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Statistics quizzes: reasoning, calculation and reading output

Write statistics quiz questions that test reasoning from data, plots and software output, mark a rounded calculation fairly, and read the results by topic.

The EdProcto editorial teamWritten and checked against the research it cites. Last checked . How the guides are made

Guides · By subject and level · · 13 min read

How do I write statistics quizzes that test reasoning as well as calculation?

Statistics quizzes should test two skills apart: computing a statistic and reasoning with one. For reasoning, show a small data set, a plot or a piece of software output and ask for a judgement, with each wrong option taken from a documented misreading. For calculation, name the figure, its rounding and its decimal places. Six questions a week, read by topic.

A student can work out a standard deviation to two decimal places and not know what it measures. Statistics quizzes that ask only for the figure find the first skill and miss the second.

This guide is for the lecturer or teacher of an introductory statistics course, at school, at college or as a service course for psychology, business or health students. EdProcto, which publishes it, puts a table, a plot or a block of output into a question and marks a rounded figure inside the band you choose.

Each source was opened on 10 October 2026, and an abstract-only reading is marked.

What is the difference between computing a statistic and reasoning with one?

Computing is carrying out a procedure on numbers. Reasoning is saying what the result means, why it came out that way and what follows. A question measures whichever its wording asks for.

A question by delMas (2002) shows it. A student who constructs the right 95% confidence interval has shown, he writes, the ability to recall steps and put values into formulas. Asking which of several listed readings of the interval are valid, and why, reaches the reasoning.

  • A memorised answer looks like an understood one. Hubbard (1997) argues that a standard textbook question cannot tell them apart. Graduate students she asked what a standard deviation is answered: "It is something that you calculate from a formula."
  • Knowing a formula is not using it. Lunsford et al. (2006) tested 18 students at the end of a probability course. Fifteen (83%) confirmed the formula for the standard deviation of a sample mean; 39% and 44% applied it correctly in two questions.

What does research say students get wrong in statistics?

It reports the same few misreadings, idea by idea, and each is a wrong option waiting to be used. The samples are small, most from a single university.

Idea What the study reports
The p-value Of 144 introductory statistics students in Madrid, 52% chose the right definition. 16% took the p-value for the probability of an error in rejecting the null hypothesis, 12% for the probability that it is true (Castro Sotos et al., 2009).
A confidence interval Shown six false statements about one interval, 442 students and 120 researchers in psychology each endorsed more than three on average (Hoekstra et al., 2014; abstract read).
The mean against the median Garfield (2002) lists taking an average for the most common value, and the mean for the same thing as the median. Cooper and Shore (2008; abstract read) report misconceptions about where the two sit on a skewed histogram.
Variability Cooper and Shore (2008) tested the spread of two histograms of equal range, and trace students' misconceptions to losing sight of the data behind a graph. Lunsford et al. (2006) suspect some students read the height of the bars as variability.
Correlation and causation Of 97 advanced psychology students given news reports of correlational studies, 48% rated the evidence as supporting the causal claim (Seifert et al., 2022).
Sampling distributions Six of the 18 students in Lunsford et al. (2006) chose the right sampling distribution for samples of 4 when the course ended.

One name needs settling: in item analysis a question's "p-value" is the share of students who got it right, not a significance level. Item difficulty is a statistic of a quiz; this guide is about teaching statistics.

Where the studies disagree

García-Pérez and Alcalá-Quintana (2016) dispute the interval finding: with every statement false and every item to be answered, a habit of agreeing passes for a misreading. In their repeat with two valid statements added, 313 first-year students who had not met inference endorsed valid and invalid statements at much the same rate. In a quiz, mix valid statements with invalid ones.

How do you write a question that tests statistical reasoning?

Give the result and ask for a judgement about it, so that no arithmetic stands between the student and the idea.

