Revision sheet: Introduction to Statistics and Sampling

📋 Course Outline

1. Statistical Investigation Cycle
2. Individuals Populations and Samples
3. Variables and Data Types
4. Parameters and Sample Statistics
5. Levels of Measurement
6. Descriptive and Inferential Statistics
7. Simple Random Sampling
8. Sampling Designs and Simulations

📖 1. Statistical Investigation Cycle

🔑 Key Concepts & Definitions

• Statistics : The study of how to collect, organize, analyze, and interpret information from data.

★ Must-know

• A statistical investigation commonly follows the cycle of posing a question, collecting data, analyzing the data, and interpreting the results.

Further detail

• A statistical procedure cannot be more accurate than the data or facts on which it is based.

💡 Memory Hook

Pose → collect → analyze → interpret

📖 2. Individuals Populations and Samples

🔑 Key Concepts & Definitions

• Individual : A person or object included in a statistical study.
• Population : Consists of every individual of interest in a statistical study.
• Sample : Consists of only some of the individuals of interest in a statistical study.

📝 Essential Points

📌 Population data come from every individual of interest, whereas sample data come from only some individuals of interest.

💡 Memory Hook

Everyone versus some

📖 3. Variables and Data Types

🔑 Key Concepts & Definitions

• Variable : A characteristic of an individual that is measured or observed.

★ Must-know

📌 A quantitative variable has numerical values for which operations such as addition or averaging make sense, whereas a qualitative variable places individuals into categories or groups.

Further detail

• For the study of people who reached the summit of Mount Everest, height, weight, and age are quantitative variables, whereas gender and nationality are qualitative variables.

💡 Memory Hook

Numbers versus categories

📖 4. Parameters and Sample Statistics

🔑 Key Concepts & Definitions

• Population Parameter : A numerical measure that describes an aspect of a population.
• Sample Statistic : A numerical measure that describes an aspect of a sample.

★ Must-know

• A parameter for a given population is fixed, whereas sample statistics may vary from sample to sample.

Further detail

• In the Mount Everest example, the number of left-handed climbers in the population is a population parameter, whereas the number of right-handed climbers in a sample is a sample statistic.

📖 5. Levels of Measurement

🔑 Key Concepts & Definitions

• Nominal Level : Consists of names, labels, or categories with no implied ordering and permits no mathematical computations; it is qualitative.
• Ordinal Level : Consists of data that can be arranged in order, but differences between values are undetermined or meaningless.
• Interval Level : Consists of ordered data with meaningful differences, but zero represents a position on a scale rather than an inherent absence.
• Ratio Level : Consists of ordered data for which differences and ratios are meaningful and that have a true zero.

📝 Essential Points

• A variable should be categorized at the highest level of measurement appropriate for its data.

📖 6. Descriptive and Inferential Statistics

🔑 Key Concepts & Definitions

• Descriptive Statistics : Consists of methods for organizing, picturing, and summarizing information from samples or populations.
• Inferential Statistics : Consists of methods for using information from a sample to draw conclusions about the population.

💡 Memory Hook

Summarize data versus generalize from a sample

📖 7. Simple Random Sampling

🔑 Key Concepts & Definitions

• Simple Random Sample : In a simple random sample, every sample of the specified size and every individual in the population have an equal chance of being selected.

★ Must-know

• To draw a simple random sample, number all population members sequentially, use a table, calculator, or computer to select random numbers, and choose the members with those numbers.

Further detail

• A random sample does not guarantee that the sample reflects every aspect of the population, because a random sample can overrepresent one group by chance.

• To select 30 cars from 500, assign the cars numbers 1 through 500 and use a random-number generator to select the corresponding numbers.

💡 Memory Hook

Number → randomize → select

📖 8. Sampling Designs and Simulations

🔑 Key Concepts & Definitions

• Simulation : A numerical representation or mathematical imitation of a real-world phenomenon, sometimes used when real-life investigation is dangerous.
• Sampling With Replacement : Leaves a selected number in the population, so the same number may be selected more than once.
• Convenience Sampling : Forms a sample from population members who are readily available.

📝 Essential Points

📌 Stratified sampling divides the population into characteristic-based strata and randomly samples from each, whereas cluster sampling randomly selects pre-existing clusters and includes every member of each selected cluster.

📌 Systematic sampling selects every kth population member after a randomly selected starting point, whereas multistage sampling uses several sampling methods to create successively smaller groups whose final sample consists of clusters.

📊 Synthesis Tables

Levels of Measurement

Level	Ordering	Meaningful operations	Zero
Nominal	No	None	Not applicable
Ordinal	Yes	Differences meaningless or unavailable	Not applicable
Interval	Yes	Differences	Not a true zero
Ratio	Yes	Differences and ratios	True zero

Sampling Designs

Design	How population is divided	Selection method
Simple random	No division	Every sample and individual has an equal chance
Stratified	Characteristic-based strata	Random sample from each stratum
Systematic	Sequential list	Every kth member after a random start
Cluster	Pre-existing clusters	Random clusters; include every member