Junior Statistician Qualification Examination common mistakes
Junior Statistician Qualification Examination · Understand the traps and how to avoid them.
When asked which measure of central tendency or dispersion is appropriate, the candidate automatically computes the arithmetic mean and standard deviation even for skewed data or ordinal categories, and reports a mean for a rating scale such as 'satisfied/neutral/dissatisfied'.
Introductory courses drill mean and SD as the default, so candidates pattern-match to the most familiar formula without first checking the variable's measurement level or the shape of the distribution. Ordinal labels encoded as numbers 1-2-3 look computable, which hides the fact that the gaps between categories are not equal.
What to do instead
Before computing anything, classify the variable (nominal, ordinal, interval, ratio) and sketch or describe the distribution. Build a decision rule you can recite: nominal to mode; ordinal to median and IQR; skewed interval/ratio to median and IQR; roughly symmetric interval/ratio to mean and SD. Practice by writing one sentence justifying the chosen measure in every practice item.
The candidate computes a probability of 'at least one' by adding the individual event probabilities instead of using the complement, and similarly adds probabilities of overlapping events without subtracting the intersection.
The addition rule P(A or B) = P(A) + P(B) is memorable and feels natural, so the correction terms P(A and B) and the complement structure of 'at least one' get dropped under time pressure. Candidates also fail to test whether events are mutually exclusive before applying the simple sum.
What to do instead
For every 'at least one' wording, immediately write 1 minus P(none) before doing any arithmetic. For union questions, always draw a two-circle Venn diagram and label the overlap before selecting a formula. Drill a mixed set of 20 items where the only decision is which rule applies, not the computation.
The candidate confuses the standard error of the mean with the standard deviation of the population, using sigma instead of sigma over root n in confidence intervals and test statistics, and therefore reports intervals that are too narrow.
The two quantities share the word 'standard' and the symbol sigma appears in both, so the divisor root n is easily omitted. Software output that already reports a standard error can also mask the distinction, leaving the candidate unable to reproduce it by hand.
What to do instead
Write the standard error formula explicitly at the top of every estimation problem and label the components (population SD, sample size). When reading software output, identify which column is the standard deviation and which is the standard error before using either. Verify with a small numeric example: quadrupling n should halve the standard error.
In hypothesis testing the candidate states conclusions as 'the probability that the null hypothesis is true is 0.03' or 'we have proven the alternative', and treats a failure to reject as evidence that the null is correct.
The p-value is introduced as a single number with a threshold, and the surrounding conditional-probability logic (probability of data given H0, not of H0 given data) is compressed in teaching. Everyday language about 'confidence' reinforces the inversion.
What to do instead
Memorise and write out the correct template once: 'If H0 were true, the probability of data at least this extreme is p.' Practise rewriting flawed conclusion sentences into correct ones, and always state the decision in terms of evidence against H0 rather than proof of either hypothesis.
The candidate interprets a regression slope as a correlation, or reads a high R-squared as proof that the predictor causes the outcome, and compares slopes across models fitted to differently scaled variables.
Slope, correlation, and R-squared all describe the strength or direction of a linear association, and software presents them side by side. The units attached to a slope are easy to ignore, and causal language is common in applied reporting.
What to do instead
For every regression output, state the slope in a full sentence with units ('a one-unit increase in X is associated with a b-unit change in Y') and separately report the correlation. Compare standardized coefficients, not raw slopes, when variables are on different scales. Add a standing sentence to your answers noting that observational association does not establish causation.
The candidate designs or critiques an experiment without random allocation or blocking, or compares groups that differ systematically at baseline, then attributes the difference in outcome to the treatment.
Randomisation and blocking are procedural details that do not appear in the arithmetic, so they are treated as optional formalities. Confounding variables are invisible in the data table, and candidates focus on the analysis rather than the design.
What to do instead
For any design question, list the three components explicitly: randomisation to groups, replication, and blocking or stratification on known nuisance factors. Ask 'what else differs between groups?' and name at least one confounder before analysing. Practise identifying whether a described study is experimental or observational and what inference each supports.
The candidate applies a parametric test to clearly non-normal small samples or to ordinal data, or uses a chi-square test with expected cell counts below about five without noting the violation.
The t-test and chi-square are the default tools in most courses, and assumption checks are taught separately from test selection, so they are skipped when the question names a comparison rather than an assumption. Small expected counts require an extra computation that is easy to overlook.
What to do instead
Before choosing a test, run a fixed checklist: measurement level, sample size, independence, and expected counts. Memorise the substitutions (Mann-Whitney for two independent groups, Wilcoxon signed-rank for paired data, Fisher's exact test for small 2x2 tables) and state the assumption check in your answer even when the question does not ask for it.
The candidate compares index numbers or monetary time series across years without deflating, mixes up a Laspeyres and a Paasche index, or computes a simple average of percentage changes instead of a weighted or compounded measure.
Index formulas differ only in which period's quantities appear in the weights, so the two are easily transposed. Nominal values rise with prices, which makes growth look real, and averaging percentages feels like the obvious way to summarise change.
What to do instead
Write the two index formulas side by side and label the weight period in each (base-period quantities for Laspeyres, current-period for Paasche). Always convert nominal series to real terms using the appropriate price index before comparing. For multi-period growth, use the geometric mean of growth factors, not the arithmetic mean of rates.
The candidate reports results to excessive precision, ignores missing values or treats them as zeros, and fails to check that a recoded or merged dataset has the expected number of rows and value ranges before analysing it.
Software prints many decimal places by default and silently drops or coerces values, so errors in the data step are invisible in the final output. Candidates trust the output table without reconciling it against the input.
What to do instead
Adopt a fixed data-handling routine: count rows and check key variable ranges before and after every recode or merge, and inspect the missing-value pattern explicitly. Round reported statistics to a sensible number of significant figures and state the handling of missing data in the methods. Keep a short script that reproduces the cleaning steps.
The candidate omits or mislabels the elements of a graph or table, such as a truncated y-axis on a bar chart, a histogram whose bins are unequal but plotted as if equal, or a frequency table whose percentages do not sum to 100 because of rounding or a missing category.
Presentation is treated as cosmetic rather than substantive, and default software settings produce truncated axes and automatic bin widths that distort the shape. Rounding errors in percentages are rarely checked.
What to do instead
Apply a presentation checklist to every figure: labelled axes with units, stated bin widths, bars starting at zero, and a title that names the variable and group. Verify that percentages sum to 100 within rounding and state the rounding convention. Practise spotting distortions in published charts and naming the specific problem.