Statistics Overview Quiz

Introduction to Statistics

• Statistics is the science of data, encompassing observations, measurements, and survey responses.
• It involves collecting, organizing, analyzing, and interpreting data to make informed decisions.
• Statistics is used in many fields, acting as a tool for researchers to draw general conclusions.

Learning Objectives

• Understanding the field of statistics.
• Recognizing how statistics applies to real-world problems.
• Connecting statistics and data.
• Differentiating between a population and sample of data.
• Differentiating between descriptive and inferential statistics.

What is Data?

• Data are pieces of information collected from observations, counts, measurements, or responses.
• Example: "People who eat three daily servings of whole grains reduce their risk of stroke by 37%." (Source: Whole Grains Council)
• Example: "Seventy percent of the 1500 U.S. spinal cord injuries to minors result from vehicle accidents, and 68 percent were not wearing a seatbelt." (Source: UPI)

Data Sets

• Population: All possible outcomes, responses, measurements, or counts of interest.
• Sample: A subset of the population.

Why Take a Sample?

• Cost of a census is often prohibitive.
• Destruction of the item being studied might be required.
• It may not be possible to test or inspect all members of the population.

Example: Identifying Data Sets

• Population: All adults in the United States.
• Sample: 1708 adults surveyed.
• Data Set: 939 yes responses, 769 no responses.

Parameter and Statistic

• Parameter: A numerical value that describes a characteristic of a population.
  • Example: Average age of all people in the United States.
• Statistic: A numerical value that describes a characteristic of a sample.
  • Example: Average age of people from a sample of three states.

Example: Distinguishing Parameter and Statistic

• Example 1: A survey of MBAs reports an average salary greater than $82,000. – Sample statistic.
• Example 2: Starting salaries for 667 MBA graduates from a university increased by 8.5% – Population parameter.

Types of Statistical Applications

• Descriptive Statistics: Organizing, summarizing, and displaying data (e.g., tables, charts, and averages).
  • Tools include: average, spread, range, frequency, histogram, median, scatter plot, mode, interquartile range, etc.
• Inferential Statistics: Using sample data to draw conclusions about a population.
  • Tools include: hypothesis test, ANOVA, confidence interval, ordinary least squares, r², margin of error, and t-values.

Fundamental Elements of Statistics

• Descriptive Statistics: (1) Population/Sample of interest, (2) Variables to be investigated, (3) Tables, graphs/numerical summary tools, (4) Identification of patterns.
• Inferential Statistics: (1) Population of interest, (2) Variables to be investigated, (3) Sample of population units, (4) Inference about the population based on the sample data, (5) Measure of reliability.

Example: Descriptive and Inferential Statistics

• Descriptive : 70% of unmarried men and 90% of married men were alive at age 65.
• Inferential : Being married is associated with a longer lifespan for men.

Steps in Inferential Statistics

• Define the experiment's objective and population of interest.
• Determine the experiment design/sampling plan.
• Collect and analyze the data.
• Make inferences about the population from the sample information.
• Determine the inference's reliability.

Uses of Statistics

• Theoretical discipline in its own right.
• Tool for researchers in other fields.
• Used to form general conclusions in numerous applications.

Learn to View Statistics Critically

• Lies, Damned Lies, and Statistics: Be cautious about how statistics may be used for misrepresentation rather than truthful reporting.
• Understand data properly, make informed decisions, and use statistics responsibly.