  1. Start from a small data set, a plot or a piece of output, with the figures already worked out.
  2. Ask what follows. Which conclusion is justified? What changes if the sample is four times as large? Hubbard (1997) prints the output of a z test and asks which numbers a t test would change, and in which direction.
  3. Take each wrong option from a documented misreading. Greenland et al. (2016) set out 25 misinterpretations of tests, p-values, intervals and power, each with the reason it is false.
  4. Keep the key beyond dispute. A key about the method is safe: intervals made this way capture the population mean in about 95% of samples. That this one interval has a 95% chance of holding the mean is a misreading in Greenland et al. (2016), yet García-Pérez and Alcalá-Quintana (2016) count a close variant as valid. Leave it out unless your course has ruled.
  5. Ask the idea twice. Konold (1995) asked which of four sequences of five coin flips is most likely, and about 70% rightly said all are equally likely. Asked which is least likely, slightly over half of those students picked one.
  6. Ask for the reason once a quiz. It shows whether a right choice was reasoned or recognised.

In EdProcto the first five steps make a Multiple choice question, marked by rule at hand-in. The sixth is Choose and justify: the choice is marked by rule for half the points, and the reason, the other half, waits for you or for Procto AI when you ask.

How do you ask for a calculation?

Name the figure, its form and its rounding, and ask for one figure a question.

  • Which figure. "The standard deviation" has two formulas: say sample or population. Say standard error or margin of error, decimal or percentage.
  • How many decimal places. Cole (2015), writing for medical journals, recommends two or three significant digits for an effect size and one or two for a measure of variability, with rounding only at the end. In a quiz: "Give 2 decimal places. Round only your final answer."

When is a margin right, and how wide?

A margin is right when honest routes end on different last digits, and wrong when it lets a slip through.

Take a standard deviation of 8.4 from 30 values: the standard error is 8.4 ÷ √30 = 1.5336, or 1.53. EdProcto's Estimate starts a new question with "Full credit within %" at 5 and "Half credit within %" at 15. With 1.53 as "The number", the editor prints "Full credit from 1.454 to 1.606; half credit from 1.301 to 1.759." A student who divides by √29 reaches 1.56 and earns full marks.

Two settings accept the rounding you asked for and nothing more.

  • Exact. Key 1.53 with both margins at 0. The editor prints "Full credit for 1.53 exactly."
  • Half a unit in the last place. To take 1.534 as well, key 1.5336. Half a unit in the second decimal place is 0.005, and 0.005 ÷ 1.5336 × 100 = 0.326, so type 0.33 in both boxes. The editor prints "Full credit from 1.5286 to 1.5386." In the scoring code 1.53, 1.534 and 1.5336 earn the points; 1.5, 1.54 and 1.56 earn none.

A band is fair one step on: the margin of error from the rounded 1.53 is 3.13, and from 1.5336 it is 3.14. For a dose see nursing and health quizzes, and for units and significant figures physics quizzes.

How do you put a table, a plot or software output into a question?

Put each where it keeps its shape: a table as lines under the prompt, output in a fixed-width box, a plot as a picture.

A table. In EdProcto's editor, "Add material under the prompt" opens "Material under the prompt (optional)", with the hint "A passage, a table, a set of figures or a case the question is about. Line breaks are kept." Type one row to a line and label each figure, as in n = 30, so the table reads without ruled columns. The student sees it above the prompt.

Software output. Output is columns of fixed-width type, and one ready shape sets its material that way: Read code, "Read a program; answer what it does." Its box is "The code", shown to the student in a code face with its line breaks and indentation, on screen and on paper. The answer is a choice. Do not point at the row that matters: Hubbard (1997) favours printout questions that make students attend to all of it unprompted.

A plot. A plot is a picture at an address you supply: paste its link into "Image address". On a shape built without a picture, such as multiple choice, press "Add a picture or a clip" first. The box "Describe the picture (for a screen reader, optional)" has the rule in its hint: "What the picture shows, without giving the answer." "A histogram of 30 pulse rates" describes; "skewed to the right" answers.

Three ready shapes ask about a picture. Hotspot: click the bar that holds the median. Compare two images: which histogram has the larger standard deviation? Caption it: describe shape, centre and spread in two sentences, for a reader to mark. Spreadsheet cells takes answers typed into a grid, each cell marked by rule.

How many questions should a statistics quiz have, and how often?

