← Use statistical methods to make a formal inference

1 Reading the notation

Inference is careful about the difference between the population and your sample, and the notation encodes that difference.

📖 Notation used in formal inference

9 terms

Cover the right column and check you can say what each one means.

Median

The middle value once the data is ordered. This is the parameter this standard compares, in both groups — not the mean. Why the median: the data you are given is usually skewed, and a median is not dragged around by one long tail. Every conclusion you write here is about medians.

Difference in medians

Median of group A − median of group B. One number, and the only one your interval and your conclusion are about.

μ (mu) and x̄

Population mean and sample mean. Worth recognising, but not what you compare in this standard. Greek = population (unknown), Roman = sample (measured). That convention runs through all of statistics, medians included.

σ and s

σ (sigma) = population standard deviation; s = sample standard deviation.

n

The sample size: how many observations you collected.

Confidence interval

A range of plausible values for the population parameter, e.g. “between 5 g and 21 g”. “95% confidence” describes the long-run reliability of the METHOD, not the probability that this one interval is right.

Bootstrap

Resampling with replacement from your own sample, many times, to see how much the statistic varies. Each resample must be the SAME SIZE as the original, because sampling variability depends on n.

Sampling variability

The natural variation between different random samples from the same population. It is what a confidence interval measures. Different from measurement error and from bias: an interval accounts for this and nothing else.

Point estimate

A single best-guess value (e.g. the sample median), as opposed to an interval.

✓

The wording that earns the marks

Your conclusion must be about the POPULATION, name the parameter, and give a direction: “I am confident the median weight of ALL apples from orchard A is greater than…”. A statement about the sample alone earns nothing.

Practice for this standard covers the whole topic — flashcards and quiz.