Lecture 5 Flashcards
Central Limit Theorem
Sampling Distribution of the Sample Mean
If we take multiple samples from a distribution we can calculate a sample mean 𝒙̅ for each of those samples. If we plot each of these sample means 𝒙̅ on a separate histogram we will soon see that the distribution of these approximates a normal distribution
What Does CLT Tell us?
Gathering more (large) samples. will result in a graph of thesample means thatwill look more like a normal distribution
CLT
The Central Limit Theorem states that thesampling distributionof thesample meansapproaches anormal distributionas thesample sizegets larger (>30), no matter the shape of the population distribution
Sampling Distribution of the Sample Means
Taking the mean of each repeat sample and plotting those means on their own graph (we could have a sampling distribution of any statistic – e.g. median, variance, range, sd etc)
What does CLT allow us to do?
Use random and independent samples to make inferences about a population
Significance and P Values
The P (probability) value is used when we want to see how likely it is that the hypothesis is true. The significance level describes the likelihood that the null hypothesis is correct.
Hypothesis Testing
A method for determining difference between 2 (or more) sets of data
Null Hypothesis (H0)
There IS NO DIFFERENCE BETWEEN TWO SAMPLES/POPULATIONS
What does a p-value of 0.5 mean?
The probability of the difference having happened (or any difference that is more extreme) is 50%
The smaller the P-Value…
The less likely it is that the difference happened by chance and so the higher the significance of the finding
How does sample size affect P-Vales?
Small samples likely to have P≥ 0.05 (insignificant) even if there is actually a difference. Large samples likely to have P < 0.05 (significant) even if the difference is small and likely irrelevant
