Game 9 · Testing and estimation
Which statistical test fits this data?
Types of data, and when to use the t-test, chi-square, ANOVA or a non-parametric test.
Read with: Choosing a test, Checking assumptions71 DNB questions
Play
Read the study, pick the test
Most rounds describe a made-up study and ask for the test. Some rounds make you walk the decision tree one question at a time, sort variables by type of data, or work out an expected count to choose between chi-square and Fisher's exact test. You have three lives.
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The idea
Three questions decide the test
The test is chosen by the data and the design, not by what gives the smallest p-value. Answer three questions in order, and write the answers in the protocol before the data are collected.
- What type of outcome? A measurement, an ordered grade, a category counted as numbers of patients, or a time to an event.
- How many groups? One group against a reference value, two groups, or three or more.
- Independent or paired? Different patients in each group, or the same patients measured more than once (or matched pairs).
For a measurement there is one more question: is it roughly normal (for paired data, are the differences roughly normal)? If yes, a parametric test such as the t-test or ANOVA uses the actual values. If the data are skewed or have outliers, a rank (non-parametric) test such as Mann–Whitney or Kruskal–Wallis is used instead.
| Feature | Parametric tests | Non-parametric tests |
|---|---|---|
| Suits | Measurements that are roughly normal | Skewed measurements, outliers, ordinal scores |
| Works on | The actual values (means, SDs) | Ranks or signs |
| Assumes | Normality, similar variances, independence, interval or ratio scale | No particular distribution |
| Examples | t-tests, ANOVA, Pearson correlation | Mann–Whitney, Wilcoxon, Kruskal–Wallis, Friedman, Spearman |
Types of data
Nominal, ordinal, interval, ratio
In 1946 S. S. Stevens described four scales of measurement. Each scale adds one property to the one before it.
| Scale | What it has | Example | Summary | Usual tests |
|---|---|---|---|---|
| Nominal | Named categories, no order | Blood group, sex, cured yes/no | Counts, percentages, mode | Chi-square, Fisher's exact |
| Ordinal | Order, unequal gaps | Pain grade, NYHA class, cancer stage | Median, percentiles | Mann–Whitney, Wilcoxon, Spearman |
| Interval | Equal gaps, arbitrary zero | Temperature in °C | Mean, SD | t-test, ANOVA if roughly normal |
| Ratio | Equal gaps and a true zero | Weight, haemoglobin | Mean, SD | t-test, ANOVA if roughly normal |
A second way to classify: qualitative (categorical) data are nominal or ordinal. Quantitative (numerical) data are either discrete, counts that take only whole numbers (seizures in a month), or continuous, measurements that can take any value in a range (haemoglobin). Coding does not change the scale: blood groups entered as 1, 2, 3 and 4 are still nominal.
NOIR: Nominal, Ordinal, Interval, Ratio. Order, then equal gaps, then a true zero.
The test map
Find the outcome, then the design
| Outcome | Two independent groups | Two paired sets | Three or more independent groups | Three or more repeated measurements | Relation between two variables |
|---|---|---|---|---|---|
| Measurement, roughly normal | Unpaired t-test | Paired t-test | One-way ANOVA | Repeated measures ANOVA | Pearson correlation |
| Measurement skewed, or ordinal scores | Mann–Whitney U | Wilcoxon signed-rank | Kruskal–Wallis | Friedman | Spearman correlation |
| Categories (counts) | Chi-square, or Fisher's exact if expected counts are small | McNemar | Chi-square (r × c table) | Cochran Q | Chi-square, logistic regression |
| Time to an event | Log-rank test | — | Log-rank test | — | Cox regression |
One group against a reference value: the one-sample t-test for a normal measurement, or the Wilcoxon signed-rank test for a skewed one. With three or more groups, do not run repeated t-tests: three tests at 5% give up to a 14% chance of a false positive. Use ANOVA or Kruskal–Wallis, then a post hoc test (Tukey, Bonferroni) if the result is significant.
The full decision tree, with worked examples of every test, is in the Choosing a test chapter. How to check normality, and when a t-test is still safe with skewed data in large groups, is in the Checking assumptions chapter.
Chi-square or Fisher
Small expected counts change the test
The chi-square p-value is an approximation. It needs adequate expected counts: no more than 20% of cells with an expected count below 5, and no cell below 1. In a 2 × 2 table one cell below 5 is already 25% of the cells, so Fisher's exact test is used instead. It calculates the exact probability and is valid at any sample size.
Expected count = row total × column total ÷ grand total
- row total
- patients in that group
- column total
- patients with (or without) the outcome, both groups together
- grand total
- all patients in the table
Teaching example from the chapter: complications in 1 of 10 patients with a new technique and 5 of 10 with the standard one. Expected complications = 10 × 6 ÷ 20 = 3 in each row, so 2 of the 4 cells are below 5. Fisher's exact test gives p = 0.14. Note that the rule is about expected counts, not observed ones.
Writing the answer
How to write this in a 10-mark DNB answer
- Start with the types of data (nominal, ordinal, interval, ratio, and discrete or continuous), one example each.
- Define parametric and non-parametric tests, and list the assumptions of parametric tests (normality, equal variances, independence, interval or ratio scale).
- Draw the test map as a table: outcome type down the side, design across the top, with the paired partners (unpaired t and Mann–Whitney, paired t and Wilcoxon, ANOVA and Kruskal–Wallis, repeated measures ANOVA and Friedman, Pearson and Spearman).
- For the test asked (t-test, chi-square, ANOVA), give its formula, degrees of freedom and one worked example with round numbers.
