Social Data Analytics - Lecture 2.1

Social Data Analytics - Lecture 2.1: From Sample to Population

• Statistics has two main branches: descriptive and inferential
• Descriptive statistics describes, organises, summarises, and displays data
• Inferential statistics uses probabilistic techniques to analyse a sample to understand the population
• A population is all members of a group (e.g., all adults in the UK)
• A census is a complete count of a population
• A sample is a subset of a population
• A statistic describes a characteristic of a sample (e.g., the mean weight of people in a sample)
• A parameter describes a characteristic of a population (e.g., the proportion voting Conservative)
• An example: To find the 2014 UK poverty rate, the UK Family Resources Survey sampled 23,000 households
• All survey estimates use a sample
• Samples are used to draw inferences about a population
• A sampling error occurs when a sample is used instead of the entire population, resulting in variation
• A non-sampling error is a mistake in the sampling process (i.e., poor questions, bias by interviewers, errors in measurements)
• To infer something about the population, random sampling is essential, along with various inference tools
• Probability sampling ensures each population member has a known non-zero chance of selection
• Simple random sampling (SRS) ensures equal chance of selection
• Other probability sampling designs include stratified simple random sampling, cluster sampling, systematic sampling, and multi-stage sampling
• If a sample is not random, inferences about the population are unreliable
• Sampling distributions are used to generalise from small samples to a population of potentially millions
• A sampling distribution represents the possible values of a statistic (like a sample mean) over repeated samples from a population, allowing inference
• The Central Limit Theorem (CLT) states that the sampling distribution of the sample means will be approximately normal, even if the population is not normal
• The mean of the sampling distribution is approximately equal to the population mean (µ), regardless of the population distribution shape
• This only applies for large random samples (typically 30 or more)
• Standard errors (SE) measure the variability of a sampling distribution, useful for inferring the population value. The formula depends on whether you're finding the SE for a mean or a proportion.
• The standard error for the sample mean is the population standard deviation (σ) divided by the square root of the sample size (n)
• The standard error for the sample proportion is the square root of (π(1- π)/n), where π is the population proportion.
• The sample standard deviation (s) is used when the population standard deviation isn't known. The sample proportion (p) is used when the population proportion isn't known.
• Larger sample sizes yield smaller SEs, thus providing more information about the population
• Key reading: Chapter 8 of "Beginning Statistics" by Foster, Diamond, and Jefferies (2015)
• Check the pre-recorded lecture for CLT demonstrations