Statistics
Chapter 1
Why is my evil lecturer forcing me to learn statistics?
Initial observation: finding something that needs explaining
To see whether an observation is true, you need to define one or more variables to measure that quantify the thing you’re trying to measure.
Generating and testing theories and hypotheses
A theory: an explanation or set of principles that is well substantiated by repeated testing and explains a broad phenomenon.
A hypotheses: a proposed explanation for a fairly narrow phenomenon or set of observations.
An informed, theory-driven attempt to explain what has been observed.
A theory explains a wide set of phenomena with a small set of well-established principles.
A hypotheses typically seeks to explain a narrower phenomenon and is, as yet, untested.
Both theories and hypotheses exist in the conceptual domain, and you cannot observe them directly.
To test a hypotheses, we need to operationalize our hypotheses in a way that enables us to collect and analyse data that have a bearing on the hypotheses.
Predictions emerge from a hypotheses. A prediction tells us something about the hypotheses from which it derived.
Falsification: the act of disproving a hypotheses or theory.
Collecting data: measurement
Independent and dependent variable
Variables: things that can change
Independent variable: a variable thought to be the cause of some effect.
Dependent variable: a variable thought to be affected by changes in an independent variable.
Predictor variable: a variable thought to predict an outcome variable. (independent)
Outcome variable: a variable thought to change as a function of changes in a predictor variable (dependent)
Levels of measurement
The level of measurement: the relationship between what is being measured and the number that represent what is being measured.
Variables can be categorical or continuous, and can have different levels of measurement.
A categorical variable is made up of categories.
It names distinct entities.
In its simplest form it names just two distinct types of things (like male or female).
Binary variable: there are only two categories.
Nominal variable: there are more than two categories.
Ordinal variable: when categories are ordered.
Tell us not only that things have occurred, but also the order in which they occurred.
These data tell us nothing about the differences between values. Yet they still do not tell us about the differences between point scale.
Continuous variable: a variable that gives us a score for each person and can take on any value on the measurement scale that we are using.
Interval variable: to say that data are interval, we must certain that equal intervals on the scale represents equal differences in
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