Study of Statistics

Purpose and Importance

Statistics is the science of collecting, analyzing, interpreting, and presenting data. Understanding statistics is essential for:

• Reading and understanding studies in any discipline

• Conducting research

• Becoming a better consumer and citizen

Definitions

Key Statistical Terms

• Variable: A characteristic or attribute that can assume different values (e.g., age, weight, ice cream preference).

• Data: Values for the variable; measured or observed (e.g., age = 32 years).

• Data Set: Collection of data values (e.g., flavor of ice cream as 8 people were observed ordering vanilla).

• Population: All people/subjects/objects of interest.

• Parameter: A numerical description of a population characteristic.

• Sample: A subset from the population from which data is collected.

• Statistic: A numerical description of a sample characteristic.

Note: The larger the sample, the better the chance that it is representative of the population.

Example: Identifying Population and Sample

"A survey of 12,082 adults in a particular country found that 47.8% received an influenza vaccine for a recent flu season. Identify the population and the sample."

1. Population: The collection of immunization statuses of all adults in the country.

2. Sample: The 12,082 adults selected.

Example: Population: All UNC students; Sample: UNC Athletes. Is this a representative sample if you are collecting data on who owns a smartphone? (Yes/No). Is this a representative sample if you are collecting data on BMI? (Yes/No).

Branches of Statistics

Descriptive Statistics

Descriptive statistics involve collecting, organizing, summarizing, and presenting data. They help describe the basic features of the data in a study.

• Example: Calculating the average test score in a class.

Inferential Statistics

Inferential statistics use methods of statistical analysis to make decisions or draw conclusions about a population based on information from a sample.

• Uses probability to estimate population parameters.

• Example: If 65% of a sample of people are married, we might estimate that 65,000 out of 100,000 people in the population are married.

• Includes hypothesis testing, determining relationships between variables, and making predictions.

Types of Variables

Qualitative vs. Quantitative Variables

Variables can be classified based on the type of data they represent:

• Qualitative (Categorical) Variables: Take on values that place subjects into categories by some characteristic or attribute (e.g., gender, hair color, zip code).

• Quantitative Variables: Take on numeric values for which arithmetic operations make sense (e.g., age, temperature, rainfall).

Examples of Variable Classification

Levels of Measurement

Types of Data Measurement

• Nominal: Data is categorized using names, labels, or qualities. No mathematical computations are possible. (e.g., gender, hair color)

• Ordinal: Data can be ordered or ranked, but differences between data entries are not meaningful. (e.g., socioeconomic status: 'wealthy', 'middle income', 'poor')

• Interval: Data can be ordered, and meaningful differences between data entries can be calculated. There is no true zero. (e.g., temperature in Celsius or Fahrenheit, IQ score)

• Ratio: Similar to interval, but has a true zero. Ratios are meaningful. (e.g., weight, height, age, blood pressure)

Note: For ratio variables, the ratio of two measurements has a meaningful interpretation. For interval variables, ratios are not meaningful.

Types of Statistical Studies

Observational Studies

Researchers observe what is happening or has happened and draw conclusions without manipulating variables.

• Example: Recording how many children order apple slices instead of fries at McDonald's.

Experimental Studies

Researchers manipulate one of the variables and try to determine how the manipulation influences other variables.

• Independent Variable: The one being manipulated.

• Dependent Variable: The result or outcome measured.

• Example: Medical testing using placebo versus trial drug.

Additional info: For more on the difference between observational and experimental studies, see: GraphPad: Types of Variables.