Fundamentals of Statistics: Data Collection and Introduction to Statistical Practice

Chapter 1: Data Collection

1.1 Introduction to the Practice of Statistics

Objectives

• Define statistics and statistical thinking

• Explain the process of statistics

• Distinguish between qualitative and quantitative variables

• Distinguish between discrete and continuous variables

1.1.1 Define Statistics and Statistical Thinking

Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. It also involves providing a measure of confidence in any conclusions.

• Data: Observations (such as measurements, genders, survey responses) that have been collected.

• Statistical thinking involves understanding variation in data and the process of making decisions based on data.

Example: Consider whether everyone in your class consumes the same number of hours watching TV each week. The variation in responses illustrates the concept of data variability.

1.1.2 Explain the Process of Statistics

• The population is the entire group of individuals to be studied.

• An individual is a person or object that is a member of the population.

• A sample is a subset of the population that is being studied.

Statistics can be divided into two main branches:

• Descriptive statistics: Consists of organizing and summarizing data using numerical summaries, tables, and graphs.

• Inferential statistics: Uses methods that take results from a sample, extend them to the population, and measure the reliability of the result.

• A statistic is a numerical summary based on a sample.

• A parameter is a numerical summary of a population.

Example: Suppose the proportion of all students on your campus who have a job is 0.849 (percentage 84.9%). This value represents a parameter because it is a summary of a population. If a sample of 250 students is obtained and the proportion with a job is 0.864 (percentage 86.4%), this value represents a statistic because it is based on a sample.

1.1.3 Distinguish Between Qualitative and Quantitative Variables

Variables are characteristics of the individuals within the population. Variables can differ among individuals, such as height, age, or education level.

• Qualitative (Categorical) variables: Allow for classification of individuals based on some attribute or characteristic (e.g., gender, university name).

• Quantitative variables: Provide numerical measures of individuals. The values can be added or subtracted and provide meaningful results (e.g., height, number of vending machines).

Example: Distinguishing Qualitative and Quantitative Variables

Variable	Type
Education level	Qualitative - attribute characteristic
Today's high temperature	Quantitative - numerical measure
Number of vending machines at school	Quantitative - numerical measure
Whether a student is prepared for class	Qualitative - attribute characteristic
Number of days per week a student eats lunch	Quantitative - numerical measure
Name of university	Qualitative - attribute characteristic
Telephone numbers	Qualitative - attribute characteristic

1.1.4 Distinguish Between Discrete and Continuous Variables

Quantitative variables can be further classified as discrete or continuous:

• Discrete variable: Has either a finite number of possible values or a countable number of possible values. Example: Number of heads obtained after flipping a coin five times.

• Continuous variable: Has an infinite number of possible values that are not countable. These values are typically measured and can take on every possible value between any two values. Example: Height of a building.

Example: Discrete vs. Continuous Variables

Variable	Type
Number of cars that arrive at a drive-thru between 12:00 p.m. and 1:00 p.m.	Discrete - countable
The distance a car can travel in city driving conditions with a full tank of gas	Continuous - not countable
The height of an office building	Continuous - not countable
The running time of a film	Continuous - not countable

Summary Table: Types of Data

Type of Data	Description
Qualitative data	Observations corresponding to a qualitative variable
Quantitative data	Observations corresponding to a quantitative variable
Discrete data	Observations corresponding to a discrete variable
Continuous data	Observations corresponding to a continuous variable

1.2 Observational Studies Versus Designed Experiments

Objectives

• Distinguish between an observational study and an experiment

1.2.1 Distinguish Between an Observational Study and an Experiment

Observational study: Researchers observe and measure characteristics of interest of part of a population but do not attempt to influence the responses.

Designed experiment: Researchers apply a treatment to individuals and attempt to isolate the effects of the treatment.

Example: Cellular Phones and Brain Tumors

• Researchers studied whether there is an association between mobile phone use and brain tumors by observing 79,171 middle-aged women over 7 years. The incidence of brain tumors was compared between those who used mobile phones and those who did not. This is an observational study.

• Researchers from the United States National Toxicology Program conducted a study to address the concern that radio-frequency radiation (RFR) may be associated with an increased risk of developing brain tumors in rats. Rats were exposed to RFR and compared to a control group not exposed to RFR. This is a designed experiment.

Explanatory and Response Variables

• The explanatory variable is the level of cell phone usage.

• The response variable is whether or not brain cancer was contracted.

• In research, we seek to determine how varying the amount of an explanatory variable affects the value of a response variable.

Additional info: These foundational concepts are essential for understanding how data is collected and analyzed in statistics, and how different types of studies can impact the interpretation of results.