Binary data

Binary Data Basics
– A discrete variable with only one state contains zero information.
– The bit, with two possible values, is the standard unit of information.
– The number of states in a collection of n bits is 2^n.
– The number of states in a collection of discrete variables depends exponentially on the number of variables.
– Ten bits have more states (1024) than three decimal digits (1000).
– Binary data consists of categorical data with two possible values.
– Binary data is often used to represent the outcome of an experiment or a yes-no question.
– Binary data is nominal data and cannot be compared numerically.
– Binary data can also represent the presence or absence of a feature.
– Binary data can be used to represent political party choices in elections.

Binary Variables
– Binary variables have two possible values.
– Independent and identically distributed binary variables follow a Bernoulli distribution.
– Total counts of i.i.d. binary variables follow a binomial distribution.
– Binary data need not come from i.i.d. variables.
– The distribution of binary variables may not be binomial if they are not i.i.d.

Counting and Conversion of Binary Data
– Binary data can be converted to count data by assigning 1 for a value that occurs and 0 for a value that does not occur.
– Grouping binary data allows for counting the occurrences of each value.
– Binary data can be simplified to a single count by considering one value as success and the other as failure.
– Count data with n=1 is binary data.
– Counts of i.i.d. binary variables follow a binomial distribution.

Binary Regression
– Binary regression analyzes predicted outcomes that are binary variables.
– Binomial regression can be used when binary data is converted to count data.
– Logistic regression and probit regression are common methods for binary regression.
– Multinomial regression models counts of i.i.d. categorical variables with more than two categories.
– Non-i.i.d. binary data can be modeled using more complex distributions like the beta-binomial distribution.

Binary Representation and Formats
– 1 and 0 represent two different voltage levels.
– Computers understand 1 as higher voltage and 0 as lower voltage.
– Different methods can be used to store two voltage levels.
– Magnetic tapes with a coating of ferromagnetic material can store 1 and 0 data.
– The orientation of magnetic domains determines whether it is interpreted as 1 or 0.
– Textual data can be represented in binary format, such as compressed or formatted files.
– Image data can sometimes be represented in textual format, like the X PixMap image format.
– Binary formats are more specific for representing data without interpretation.
– Textual formats may include formatting codes and other text-related elements.
– The choice between binary and textual formats depends on the nature of the data.