STAT1008 Study Guide - Final Guide: Simple Random Sample, Dependent And Independent Variables, Sampling Bias
Collecting Data
• Data are a set of measurements taken on a set of individual units.
1.1 The Structure of Data
• Cases - the subjects/objects that we obtain information about.
• Variable - any characteristic that is recorded for each case.
• Each case makes up a row in a dataset, and each variable makes up a column.
• Can be categorical or quantitative variables.
• If using one variable to help understand or predict values of another variable, we call the
former the explanatory variable and the latter the response variable.
1.2 Sampling From a Population
• Population - all individuals or objects of interest.
• Sample - a subset of the population.
• Statistical inference - using data from a sample to gain information about the population.
• Sampling bias - occurs when the method of selecting a sample causes the sample to
inaccurately reflect the population in some relevant way.
• Simple random sample - each unit of the population has an equal chance of being selected.
• Other forms of bias – leading questions, context and inaccurate responses.
1.3 Experiments and Observational Studies
• Association - two variables are associated if values of one variable tend to be related to the
values of the other variable, eg: hot weather increases the price of drinks.
• Association does not imply causation.
• Causation - two variables are causally associated if changing the value of the explanatory
variable influences the value of the response variable, eg: smoking causes lung cancer.
• Confounding variables - a third variable that can offer a plausible explanation for an
association between the explanatory variable and the response variable.
• Eg: People who own a yacht are more likely to buy a sports car – confounding variable=wealth.
• Whenever confounding variables are present, a causal association cannot be determined.
• Experiment - a study in which the researcher actively controls one or more of the explanatory
variables.
• Observational study - a study in which the researcher does not actively control the value of
any variable but simply observes the values as they naturally exist.
• Observational studies can almost never be used to establish causality.
Randomisation
• Randomised experiment - randomly assign values of the explanatory variable for each unit, to
avoid confounding variables, eg: use technology or pull names out of a hat.
• If a randomised experiment yields an association between the two variables, we can establish
a causal relationship from the explanatory to the response variable.
• Control group – critical for comparison in a randomised experiment to establish causation, eg:
placebo or double-blinding (neither participant or researcher knows which treatment patient
is getting).
• Matched pairs experiment - each case gets both treatments in a random order and we
examine individual differences in the response variable between the two treatments.
• Randomised comparative experiment - we randomly assign cases to different treatment
groups and then compare results on the response variables.
• Treatment – the different levels of the explanatory variable.
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Document Summary
Collecting data: data are a set of measurements taken on a set of individual units. If using one variable to help understand or predict values of another variable, we call the former the explanatory variable and the latter the response variable. 1. 2 sampling from a population: population - all individuals or objects of interest. Statistical inference - using data from a sample to gain information about the population. Sampling bias - occurs when the method of selecting a sample causes the sample to inaccurately reflect the population in some relevant way. Simple random sample - each unit of the population has an equal chance of being selected: other forms of bias leading questions, context and inaccurate responses. Randomisation: randomised experiment - randomly assign values of the explanatory variable for each unit, to avoid confounding variables, eg: use technology or pull names out of a hat.
