can statistics be misused? explain with two examples
Answers
Answer:
Yes
Explanation:
Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. The false statistics trap can be quite damaging for the quest for knowledge. ... For example, in medical science, correcting a falsehood may take decades and cost lives.
example:
- Statics can trick the casual observer into believing something other than what the data shows
Answer:
Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. The false statistics trap can be quite damaging for the quest for knowledge. ... For example, in medical science, correcting a falsehood may take decades and cost lives.
say 1 out of 100,000 people in the general population have some particular cancer. and suppose a test has a sensitivity of 95%— that is, of 100 people that have the disease, the test will correctly identify 95 of them (and 5 people who actually have the disease the test will falsely say are negative for it). and suppose that test also has a 95% specificity— that is, of 100 people who do NOT have the disease, the test will correctly report a negative result for 95 of them (and will incorrectly show positive for 5 people who really don’t have the disease).
what people don’t realise is _how IMPORTANT_ the overall rate of occurrence is. if only 1 in 100k people have the disease, then in a million people, ten will actually have the disease. but our test gives a false positive in 5% of cases; therefore, of a million people tested, 95% of those with the disease will be correctly identified (10 people have the disease, 9 of whom will correctly test positive for it); but 5% of those WITHOUT the disease also will test positive for it. there are 999,990 people WITHOUT the disease in our sample, and 5% of them, or almost 50k people will falsely test positive. if you receive a positive test result for something that is very rare in the population, even WITH a POSITIVE test result, statistically you still are quite unlikely actually to have the disease!
when you consider that being a terrorist also is quite rare, and that our detection tests for terrorists may flag a lot of false positives, this statistical concept shows you that MOST people flagged as terrorists in fact are NOT.
this is just one of many awesome and practical math ideas you will learn from dr. john allen paulos’s books!!