SECTION 4.1

INFERENCE The purpose of a sample is to give us information about a larger population. The process of drawing conclusions about a population on the basis of a sample is called inference. Sample results are only ESTIMATES of the truth about the population. If we select two samples at random from the same population, we will almost certainly choose different individuals and the sample results will defer by chance.

INFERENCE So, why can we trust random samples? The results still obey the laws of probability. These laws allow us to say how likely it is that our sample results are representative of the population. Results from random samples come with a margin of error that sets bounds on the size of the likely error. The margin of sampling error is the price you pay for not talking to everyone in your population group. It describes the range that the answer likely falls between if we had talked to everyone instead of just a sample.

INFERENCE NOTE: A margin of error is NOT a mistake. The margin of error compensates for the variability that results from taking a random sample. What is the benefit of increasing the sample size? Larger samples give better information about the population than smaller samples. By taking a larger sample, you can be confident that the sample result is very close to the truth about the population.

SAMPLE SURVEYS: WHAT CAN GO WRONG? Most sample surveys are affected by errors in addition to sampling variability. Good sampling technique includes the art of reducing all sources of error. Sampling often begins with a list of individuals from which we will draw our sample. This list is called a sampling frame. Ideally, the sampling frame should list every individual in the population.

UNDERCOVERAGE Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Examples: -An opinion poll conducted by calling landline telephones will miss households that have only cell phones. -The Literary Digest voter survey predicted that Alfred Landon would beat Franklin Roosevelt in the 1936 presidential election. The sample was drawn from telephone directories and car registration lists.

NONRESPONSE Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate. Example: In 1988, Shere Hite published a book entitles Women and Love: A cultural Revolution in Progress, in which she claimed that 70% of women who have been married five years or more are having extramarital affairs. Hite’s survey was sent to 100,000 women and her conclusions were based on the 4500 women who responded.

RESPONSE BIAS A systematic pattern of incorrect responses in a sample survey leads to response bias. There are many aspects of a survey that can lead to response bias, such as the gender of the interviewer and the order that the questions on a survey are asked in. However, the wording of questions is the most important influence on the answers given to a sample survey.

RESPONSE BIAS Wording of the questions: (aka “push polling”) The questions below are almost certain to produce different estimates: 1. Do you agree that abortion, the killing of innocent beings, should be outlawed? 2. Do you agree that there are circumstances under which abortion should be legal to protect the rights and well-being of the mother?

RESPONSE BIAS Example: A random sample of college students were asked the following 2 questions: “How happy are you with your life in general?” “How many dates have you been on in the past month?” There is almost no association between responses to the two questions when asked in this order. However, reverse the order and a much stronger relationship appears.