4.1 Introducing Hypothesis Tests 4.2 Measuring significance with P-values Visit the Maths Study Centre 11am-5pm This presentation is viewable on Check out the website

Statistical inference is the process of drawing conclusions about the entire population based on information in a sample by: constructing confidence intervals on population parameters or by setting up a hypothesis test on a population parameter

Inference using confidence intervals We use the statistic from a sample as a point estimate for a population parameter. But sample statistics vary from sample to sample. To find out much uncertainty surrounds the sample statistic we can construct confidence intervals either by: - the sampling distribution (the distribution of sample statistics computed for different samples of the same size from the same population). As the sample size n increases, the variability of the sample statistics tends to decrease and the sampling distribution tend to be centered closer to the true value of the population parameter. - the bootstrap distribution (in reality we only have one sample. So to find out the variability of the sample statistics, we can bootstrap samples from the original sample). A bootstrap sample is a random sample taken with replacement from the original sample, of the same size as the original sample. As the sample size n increases, the variability of the sample statistics tends to decrease and the sampling distribution tend to be centered closer to the original sample statistic. Luckily, we don’t care about the centre…we care about the variability!

We are 95 % confident that the true population parameter of context of study is between statistic-2*SE and statistic+2*SE.

We construct bootstrap samples when we only have one sample and use the standard deviation of the bootstrap distribution as the standard error. We are 95 % confident that the true population parameter of………is between statistic-2*SE and statistic+2*SE.

Inference using Hypothesis Testing Hypothesis Tests use statistics from a sample to assess a claim about the population parameters If the sample statistic is statistically significant, we have convincing evidence against the null hypothesis, and in favour of the alternative.

Statistical Significance We can determine whether a sample statistic is statistically significant or not by measuring the p-value.