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Data, Variables, Hypothesis

This document provides an overview of key concepts in data analysis, including: 1) Data is organized in a matrix with observations as rows and variables as columns. 2) There are two types of variables - numerical/quantitative and categorical/qualitative. Numerical variables can be continuous or discrete. 3) Variables can be associated (dependent) if connected or independent if no evident connection. Hypothesis testing involves starting with a null hypothesis, conducting a test assuming it is true, and either rejecting or not rejecting the null in favor of the alternative hypothesis based on test results.

Data & Analytics◦
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+ Data Basics Slides edited by Valerio Di Fonzo for www.globalpolis.org Based on the work of Mine Çetinkaya-Rundel of OpenIntro The slides may be copied, edited, and/or shared via the CC BY-SA license
Data matrix Data are organized in what we call a data matrix, where each row represents an observation or a case, and each column represents a variable:
Types of variables There are two types of variables, numerical and categorical. Numerical, in other words quantitative, variables take on numerical values. It is sensible to add, subtract, take averages, et cetera, with these values. Categorical, or qualitative, variables. Take on a limited number of distinct categories. These categories can be identified with numbers. For example, it is customary to see the gender variable coded as zero for male and one for females, but it wouldn't be sensible to do arithmetic operations with these values. Numerical variables can further be categorized as continuous or discrete. Continuous numerical variables are usually measured, such as height. These variables can take on any number of infinite values given, within a given range. Discrete numerical variables are those that take on one of a specific set of numeric values where we're able to count or enumerate all of the possibilities. One example of a discrete variable is the number of cars a household owns. In general, count data are an example of discrete variables. Categorical variables that have ordered levels are called ordinal. Think about a survey question where you're asked how satisfied you are with the customer service you received. And the options are very unsatisfied, unsatisfied, neutral, satisfied, and very satisfied. These levels have an inherent ordering. Hence the variable would be called ordinal. If the levels of categorical variable do not have an inherent ordering to them, then the variable is simply called categorical.
Types of variables (cont.) gender - categorical sleep - numerical, continuous bedtime - categorical, ordinal countries - numerical, discrete dread - categorical, ordinal (could also be used as numerical)
Associated vs. independent ● When two variables show some connection with one another, they are called associated variables. ○ Associated variables can also be called dependent variables and vice-versa. ● If two variables are not associated, i.e. there is no evident connection between the two, then they are said to be independent.
Hypothesis Testing Framework ● We start with a null hypothesis (H0) that represents the status quo. ● We also have an alternative hypothesis (HA) that represents our research question, i.e. what we're testing for. ● We conduct a hypothesis test under the assumption that the null hypothesis is true, either via simulation or theoretical methods. ● If the test results suggest that the data do not provide convincing evidence for the alternative hypothesis, we stick with the null hypothesis. If they do, then we reject the null hypothesis in favor of the alternative. N.B. The slides of the case study on gender discrimination provide specific information regarding hypothesis testing.