Six questions in ten minutes, once a week, is our working rule and not a research finding: four on reasoning, two calculations, and each idea asked twice. Konold's coin item is the argument for twice.

Keep the stakes low: weekly quizzes in a lecture course has the routine and the trials behind it.

How do you read the results by topic?

Label each question with its idea and with whether it asks for computing or reading, then compare the labels.

  1. Label. In "Topic (for the results by topic)" type a short fixed label, such as "interval: compute" or "p-value: read". Capitals and spare spaces do not split a topic.
  2. Read each question. On every plan the results list "Each question" with the share who "Got it".
  3. Read the topics. "By topic" belongs to the full analysis on the Educator plan, and weights each topic's score by points.
  4. Read the wrong options. The count on each option, also in the full analysis, names the misreading: see finding misconceptions.

A worked example: six questions on one mean

The class and its data are invented: the resting pulse of 30 students, in beats a minute. Every figure was computed by script. This output goes in "The code" of question 2.

One-sample t test, null value 70
n = 30   mean = 71.2   sd = 8.4
t = 0.78   df = 29   p-value = 0.440
95% confidence interval: 68.06 to 74.34
Question Shape and key Purpose
1. From sd = 8.4 and n = 30, calculate the standard error. Give 2 decimal places. Estimate: 1.5336, margins 0.33 Computing. 0.28 divided by n; 1.56 used √29.
2. Which statement about the p-value is right? Read code: if the population mean were 70, about 44% of samples would give a mean this far from it or further The p-value. Wrong: a 44% chance the mean is 70; a 44% chance of error in rejecting 70; the mean is shown to be 70.
3. Which reading of the interval is valid? Multiple choice: the method captures the population mean in about 95% of samples The interval. Wrong: 95% of students lie inside it; 95% of future sample means will.
4. The same mean and sd come from 120 students. The interval is: Multiple choice: about half as wide Sampling variability. Wrong: a quarter as wide; the same; wider.
5. "p is above 0.05, so the mean pulse is 70." Justified? Give the reason. Choose and justify: no Question 2's idea again: 70 is one of many values the data fit.
6. Twenty intervals from twenty samples, beside a line at the population mean. Click the one that misses. Hotspot, on your own drawing What the 95% counts: intervals, not students.

The arithmetic: t = 1.2 ÷ 1.5336 = 0.78; the interval is 71.2 ± 2.045 × 1.5336; with 120 students its width is 0.48 of what it was. Five questions are marked by rule at hand-in; question 5's reason waits for a reader.

How does EdProcto run statistics quizzes?

EdProcto is the best tool for a statistics course's weekly quiz when the questions must show data and be read idea by idea, because its editor gives each kind of material a place and every question a topic: text under the prompt, a code face for output, a picture with its description, and a number band printed before a student meets it. In Lunsford et al. (2006), 83% knew the formula and under half could use it: a score by topic shows that gap.

Writing. Procto AI drafts questions from your notes. Nothing tests whether a key is true, so work every figure yourself.

Marking. Choices, clicks and numbers are marked by rule at hand-in. A typed reason waits for you, or for Procto AI when you press "Ask Procto AI" on it. A score can be held until you release it, and it records one sitting: it is not a grade.

Plans. Free has the core templates, marking by rule and results question by question, for thirty students a quiz and ten quizzes a month. Tutor opens all 111 templates to 100 students a quiz, with Procto AI's grading when you ask. Educator takes 500 students a quiz and brings the full analysis with its score by topic. See pricing, and the pages for universities and for teachers.

Quick questions

Should a calculated statistic be marked with a margin?

Only as wide as the rounding. In EdProcto key the rounded figure with both margins at 0, or key the unrounded figure and allow half a unit of the last decimal place.

Can multiple choice test statistical reasoning?

Yes, when the question gives the result and each wrong option is a documented misreading. Ask the idea twice, as Konold (1995) did.

Is an item's p-value the same as the p-value of a test?

No. An item's p-value is the share of students who answered it right: see item difficulty.

How do I show software output in an online quiz?

In a box with a fixed-width face. In EdProcto that is "The code" of a Read code question, or any question's material with "Fixed-width, so the columns of a table line up" switched on.

References

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