- Add the conditions: Fisher's exact test when expected counts are below 5, a post hoc test after a significant ANOVA, McNemar for paired proportions.
- End with one line on reporting: name the test, give the exact p-value with the effect size and its 95% CI.
The one thing to remember
The outcome type, the number of groups and pairing choose the test. Decide all three before you see the data.
Past papers
DNB questions this game helps you answer
Questions from NBE theory papers for DNB, DrNB and Diploma courses, most often asked first. The tag after each question is the specialty and the year it was set.
- ×7ANOVA.
- ×2Student's t test.
- ×2a) Non-parametric tests. b) Principles of randomization. c) Names of randomized multi institutional trials with respect to coronary artery bypass surgery and their salient findings.
- ×1Brief summary of non parametric tests. [2.5]
- ×1Student's t-test. [2]
- ×1Types of variables. [5]
- ×1ANOVA. [2.5]
- ×1Chi square test, paired T test, triple blind study, p value. [2+2+2+1]
- ×1Chi-square test.
- ×1Discuss the different statistical measures to observe for test of significance related to parametric and non-parametric data.
- ×1Enumerate the statistical tests used for quantitative data. Write in brief about any one of them.
- ×1Student's t-test. [2.5]
- ×1What is Chi-square test and its uses?
- ×1Wilcoxon signed rank test.
- ×1Chi Square test.
- ×1One way ANOVA test.
- ×1Post hoc comparisons after ANOVA test.
- ×1a) Measures of Central Tendency. b) Parametric and non parametric tests. c) Analysis of variance.
- ×1Compare parametric and nonparametric tests.
- ×1Explain the chi-square test.
- ×1Non parametric tests.
- ×1Paired t test.
- ×1Student's t-test.
- ×1What is normal distribution? What are the prerequisites for applying parametric tests?
- ×1't' Test and Chi Square test.
- ×1Chi square test.
- ×1Describe various parametric tests used in reasearch.
- ×1What are the types of errors in research ? What is Chi-square test ?
- ×1Compare parametric versus non parametric tests. Give two examples for each one of them.
- ×1Describe parametric and non-parametric statistical tests and their application.
- ×1Discuss parametric versus non-parametric statistical tests.
- ×1Enumerate and describe various parametric and non-parametric statistical tests for studying differences and correlation in two different groups of subjects.
- ×1Non-parametric tests.
- ×1Briefly discuss analysis of variance (ANOVA) with an example. List three post hoc tests commonly used after results are significant for ANOVA.
- ×1Parametric Versus Non-Parametric tests.
- ×1a) One-way ANOVA and its Post-hoc tests. b) Tests to check normal distribution of data.
- ×1Chi square test
- ×1Non-Parametric tests of significance.
- ×1Parametric tests of significance.
- ×1Student’s t test and chi square test.
- ×1Various non-parametric tests and their utility.
- ×1What is Analysis of Variance (ANOVA)? What are the types of ANOVA? Write about the applications of ANOVA in Psychiatry.
- ×1When the same patient group is analyzed prospectively and retrospectively, what is the type of Student’s t test used?
- ×1a) Statistical significance of difference in means. b) The Chi-square test.
- ×1"Student t test" and "Chi-square test"
- ×1Chi-Square test.
- ×1Enumerate Non-parametric tests. Explain them with example for qualitative data.
- ×1a) ANOVA. b) Chi- Square test and t- test. c) Correlation and regression coefficients in statistical analysis.
- ×1ANOVA
- ×1Chi Square Test.
- ×1Chi-Square test
- ×1Mention and justify the statistical tests which would be most appropriate for the following data: a. Comparison of two groups of sample size 150 each where the parameter /data is a continuous variable and is normally distributed. b. Comparison of two different groups of sample size 20 each where the data is a continuous variable but is not normally distributed. c. Comparison of bilirubin values pre and post therapy (4 weeks) in patients with acute hepatitis E who are given an experimental new drug. Sample size is 200 patients. d. Comparison of outcome (alive or dead) in patients given an experimental drug for severe enteric fever. The control group was given inj. Ceftriaxone. Sample size 50 in each group.
- ×1Parametric Tests.
- ×1Utility and limitations of non-parametric tests of significance.
- ×1Differentiate between parametric and non-parametric tests for statistical significance.
- ×1How is correlation analysis performed for a nonparametric data?
- ×1Non Parametric tests.
- ×1Paired t-test.
- ×1Parametric versus Non-Parametric tests.
- ×1Define the types of variables that the researcher will be analyzing.
- ×1Chi Square test
- ×1Differentiate between parametric and non parametric tests of significance.
- ×1Discuss applications of statistical tests. What are limitations and deficiencies of these tests, related to research skills in cardiac surgery?
- ×1What are parametric and nonparametric tests employed in Research?
- ×1What do you mean by parametric and nonparametric data? What statistical tests are performed to find out the significance of difference in these data between two groups?
- ×1When would you use the Wilcoxon Rank Sum Test?
- ×1Briefly discuss the following: (a) Preanalytical variable (b) Total quality management (c) ANOVA
- ×1What are non-parametric tests of significance? Classify and enumerate these tests and briefly discuss non-parametric tests of significance for nominal data.
- ×1What is Chi-Square test? Discuss its application in clinical medicine?
- ×1What is the difference between nominal and ordinal data? Describe student t test and its use. What is a case control study? What does P value signify?
- ×1Discuss parametric and non parametric tests in evaluating results of biomedical research. Mention different tests and their applicability.
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