Ch1: Statistics and Samples

What is statistics?

Is to study methods to describe and measure aspects of nature from samples.

→ provides tools to quantify uncertainty of measures, allowing us to determine the amount of truth they hold.

When is statistics necessary?

It is necessary when you have limited information (a sample) but want to infer something about the population

What are the two primary goals of statistics?

1. Estimate the values of important parameters

2. Test hypotheses about these parameters

Define population and give an example

The entire collection of individual units that a researcher is interested in (e.g. all ubc students)

Define parameter and give an example

A characteristic of a population (e.g. average height)

What is the importance of an unbiased sample?

This ensures your findings accurately represent the entire population.

Why is it important to have a large sample size?

Large sample sizes = increased precision and reliability of results, and reduce the margin of error.

Why are replication studies important?

Replication studies are important because they validate findings, ensure scientific accuracy, and ensure data is not due to chance.

Why are experiments with random assignment of treatments not always used?

Random assignment may not be ethical, especially when studying injuries, diseases, etc.

Define a variable

A variable is a characteristic measured on individual (drawn from a population under study).

Define data

data = measurements of one or more variables on a collection of individuals

What is a response variable?

Aka dependent variable = the factor measured to see how it changes in response to manipulation.

What is a explanatory variable?

Aka independent variable = the factor that researcher observe to see if it influences/explains changes in another variable.

What is a mosaic plot?

A plot used to visually display categorical data, showing relationships between two or more variables.

What is the difference between parameters and estimates?

parameters = fixed, due to the value describing the population.

estimates = calculated from sample data to approximate those unknown population parameters.

Define Bias

Bias = a systematic tendency of a measurement process to over or under estimate the value of a true population characteristic (e.g. the 1936 US presidential election).

What is volunteer bias?

Volunteer bias = volunteers for a study are likely to be different, on average, from the population

→ prevents random sampling

What is considered accurate?

Getting the correct answer, on average

What is considered precise?

Getting a similar answer repeatedly

What is needed for a sample to be considered good?

1. sufficiently large

2. individuals have equal probability of being included (random sampling)

3. independent selection of individuals (random selection)

What is another way to describe a random sample?

Independent and identically distributed (i.i.d.)

What is independent sampling?

aka random sampling = the sample has no connection to another, and the selection is random.

What are some examples of non-independence?

cluster sampling, repeated measures (time-series data), and example (catching one fish may disturb the water effecting behavior of other fish)

What is absolute frequency compared to relative frequency?

absolute frequency = “how many?” - raw count of how many times an event occurs

relative frequency = “how common?“ - a proportion of the total times

What is the default frequency in R?

The absolute frequency

What is a sampling error?

Sampling error = the chance difference between an estimate and the population parameter being estimated.

trend → larger samples tend to have less sampling error.

What is the difference between bias and error?

bias = systematic discrepancy (tending in a certain direction)

error = random difference (not tending in any direction)