Sunday 4 June 2017

Reading notes: Statistics 101 (Part 1)

Learning from Andy Field, on my daily travelling between Jurong East MRT Station and Expo MRT Station

Overview
From an initial observation, explanations, or theories are generated for those observations, from which predictions (hypotheses) can be made. This is where the data come into the process because to test those predictions data are needed.
- First, collect some relevant data (i.e. identify things that can be measured) and then analyse those data.
- The analysis of the data may support the theory or give the cause to modify the theory.
- As such, the processes of data collection and analysis and generating theories are intrinsically linked: theories lead to data collection/analysis and data collection/analysis informs theories.

In the process of generating theories and hypotheses, data are important for testing hypotheses or deciding between competing theories. In essence, two things need to be decided: (1) what to measure, and (2) how to measure it.

To test hypotheses we need to measure variables.
Variables are just things that can change (or vary); they might vary between people (e.g., IQ, behaviour) or locations (e.g., unemployment) or even time (e.g., mood, profit, number of cancerous cells).

The key to testing scientific statements is to measure a proposed cause (the independent variable) and a proposed outcome (the dependent variable).

Independent variable: A variable thought to be the cause of some effect. This term is usually used in experimental research to denote a variable that the experimenter has manipulated.
== Predictor variable: A variable thought to predict an outcome variable. This is basically another term for independent variable .

Dependent variable: A variable thought to be affected by changes in an independent variable. You can think of this variable as an outcome.
==Outcome variable: A variable thought to change as a function of changes in a predictor variable; aka dependent variable.

Levels of measurement
Variables can be split into categorical and continuous, and within these types there are different levels of measurement:
1. Categorical (entities are divided into distinct categories):
1.1 Binary variable: There are only two categories (e.g., dead or alive).
1.2 Nominal variable: There are more than two categories (e.g., whether someone is an omnivore, vegetarian, vegan, or fruitarian).
1.3 Ordinal variable: The same as a nominal variable but the categories have a logical order (e.g., whether people got a fail, a pass, a merit or a distinction in their exam).

2. Continuous (entities get a distinct score):
2.1 Interval variable: Equal intervals on the variable represent equal differences in the property being measured (e.g., the difference between 6 and 8 is equivalent to the difference between 13 and 15).
2.2 Ratio variable: The same as an interval variable, but the ratios of scores on the scale must also make sense (e.g., a score of 16 on an anxiety scale means that the person is, in reality, twice as anxious as someone scoring 8).

Two measurement-related issues
1. Standard units of measurement
2. Difference in results between studies.

One way to try to ensure that measurement error is kept to a minimum is to determine properties of the measure (validity and reliability) that give us confidence that it is doing its job properly.
Validity: whether an instrument actually measures what it sets out to measure. Reliability: whether an instrument can be interpreted consistently across different situations.

Criterion validity: whether an instrument measures what it claims to measure through comparison to objective criteria.
- In an ideal world, you assess this by relating scores on your measure to real-world observations.

== Concurrent validity: a form of criterion validity where there is evidence that scores from an instrument correspond to concurrently recorded external measures conceptually related to the measured construct.

== Predictive validity: a form of criterion validity where there is evidence that scores from an instrument predict external measures (recorded at a different point in time) conceptually related to the measured construct.

- Assessing criterion validity (whether concurrently or predictively) is often impractical because objective criteria that can be measured easily may not exist.
- With attitudes it might be the person’s perception of reality rather than reality itself that you’re interested in.

Content validity: evidence that the content of a test corresponds to the content of the construct it was designed to cover.

Validity is a necessary but not sufficient condition of a measure.
A second consideration is reliability, which is the ability of the measure to produce the same results under the same conditions.
To be valid the instrument must first be reliable.
The easiest way to assess reliability is to test the same group of people twice: a reliable instrument will produce similar scores at both points in time (test–retest reliability).
Sometimes, however, you will want to measure something that does vary over time.

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