Probability and Statistical Inference

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In this material, various aspects of variables, measurements, and data collection in Statistics are discussed. It covers the definition of variables, examples of variables, the concept of measurements, and data collection processes. Additionally, it touches on exploratory data analysis techniques. The content also addresses practical applications in educational settings, including the use of ASSISTments for homework assignments. Overall, the discussion aims to build a foundational understanding of essential statistical concepts.

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HUDM4122 Probability and Statistical Inference January 26, 2015

ASSISTments Did everyone get an account for the ASSISTments system? Did anyone have difficulties setting up an account? First homework is due in a week

Today Ch. 1 in Mendenhall, Beaver, & Beaver Variables and Variable Types Graphing Data Basic Exploratory Data Analysis

Variables What is a variable?

Variables What is a variable? A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration. MBB p. 8

Which of these are examples of variables? GPA Shoe size Age Number of correct answers in ASSISTments Number of times gamed the system in ASSISTments Favorite vegetable Favorite type of pie Pi

What is a measurement?

What is a measurement? A measurement is the result of measuring a variable on a single experimental unit A person, if you are studying people A class, if you are studying classes A pizza, if you are studying pizzas

A measurement Person furthest towards my left in the front row, what is your name?

Now I have a measurement

A measurement Person furthest towards my right in the second row, what is your name?

Now I have data A set of measurements

Now I have data A set of measurements Note that in stats class or education journals, the word data is plural

Now I have data A set of measurements Note that in stats class or education journals, the word data is plural I only know one exception

Now I have data A set of measurements Note that in stats class or education journals, the word data is plural I only know one exception

Everyone repeat after me

Everyone repeat after me My data are in this Excel file.

Everyone repeat after me My data are in this Excel file. Your data aren t evidence for that conclusion.

Everyone repeat after me My data are in this Excel file. Your data aren t evidence for that conclusion. His data were hard to collect.

However

However I do not recommend insisting that data is plural in bars, on first dates, or at Thanksgiving dinner

Any questions or concerns?

Univariate Data A single variable is collected Height 5 11 5 11 5 10 5 6

Univariate Data Two variables are collected (for the same data point) Height Drum-Playing Skill 5 11 1 5 11 2 5 10 4 5 6 8

Multivariate Data 3+ variables are collected Name Height Drum-Playing Skill John Lennon 5 11 1 Paul McCartney 5 11 2 George Harrison 5 10 4 Ringo Starr 5 6 8

Any questions or concerns?

Types of Variables

Quantitative/Numerical Data Data that can be expressed as numbers

What are some examples Of numerical data?

Ordinal Data Refers to data where there is a known order, but either The data clearly isn t numbers The space between values is not guaranteed to be equal

Examples of Ordinal Data Months of the year: January, February, March, April, Agreement level: Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree Quality of university: Highly selective, selective, somewhat selective, non-selective

Other examples of ordinal data?

Nominal data Values have no order or spacing Name State of Residence New Jersey is not greater or less than New York

Nominal data Values have no order or spacing Name State of Residence New Jersey is not greater or less than New York Although my brother might disagree

Other Examples of Nominal Data?

Another name Nominal data is often also called categorical data

Another name Nominal data is often also called categorical data Technically ordinal data is also categorical, but no one ever uses the term that way

Any questions or concerns?

Exploratory Data Analysis Analyzing data sets to summarize their main characteristics Seeing what the data can tell us beyond the formal modeling or hypothesis testing task