Statistical Definitions

Potential statistical scenarios:

~~Sampling distribution of the statistic that estimates the parameter.~~
~~Confidence interval prodecure to estimate the parameter to within an interval of possibilities.~~
Hypothesis test procedure to test whether the parameter equals a specified value.

For clarity below are some of the definitions the statistics in CerebUnit is based upon.

definition of sample data vs observation

Sample data

Data that have been collected when measurements have been taken from a subset of a population.

Observation or observation unit

Individual entity in a study. An individual measurement.

definition of a variable

A variable

A characteristic that may differ among individuals.

types of variable

Categorical variable

Raw data consists of category (groups) names that don't necessarily have any logical ordering.

Ordinal variable

Ordered categorical variable.

Quantitative variable

Raw data of numerical measurements or counts taken on each individual.

types of variable

Two-way table (contingency table)

Table of counts of individuals falling into each possible combination of categories of two categorical variables.

Row percentages

Percentages within a row of a contingency table.

Column percentages

Percentages within a column of a contingency table.

Individuals in one sample are not coupled in anyway with individuals in other sample. Measurements in one sample are not related to the measurements in the other sample.

Parameters of interest for quantitative variable

Difference in two population means, μ₁ − μ₂.

random samples from two populations

Random samples are taken separately from two populations,
the same response variable is recorded from each individual.

one random sample then categorized into two populations

One random sample is taken,
a variable is recorded from each individual,
each individual is categorized as belonging to one or other population.

individuals randomly assigned to one of two treatment conditions

Randomly assign participants into one of two treatment conditions,
record same variable from each individual.

two random samples from a population

Two random samples taken from a population,
a separate variable is measured in each sample,
results are compared.

Samples taken as matched pairs because two values for a pair are not statistically independent.

Parameters of interest for quantitative variable

Population mean of paired difference, μ_d.

measured twice under different conditions or times

On each individual the same measurement is taken twice,
either under different conditions,
or at different times.

pair similar individuals with each receiving different treatments

Similar individuals are paired,
each pair member receives a different treatment,
same response variable is measured.

two different variables for each individual

For each individual two different variables are measured,
results are compared.

Statistical Definitions

1

Sample data and observation

2

Statistical variable

Variable types

3

Two-way table a.k.a contingency table

4

Independent samples

Random samples taken separately from two populations.

One random sample and categorization into two populations.

Individuals randomly assigned to one of two treatment conditions.

Two random samples taken from a population.

5

Dependent samples a.k.a paired data

Same measurement twice under different conditions or times.

Pair similar individuals with each receiving different treatments.

Two different variables measured for each individual.