Lecture 1: Introduction to Statistics, Sampling and Data Representation

What is statistics?

The science of collecting, analyzing, interpreting, and presenting data.

Why is sampling important in statistics?

Studying an entire population is almost always impossible, so a well-chosen subset (sample) can produce a good estimate of the population parameter we are interested in knowing about, at a fraction of the cost and time.

What is a hypothesis in statistics?

A testable statement about a particular population parameter that is tested using data from a sample.

What sampling issue is present in Whitney & Melhaff’s 1987 study on feline “high-rise syndrome”?

The main issue is survivorship bias caused by using a sample of convenience. Only cats that were taken to the vet were included. Not all cats that fell were taken to a vet: some cats that fell from lower floors might not have been brought in, while cats falling from much higher floors could have died before reaching the vet. Because fatal falls from extreme heights were excluded from the data, the study made it look like cats survived higher falls better than lower ones, when it actually just missed the cats that died.

What is the difference between a sampling unit and an observational unit?

The sampling unit is what you select from the population; the observational unit is what you measure.

What is sampling error, and how does it relate to precision?

Sampling error (Error Type I) is the difference between your estimate of a given population parameter and its true value that occurs simply due to chance. It can be overcome by increasing sample size. A smaller sampling error means a more precise estimate, i.e., your measurements are very close to each other.

What is sampling bias, and how does it relate to accuracy?

Sampling bias (Error Type II) occurs when the sampling process systematically produces a sample that is not representative of the population. Increasing sample size will not fix the problem: it will just give more and more inaccurate data, i.e., measurements that are far from the true value.

Under what conditions is a sample considered random?

A sample is random when every unit in the population has an equal chance of being selected and the selection of units is independent.