Statistics

What this covers

• Study design: distinguishing observational studies from experiments, identifying confounding, and using random sampling and random assignment to justify generalisation versus causal claims
• Describing univariate data: shape, centre and spread, resistant vs non-resistant measures, boxplots and outlier rules, z-scores and normal distribution calculations in both directions
• Bivariate data: scatterplots, correlation, least-squares regression, slope and intercept interpretation in context, residual plots, r-squared, and the effect of influential points
• Probability and random variables: two-way tables, conditional probability and independence, expected value and standard deviation of random variables, binomial and geometric settings
• Sampling distributions: the difference between a population, a sample and a sampling distribution, unbiasedness, standard error, and the Central Limit Theorem for means and proportions
• Inference: one- and two-sample confidence intervals and hypothesis tests for proportions and means, t-procedures, chi-square tests for goodness of fit and independence, plus Type I/II errors and power

Where learners get stuck

Reading a 95% confidence interval as 'there is a 95% probability the population mean is between these two numbers'

The parameter is fixed, not random; the randomness lives in the interval. Students carry over intuition from probability chapters where every quantity had a distribution, so they attach probability to the wrong object. Correct phrasing describes the long-run capture rate of the method.

Treating a p-value as the probability that the null hypothesis is true, or treating a large p-value as proof the null is true

Conditional probability is easy to reverse, and 'fail to reject' feels like an unsatisfying non-answer. Students need repeated practice stating the p-value as 'probability of a result this extreme assuming the null is true' and writing conclusions that stop short of proving anything.

Drawing causal conclusions from a strong correlation, or refusing to draw one even after a randomised experiment

The rule 'correlation is not causation' gets memorised as an absolute. Which conclusion is allowed depends on how the data were produced, so sessions link every conclusion back to whether there was random assignment and whether there was random sampling.

What a session looks like

Sessions run by voice. Evelyn asks you to talk through a scenario before any arithmetic happens: what were the units, what was measured, was there random assignment, what parameter is in question. For calculation-heavy work you describe your setup and the numbers you got, and Evelyn checks the conditions you claimed and the way you stated the conclusion. Common activities include naming which of two similar procedures fits a described study, reading regression or test output aloud and interpreting each piece, and rewriting a sloppy conclusion sentence until it says only what the data support. Work can follow your class textbook order or focus on one unit, such as inference for proportions.

Helpful to know first

• Algebra 1 and 2: solving equations, working with square roots, and manipulating formulas to isolate a variable
• Comfort reading and plotting data on graphs, including slope-intercept lines
• Basic probability from earlier grades: fractions, percentages and simple two-event problems
• Access to a graphing calculator or statistics software is helpful but not required for discussion-based sessions

Questions

Does this cover the same material as a first-year college statistics course?

The content overlaps heavily. Grade 11-12 statistics and an introductory college course both run from data description through to inference for means, proportions and chi-square. The main differences are pace and how much regression inference is included, so tell Evelyn which syllabus you are following.

My child can do the calculator steps but loses marks on the written answers. Can that be worked on?

Yes, and it is the most common issue at this level. Marks are usually lost for missing condition checks, conclusions without context, or interpretations that misstate what a p-value or interval means. Sessions target the wording directly by having the learner say the conclusion out loud and revising it.

Is statistics easier than calculus?

It is less algebraically demanding but requires more careful reading and writing. Students who are strong at procedural algebra sometimes find the ambiguity of study design and interpretation harder than a derivative problem, which has one clear method.

Can Evelyn help with a project or lab that uses collected data?

Evelyn can discuss sampling methods, help you decide which summary statistics and graphs suit your variables, and talk through which inference procedure your question calls for and whether its conditions are met. You describe your data and results out loud during the session.