackexchange.com).

Anyway you're probably confused because the percentages refer to different base lines. Note that the 60% of disease at B in 2017 refers to 40% of the population, whereas the 30% in 1917 refers to 30% of the population, so they are hard to compare.

Try working it out in absolute numbers to get a clearer picture:

In 1917 if there are 100 people, 70 of ethnicity A, 30 of B. Of the 70 people of A 7 (10% of 70) get sick, of B 9 get sick (30% of 30)

In 2017 there are 100 people, 60 of ethnicity A, 40 of B. Of the 60 people of A now 18 catch the disease (30% of 60), and of B 24 catch the disease (60% of 40).

Observations: overall sickness has increased (16 vs 42). The absolute increase in sick B people (15) is larger than that in A people (11), but this in part due to the fact that there are more B people now

• Thanks - both for the answer, and for the pointer on where I should have posted. Commented Oct 12, 2017 at 0:43