P&SIA L1 C4 S5

ntro Stats Islamic Approach -- Part 2 Prob & Stats

Lecture 1 Random Samples, Concept 4: Simple Random Samples

S5: The Biggest Sample Which Led to the Biggest Mistake in history of polls

Even very small Random Samples are (usually) representative of the population. Even VERY LARGE samples which are not random may not be representative at all. Here is a real world example of a catastrophic mistake in a very large sample.

In 1936, Franklin Delano Roosevelt was completing his first term of office as president of the us. It was an election year, and the Republican candidate was Governor Alfred Landon of Kansas. The country was struggling to recover from the Great Depression. There were still nine million unemployed: real income had dropped by one-third in the period 1929-1933 and was just beginning to turn upward. But Landon was campaigning on a program of economy in government, and Roosevelt was defensive about his deficit financing.

The Nazis were rearming Germany, and the Civil War in Spain was moving to its hopeless climax. These issues dominated the headlines in the New York Times, but were ignored by both candidates. Most observers thought Roosevelt would be an easy winner. Not so the Literary Digest magazine, which predicted an overwhelming victory for Landon, with Roosevelt getting only 43% of the popular vote. This prediction was based on the largest number of people ever replying to a poll-about 2.4 million individuals. It was backed by the enormous prestige of the Digest, which had called the winner in every presidential election since 1916. However, Roosevelt won the 1936 election by a landslide-62% to 38%. (The Digest went bankrupt soon after.)

Here is an amazing example, which has a lot to teach us. The Literary Digest Poll got responses from 2.4 MILLION people. In this sample, Roosevelt got only 43% of the vote, While Landon got an easy victory with 57% majority. HOWEVER, the reality was VERY different. In the real election, Roosevelt got 62% and Landon only got 38% -- Why was there such a HUGE error, when the Literary sample size was so extremely large? ANSWER -- Literary Digest sample WAS NOT A RANDOM SAMPLE. It was chosen by sending letters to readers of Literary Digest and asking them to respond. This is sometimes called a SAMPLE OF CONVENIENCE. Samples of convenience NEED NOT BE REPRESENTATIVE of the population, like Random Samples are.