I see these two very often. I will write them both out than give the answer.
(Note: They are all made up scenario’s and made up numbers but assume they are true)
- A US Army recruiter is trying to convince NYC residents to join the Iraq war. He states that the death rate in the Iraq war for US soldiers the past 10 years was 5 per 1,000, while the death rate in NYC for the same period was 15 per 1,000. Therefore, you are less likely to die going to fight in Iraq than living in NYC.
- An author is writing about the rise of small businesses in America. He defines a small business as any company that hires less than 50 employees. He states that the amount of small businesses in America was 30 million in 2008 compared to 35 million by the end of 2018. Therefore, small businesses are on the rise.
Statistical Fallacy #1
The army recruiter is not comparing the same two groups. The death rate in NYC has very old people, very sick people and infants. Those in the army are between the ages of 18-35. The army recruiter is not comparing like for like.
Statistical Fallacy #2
Never use absolute numbers. Always use percentage. If there was 100 million businesses in 2008, the percentage of small businesses would be 30%. If in 2018, there was a total of 150 million businesses the percentage of small businesses would be 23%.
Changes in the subject matter and changes in which the data is collected is another one I see a lot. Is cancer on the rise, or are we getting more accurate reports and diagnosis? Is heart disease on the rise, or are changes happening in the classification of what constitutes death by heart disease? Is the temperature of the earth really increasing, or are we getting better at measuring it with more and more temperature recording devices?