How do we get samples?

• We want a sample that represents our population.
• Representative samples reflect the relevant characteristics of our population.
• In general, we get representative samples by selecting our samples at random and with an adequate sample size.

A non-representative sample is said to be biased.

Ex: A sample of chihuahuas to represent all dogs.

These can be a result of convenience sampling, choosing a sample based on ease.

Common sources of bias in our daily lives:

• Anecdotal evidence is data based on personal experience or observation.
  • Typically this consists of only one or two observations and is NOT representative of the population.
• Availability bias is your brain’s tendency to think that examples of things that come readily to mind are more representative than is actually the case.

• We avoid bias by taking random samples.
• One type of random sample is a simple random sample.
  • We can think of this as “raffle sampling”, like drawing names out of a hat.
  • Each case (or each possible sample) has an equal chance of being selected.
  • Knowing that A is selected doesn’t tell us anything about whether B is selected.
• Instead of literally drawing from a hat, we usually use a random number generator from a computer.

When we do research, we have two options:

1. Conduct an experiment, where researchers assign treatments to cases.
1. Treatments are experimental conditions.
2. In an experiment, cases may also be called experimental units (items or individuals on which the experiment is performed).
2. Conduct an observational study, where no conditions are assigned. These are often done for ethical reasons, like examining the impacts of smoking cigarettes.

Experiments allow us to infer causation. Observational studies do not.

• Control: two or more treatments are compared.
• Randomization: experimental units are assigned to treatment groups (usually and preferably at random).
• Replication: a large enough sample size is used to test each treatment many times (on many different experimental units).
• Blocking: if variables other than treatment are likely to have an impact on study outcome, we use blocks.

An experiment without blocking has a completely randomized design; an experiment with blocking has a randomized block design.

In an experimental setting, we talk about

• Response variable: the characteristic of the experimental outcome being measured or observed.
• Factor: a variable whose impact on the response variable is of interest in the experiment.
• Levels: the possible values of a factor.
• Treatments: experimental conditions (based on combinations of factor levels).

In human subjects research, we do a little extra work:

• If subjects do not know what treatment group they are in, the study is called blind.
• We use a placebo (fake treatment) to achieve this.
• If neither the subjects nor the researchers who interact with them know the treatment group, it is called double blind.

This helps avoid bias caused by placebo effect, doctor’s expectations for outcome, etc.!

A study published in 2009 sought to examine whether supplementing with chia seeds contributed to weight loss. Researchers recruited 76 individuals and randomly assigned them into either a treatment group or a control group. The treatment group was given a set quantity of daily chia seeds; the control group was given a placebo. At the end of the 12-week study, they found no difference in average weight lost between the treatment and control group.

1. Is this an observational study or an experiment? Explain.

2. Identify the (a) cases and (b) response variable.