Statistics: Descriptive, Inferential, Sampling & Data Types

Descriptive Statistics

Utilizes numerical and graphical methods to explore data, i.e., to look for patterns in a data set, to summarize the information revealed in a data set, and to present the information in a convenient form

inferential statistics

Involves drawing conclusions about populations from samples

Sample

A subset of the units or objects of a population that we have access to

Population

The entire set of units or objects we are interested in studying

Parameter

A summary measure calculated from a population, e.g., the proportion of voters who vote for a political candidate

Statistic

A summary measure calculated from a sample, e.g., the proportion of voters in our sample who support the political candidate

Quantitative Data

Measurements that are recorded on a naturally occurring numerical scale.

Qualitative Data

Measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories.

Ordinal Data

A type of qualitative data that groups variables into hierarchical categories, e.g., low to high or the rank order of the outcome

Observational Study

Used to investigate research questions based purely on what the researcher observes.

Randomized Experimental Design

Provides the greatest reliability and validity of statistical estimates of treatment effects.

Simple Random Sample

Every individual or item from the frame has an equal chance of being selected.

Stratified Random Sample

Involves dividing a population into smaller subgroups called strata based on specific characteristics such as race, gender identity, location, etc.

Cluster Sample

A method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed

Judgement Sample

Units selected by expert judgment

Convenience Sample

Units selected by ease of selection

Frequency Table

Lists the individual categories together with their respective counts or frequencies (Is one of the simplest ways to describe qualitative data)

Bar Chart

A visual display of a frequency table, where the counts or percentages are displayed as bars

Pie Chart

An alternative visual display where the relative frequencies are displayed as slices of a pie

Dot Plot

A simple form of data visualization that consists of data points plotted as dots on a graph (Also known as a strip plot)

Stem-and-leaf Display

A display where each data value is split into a "leaf" and a "stem" (The "stem" groups the scores and each "leaf" indicates a score within that group)

Scatterplot

A useful visualization of the relationship between two quantitative variables.

Time Plot

A graphical display used to show trends and changes in the data over time

Mean

The sum of the values divided by the number of values contained in the data set

Median

The middle number when the measurements are arranged in ascending (or descending) order

Mode

The measurement that occurs most frequently in the data set

Range

Is equal to the largest measurement minus the smallest measurement (largest value - smallest value)

Variance

The average squared deviation of a set of numbers from its mean

Standard Deviation

The positive square root of the variance

Percentile

Descriptive measures of the relationship of an observation to the rest of the data

Quartile

Percentiles that partition a data set into four categories, each category containing exactly 25% of the measurements,

Z-Score

Measures the distance between a given value x and the mean, expressed in standard deviations

IQR

The difference between the upper and lower quartiles

Measures of Central Tendency

Mean, median, and mode

Measures of Variability

range, IQR, variance, standard deviation

Measures of Relative Standing

Percentile, Quartiles, Z-Score