Chapter 1 stat pt 1
Ice Breaker: Rules of Inclusive Engagement
How can we include everyone in class discussions?
What are examples of inclusive language?
How should we handle disagreeing with someone else during discussion?
What is the difference between disagreeing and being offensive?
1.1 What Is Statistics?Section Objectives
By the end of this section, you should know how to:
Spot what's being measured in a study (variables).
Tell the difference between numbers that can be added/averaged (quantitative) and descriptions (qualitative).
Identify the whole group (population) versus a smaller group (sample) in a study.
Understand the difference between a measurement for a whole group (parameter) and a measurement for a smaller group (statistic).
Figure out how specific or detailed a measurement is (level of measurement).
Compare how we describe data (descriptive statistics) versus how we make guesses about bigger groups (inferential statistics).
Statistics
Statistics is about collecting, organizing, understanding, and explaining numerical information from data.
It's both the science of dealing with uncertainty and the way we get useful information from data.
Individuals and Variable
Individuals are the people or things we are studying.
Example: In a study of student heights, the individuals are the students.
A variable is a feature or characteristic of an individual that we can measure or observe.
Example: For students, variables could be their height, age, or favorite subject.
Distinguish Between Quantitative and Qualitative Variables
A quantitative variable is something you can count or measure with numbers, where operations like adding or finding an average make sense. (e.g., height, age).
More examples: Number of siblings, exam scores, daily temperature in Celsius.
A qualitative variable describes an individual by putting them into a group or category. (e.g., hair color, favorite food).
More examples: Marital status (single, married, divorced), political affiliation, types of cars (sedan, SUV, truck).
Population Data and Sample Data
Population data includes information from every single individual we are interested in.
Example: The heights of all students currently enrolled in a university.
Sample data includes information from only some of the individuals we are interested in.
Example: The heights of 50 randomly selected students from that university.
Distinguish Between Population Parameter and Sample Statistic
A population parameter is a numerical value that describes a characteristic of the entire population. (e.g., the average height of all adults in a country).
Example: The true average height of all students currently enrolled in a university.
A sample statistic is a numerical value that describes a characteristic of a sample. (e.g., the average height of 100 randomly selected adults).
Example: The average height of the 50 randomly selected students from that university.
Guided Exercise 1 (1 of 3)
How important is music education in school (K–12)? The Harris Poll surveyed 2286 adults (18 and older) in the U.S. They asked if people agreed with the statement, “Learning and habits from music education equip people to be better team players in their careers.” In this survey, 71\% of the participants agreed.
Guided Exercise 1 (2 of 3)
Who were the individuals in this study, and what was the variable being measured?
Is this data a sample? If so, what is the full population it represents?
Is the variable (agree/disagree) qualitative or quantitative?
Guided Exercise 1 (3 of 3)
Can you think of a different numerical variable that might be interesting to study here?
Is the 71\% of respondents who agreed a statistic or a parameter?
Guided Exercise 1: Solution (1 of 3)
(a) Solution: The individuals are the 2286 adults surveyed. The variable is their answer: "agree" or "disagree" with the statement about music education and career teamwork.
(b) Solution: Yes, this data is a sample. The full population would be all adults in the United States.
Guided Exercise 1: Solution (2 of 3)
(c) Solution: Qualitative. The answers are categories (agree or disagree), not numbers that can be added or averaged.
(d) Solution: Their age or income could be a quantitative variable of interest.
Guided Exercise 1: Solution (3 of 3)
(e) Solution: It's a statistic, because 71\% was calculated from the sample data, not from all adults in the U.S.
Levels of Measurement (1 of 2)
The nominal level is for data that are just names, labels, or categories with no specific order. Data at this level can only be classified and counted. No mathematical operations (like addition or subtraction) make sense.
Example: Colors (red, blue, green), types of cars (sedan, SUV), gender (male, female), zip codes.
Key Characteristic: Categories only; no order, no numerical meaning.
The ordinal level is for data that can be put in order, but the differences between the values aren't meaningful or fixed. While there's an order, the magnitude of difference between categories isn't uniform or quantifiable.
Example: Small, medium, large; movie ratings like 1 to 5 stars (a 4-star rating is better than a 3-star, but the difference between 4 and 3 might not be the same as between 2 and 1); education level (high school, bachelor's, master's, PhD); customer satisfaction (very unsatisfied, unsatisfied, neutral, satisfied, very satisfied).
Key Characteristic: Categories with a meaningful order; differences between values are not quantifiable.
Levels of Measurement (2 of 2)
The interval level is for data that can be ordered, and the differences between data values are meaningful. However, there's no true zero point, meaning zero doesn't mean the absence of the quantity. Instead, zero is just another point on the scale. Ratios are not meaningful at this level because of the arbitrary zero.
Example: Temperature in Celsius or Fahrenheit (0^\circ ext{C} does not mean no temperature, it's just a point on the scale); years (e.g., 1990, 2000); IQ scores. You can say 20^\circ ext{C} is 10^\circ ext{C} warmer than 10^\circ ext{C}, but you can't say it's twice as warm.
Key Characteristic: Ordered data, meaningful differences, but no true zero point.
The ratio level is for data that can be ordered, differences are meaningful, and there is a true zero point. A true zero point indicates the absence of the quantity, and ratios are meaningful (e.g., 20 kg is twice as heavy as 10 kg). All mathematical operations are valid.
Example: Height, weight, age, income, number of items sold (0 kg means no weight, 0 income means no income, 0 items sold means none). A person earning $40,000 earns twice as much as someone earning $20,000. The value 0 truly means 'nothing' or 'none'.
Key Characteristic: Ordered data, meaningful differences, and a true zero point; ratios are meaningful.