University:
Western Sydney University
Course:
MEDI 2003 | Clinical Sciences 2
Academic year:

2024
Views:

375

Pages:

2
Author:

Mariam A. A.

STAT S FOR FUT URE DOCT ORS LESSON T WO Sample vs. population • You ideally want a representative sample of the population to make an inference about the population o Roughly representative in age 🡪 have enough young, middle aged and elderly (>65yo) people in the cohort your sampling o Roughly representative according to gender How to study samples • Random selection o Where every member of the population has an equal chance of being sampled o Randomisation in RCT (randomised control trial) Important properties of the sampling of distributions of the means • Approximately normal i.e. Gaussian applies if: o Underlying distribution of the population of individuals is normal o Central Limit Theorem states that distribution of the variable will be normal if the same size is sufficiently large Inferential statistics • Draw conclusions from a sample of the population about a research question you want answered • Assumes a random sample or random assignment was carried out Point estimation • Where you gather information about the average or mean • Typically involves a single answer e.g. what is the mean fasting BSL among Australian men • This could be 5.3 mmol/L (normal ranges from 4-6 mmol/L) 23 • Estimate of a specific value of a population parameter (e.g. the mean) • The best estimate of the mean of a population is the mean of a sample taken from that population • Standard error [SE] = SD / (square root of n) o SE of distribution is a measure of the accuracy (precision) of the point estimate: ▪ Large SE = imprecise estimate ▪ Small SE = precise estimate Confidence Intervals (Cis) – often 95% or 99% • CI is a range of values that is likely to cover the true but unknown population value • Based on a concept of repetition of the study under consideration • CI extends either side of the point estimate (very important for interpreting forest plots! – you will see these in journal articles, meta-analyses, journal club…) Putting it into perspective • Suppose we want to determine the mean weight of individuals sitting in this lecture theatre • We don’t have time to calculate the weight of each-individual so we calculate the weight from a sample of your cohort (the first 10 people to walk in the class) • The sample mean weight is found to be 70 kg. (Note: this may or may not be an accurate measure of the population mean!) • This sample mean is a point estimate of the population mean (population = entire cohort sitting in this lecture theatre) • On its own the point estimate has limited use since we don’t know how far the sample mean deviates from the population mean • Confidence intervals provide us with more useful information • Cis for means are intervals that contain the population mean a specified proportion of the time: o Most commonly 95% or 99% of the time (95% and 99% confidence intervals respectively). o E.g. 95% CI = 47.85kg < μ < 101.15kg (where μ = population mean) o i.e. we are pretty convinced the population mean lies between 47.85kg and 101.15kg since 95% of the time confidence intervals contain the true mean • The smaller the distance (size of the whiskers) either side of the sample mean the more precise the 95% CI • Width of the CI depends on the standard error 24 • Increasing sample size decreases width of the CI (i.e. you will get a more precise estimate with larger sample sizes – that’s why you aim for large numbers in clinical trials…)