Basic of statistics 2/RStudio: RMarkdown, Functions, data structures

quantitative variables (what are they? Be able to identify examples)

These variables take on numerical values (that represent a magnitude)

Examples include an individual's weight, the number of home runs hit in a baseball season, or an exam score.

qualitative variables (what are they? Be able to identify examples)

These variables represent a described quality or membership in a category.

Examples include eye color or a person's favorite food.

nominal scale (what is it? Be able to identify examples)

This scale labels observations into different categories with no quantitative or magnitude distinction between them.

Ex: car brands (Ford, Chevy, Toyota) are nominal because one is not inherently "more" or "less" than the other, and you cannot meaningfully calculate an average of these categories.

ordinal scale (what is it? Be able to identify examples)

Similar to nominal, but the categories are ranked in an order of magnitude.

While there is an ordering (e.g., academic degrees: High School < Associate's < Bachelor's), the difference between each rank has no quantifiable or consistent meaning.

interval scale (what is it? Be able to identify examples)

Each point on this scale is separated by an equal interval, and calculations like averages are meaningful.

However, it lacks a true "zero point" (a zero does not mean a complete absence of the variable in this sense), meaning you cannot meaningfully discuss ratios (e.g., 80 degrees Fahrenheit is not "twice as hot" as 40 degrees).

ratio scale (what is it? Be able to identify examples)

This scale has equal intervals and a true "zero point" representing a complete lack of the quality being measured.

This allows for meaningful ratios; for example, weight is a ratio scale because 20 lbs is exactly half of 40 lbs. Other examples include height, time, and age.

discrete variable (what is it? Be able to identify examples)

These variables can only take on specific, separate values (usually whole, countable numbers) with no intermediate values possible between adjacent points.

Rolling a die is an example, as you can only get a 1, 2, 3, 4, 5, or 6—never a 3.5.

continuous variable (what is it? Be able to identify examples)

These can take on any value within the scale's range, meaning there is always another possible value between any two given points. (3.5, 78.3, 28.1)

These are typically the result of measuring things, such as response time, height, or weight.

independent variable (what is it? Be able to identify in an example)

This is the variable manipulated by the experimenter to see if it causes an effect.

usually consists of the different conditions subjects are exposed to, such as a 70-degree room versus a 90-degree room in a study on memory.

dependent variable (what is it? Be able to identify in an example)

This is the variable that is measured to assess the effect of the independent variable.

In the room temperature example, the number of words recalled would be the dependent variable.

statistical notation (Know the different notation for sample vs. population mean

Mean: A population mean is denoted by the Greek letter mu (μ), while a sample mean is denoted by an X with a bar over it ( x).

Know the notation for the number of scores in a data set; Understand summation notation; Be able to solve simple summation examples)

Data set size: The number of scores is represented by N for populations (uppercase) and n for samples (lowercase).

Summation (Σ): The Greek letter sigma indicates the summation of a set of scores. In solving expressions, follow the order of operations: ΣX^2 means square each score then sum them, whereas (ΣX)^2 means sum the scores first, then square the total.

code chunks (what are they)?

These are specific areas in an RMarkdown (.rmd) file where you can enter and execute R code.

Any output generated by the code within these chunks will be included in the final knitted document.

what does adding two "white spaces" to the end of a text line accomplish in the PDF output of a knitted .rmd file?

Adding two spaces to the end of a line of text in an .rmd file forces a new line (line break) in the final PDF output.

Without these spaces, RMarkdown may combine adjacent lines of text into a single paragraph.

basic data types (how is a variable's data type determined? what are R's basic data types? examples of each?)

A variable's data type is automatically determined based on the value assigned to it. R's basic types include:

Numeric: Real numbers (e.g., 10.5).

Integer: Whole numbers (e.g., 34L).

Complex: Numbers with imaginary parts (e.g., 4+2i).

Character: Text strings (e.g., "Fred").

Logical: TRUE or FALSE.

how do you specify that a value is an integer rather than numeric?

To declare a value specifically as an integer rather than numeric, you must append an "L" to the number (e.g., 34L).

how do you specify a character string? (double quotes? single quotes?)

These must be enclosed in quotes. While single quotes work, double quotes are the preferred standard for this course.

functions (what are they? what are arguments? what are parameters?)

Functions are reusable blocks of code that perform specific tasks.

Arguments are the actual values you "pass" or send to a function to control its behavior.

Parameters are the internal variables defined by the function itself that receive those arguments.

arguments (what is passing "by position"? what is passing "by name"?)

By position: Arguments are provided in a specific order defined by the function; no parameter names are required.

By name: Arguments can be provided in any order, but you must include the parameter name followed by an equals sign (e.g., print(digits = 3, MyNum)).

RStudio: class() function (what does it do?)

This function is used to confirm or return the data type of a specific variable.

RStudio: print() function (what does it do? "digits" parameter? "quote"

parameter?)

digits parameter: Specifies the number of significant digits to display for numeric values.

quote parameter: A logical value (TRUE/FALSE) that determines if surrounding double-quotes should be shown when printing character strings.

R data structures (what is meant by the "dimensionality" of a data structure?

what is meant by the "homogeneity" vs. "heterogeneity" of a data structure?)

Dimensionality: Refers to whether a structure stores values in one dimension (like a row), two dimensions (rows and columns), or multiple dimensions.

Homogeneity vs. Heterogeneity: Homogeneous structures can only hold one data type (e.g., all numeric), while heterogeneous structures can hold multiple data types (e.g., a mix of numeric and character data).

R's basic data structures (Know the dimensionality and

homogeneity/heterogeneity of vectors and data frames)

Vector: One-dimensional and homogeneous.

Data frame: Two-dimensional (rows and columns) and heterogeneous; these are the most common structures for statistical data in R.