The Will Rogers Phenomenon Statistical Paradox zwBmFZetWhY 00 02 54

[Music] before we discuss today's topic let's take a look at the following example there are two groups of numbers the first group contains numbers 1 to four and the second group contains numbers 5 to 9 the arithmetic mean of the first group is 2.5 and the arithmetic mean of the second group is 7 now let's move number five from the second group to the first group what will happen in the AR metic mean of two groups you can see the arithmetic mean values in two groups are both increased to three and 7.5 respectively intuitively we may think if we move some values from one group to another one the arithmetic mean of one group should go up and another one should go down but this example shows a totally different result this illustrates the famous Will Rogers phenomenon which was attributed to us comedian Will Rogers sometimes we may see Will Rogers phenomenon appear in the medical statistical data there is a term called medical stage migration which indicates that the everchanging illness detection technology will enable more illness to be detected in their early stage which causes the movement of those people from healthy to Patient groups from the statistical point of view for example there are two groups of people included in the medical statistics one group has two cancer patients whose estimated life expectancy is 40 years and 50 years old old another group has four healthy people whose estimated life expectancy is 60 70 80 and 90 years old the statistics show that the average life expectancy of both groups are 45 years and 75 years old now we have an advanced cancer detection technology which can detect cancer in its early stage in the group of healthy people the technology can help identify that the person whose estimated life expectancy is 60 is in the early stage of the cancer so this person will be moved from the healthy group to the patient group if we recalculate the average life expectancy of those two groups we will find that the numbers are increased in both groups to 50 years old and 80 years old respectively from this example we can see the lifespan statistics before and after a stage migration use different meanings of unhealthy as the cut off for detection is different also if you see the some reports saying that the patient group's life expectancy has increased it might not because there is a better treatment method instead it might because some patients are moved from the healthy group to the patient group due to the early detection of the disease thanks for watching if you like the video please hit the like button or subscribe button for more interesting topics [Music]