DQ 2 :Compare and contrast descriptive and inferential statistics.

Descriptive statistics summarise the data you have: counts, proportions, rates, measures of central tendency and spread, and the tables and charts that carry them. Inferential statistics use a sample to make a claim about a population you did not measure, through estimation with confidence intervals and hypothesis tests. The cleanest way to hold them apart is to ask what would change if you had measured everyone: descriptive statistics would be unchanged and inferential statistics would be unnecessary. That test also explains why the distinction is unusually interesting in public health, where a state's complete birth certificate file or a full notifiable disease register is the population rather than a sample from it, and a rate computed from it is a fact rather than an estimate. Public health is unusual in that some of its data sets genuinely are the whole population, which is where the contrast becomes concrete rather than textbook.

So why does public health need both? Because much of its data is not a census. Survey systems such as national health interview and behavioural risk surveys are samples, and every prevalence figure from them carries sampling error that a confidence interval has to express. Programme evaluations compare groups and need to know whether an observed difference is larger than chance variation. Small-area estimates are unstable precisely because the counts are small, and inference is what tells you a county rate based on four events cannot support the conclusion someone wants to draw from it. Meanwhile descriptive work retains a role no inference replaces: it is how a problem is characterised in the first place, how a trend becomes visible, and how a finding is communicated to people who will never read a p-value. Say that they answer different questions and that public health asks both, and the second half is genuinely answered.