Read the comic at this link: https://xkcd.com/882/. (a) How many colors of jelly
ID: 3220113 • Letter: R
Question
Read the comic at this link: https://xkcd.com/882/. (a) How many colors of jelly beans were tested? How many colors turned out to be statistically significant? (b) What was the probability of type I error in each test? Based upon the probability of type I error, what percentage of tests would we naturally expect to give a statistically significant result when there really is no effect? (c) Summarize the dangers of publication bias, which results when only statistically significant results are published.Explanation / Answer
a) There are 20 colors tested and out of 20 colors, Green color jelly found causing acne.
These Scientists were trying to find whether there is a significant link between jelly causing acne. When they tried to check on the whole jelly they found that there is no significant link between jelly and acne. Then they checking each stratum based on the color. Then they found that Green color jelly has a significant link with acne. Let's look how I conclude saying that green jelly causes acne.
Scientist before conducting the research they framed the hypothesis as follows,
H0 = There is no significant link between Jelly and Acne
H1 = There is a significant link between jelly and acne.
After they perform the statistical test, they conclude it by saying P value. If the P value is less than 0.05 then we reject the null hypothesis.
b) The level of significance is the probability of type I error. The level of significance is 0.05 from the question. So, the probability of type 1 error is 0.05. And setting this level of significance is based on the scenario you are working. If it is health related research then scientist prefer the level of significance as 1% and when the risk-free research scientist comfortably goes with 10% of error.
c) When the null hypothesis is rejected case like Green jelly, p-value is lesser than the level of significance, we CANNOT say that alternative hypothesis is true because while hypothesis testing we conclude only by saying when P-value is less than level of significance, we reject the null hypothesis and we fail to reject the null hypothesis when P-value is greater than level of significance.
Likewise, publication goes bias when the sample is biased with the only acne causing green jelly, then obviously our test reject the null hypothesis. In this case, we need to carefully do sampling and conduct the hypothesis testing. And other cases, we might increase the sample size and crosscheck again the null hypothesis rejection.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.