Question
A researcher wants to compare a measured numerical variable between groups. The values are approximately bell-shaped/normal in distribution. Which statistical test is most appropriate?
a. Chi-square test
b. Spearman rank correlation
c. Wilcoxon signed-rank test
d. Mann–Whitney U test
e. Student’s t-test
Answer: e. Student’s t-test
Detailed explanation
The key phrase is measured data which follows a normal distribution. This means the data is continuous parametric data, for example height, weight, blood pressure, cholesterol level, haemoglobin, or serum sodium, assuming the distribution is approximately normal.
For such data, when we want to compare means, the correct test is usually the Student’s t-test.
Student’s t-test can be:
Unpaired t-test
Used when comparing the mean of a continuous normally distributed variable between two separate groups.
Example:
Mean systolic BP in patients taking drug A versus patients taking drug B.
Paired t-test
Used when comparing the mean of a continuous normally distributed variable in the same subjects before and after an intervention.
Example:
Mean LDL before statin treatment versus mean LDL after statin treatment in the same patients.
The other options are wrong because they are mainly used for categorical data, non-parametric data, or correlation.
Chi-square test is used for categorical data, usually proportions or percentages.
Example: comparing the percentage of smokers with MI versus non-smokers with MI.
Spearman’s rank correlation is used to assess correlation between ranked or non-normally distributed variables.
Example: correlation between disease severity rank and quality-of-life rank.
Wilcoxon signed-rank test is a non-parametric test for paired data.
Example: pain score before and after treatment in the same patients, when the data is not normally distributed.
Mann–Whitney U test is a non-parametric test for two independent groups.
Example: comparing non-normally distributed CRP levels between patients with disease A and disease B.
The exam trick is this:
Measured + normal distribution = parametric test = t-test or Pearson correlation.
Categorical = chi-square.
Non-normal or ordinal = non-parametric test.
Cheat sheet for exam
Step 1: What type of data?
Continuous measured data:
Use parametric tests if normally distributed.
Categorical data:
Use chi-square test.
Ordinal or non-normally distributed data:
Use non-parametric tests.
Correlation:
Use Pearson if normal/linear; Spearman if ranked or non-parametric.
Step 2: Are the groups paired or unpaired?
Same patients before and after intervention:
Paired data.
Different patients in two separate groups:
Unpaired data.
Step 3: Choose the test
Continuous, normally distributed, two independent groups:
Unpaired Student’s t-test
Continuous, normally distributed, same group before and after:
Paired Student’s t-test
Continuous, normally distributed, correlation:
Pearson correlation coefficient
Ordinal/non-normal, two independent groups:
Mann–Whitney U test
Ordinal/non-normal, paired observations:
Wilcoxon signed-rank test
Categorical proportions:
Chi-square test
Ranked/non-parametric correlation:
Spearman rank correlation
Flash cards
Q: Which test compares means of normally distributed continuous data between two groups?
A: Student’s t-test.
Q: What type of data is analysed using Student’s t-test?
A: Continuous measured parametric data, usually normally distributed.
Q: Which test is used for categorical proportions?
A: Chi-square test.
Q: Which non-parametric test compares two independent groups?
A: Mann–Whitney U test.
Q: Which non-parametric test compares paired before-and-after data?
A: Wilcoxon signed-rank test.
Q: Which correlation test is used for normally distributed continuous variables?
A: Pearson correlation coefficient.
Q: Which correlation test is used for ranked or non-parametric data?
A: Spearman rank correlation coefficient.
Q: What is the non-parametric alternative to the unpaired t-test?
A: Mann–Whitney U test.
Q: What is the non-parametric alternative to the paired t-test?
A: Wilcoxon signed-rank test.
Q: What is the main difference between paired and unpaired data?
A: Paired data comes from the same subjects measured twice; unpaired data comes from different groups.
MCQs to test yourself
- A trial compares mean systolic blood pressure between patients receiving amlodipine and patients receiving placebo. BP values are normally distributed. Which test is most appropriate?
a. Chi-square test
b. Unpaired Student’s t-test
c. Wilcoxon signed-rank test
d. Spearman correlation
Answer: b. Unpaired Student’s t-test
Explanation: The outcome is continuous measured data, systolic BP. The data is normally distributed. The groups are independent because the amlodipine and placebo groups contain different patients. Therefore, an unpaired Student’s t-test is the best test.
- A study compares cholesterol levels before and after statin therapy in the same 40 patients. The cholesterol values are normally distributed. Which test should be used?
a. Mann–Whitney U test
b. Chi-square test
c. Paired Student’s t-test
d. Spearman rank correlation
Answer: c. Paired Student’s t-test
Explanation: The same patients are measured before and after treatment, so the observations are paired. The variable is continuous and normally distributed. Therefore, the paired Student’s t-test is appropriate.
- Which of the following is false regarding Student’s t-test?
a. It is used for continuous normally distributed data
b. It can be paired or unpaired
c. It is mainly used to compare proportions
d. It compares means
Answer: c. It is mainly used to compare proportions
Explanation: Student’s t-test compares means of continuous normally distributed data. It does not compare proportions. Proportions or percentages are usually analysed using the chi-square test.
- A researcher compares the proportion of patients who improved after drug A with the proportion who improved after drug B. Which test is most suitable?
a. Chi-square test
b. Student’s t-test
c. Pearson correlation
d. Wilcoxon signed-rank test
Answer: a. Chi-square test
Explanation: The outcome is categorical: improved or not improved. When comparing proportions or percentages between groups, the chi-square test is generally used.
- Pain scores before and after physiotherapy are compared in the same patients. The pain score data are ordinal and not normally distributed. Which test is most appropriate?
a. Pearson correlation
b. Mann–Whitney U test
c. Chi-square test
d. Wilcoxon signed-rank test
Answer: d. Wilcoxon signed-rank test
Explanation: The data are paired because the same patients are assessed before and after treatment. The data are ordinal/non-parametric. Therefore, the Wilcoxon signed-rank test is the correct non-parametric paired test.
- CRP levels are compared between patients with rheumatoid arthritis and healthy controls. The CRP values are highly skewed. Which test is most appropriate?
a. Paired t-test
b. Mann–Whitney U test
c. Chi-square test
d. Pearson correlation
Answer: b. Mann–Whitney U test
Explanation: The data are continuous but not normally distributed. The two groups are independent. The Mann–Whitney U test is the non-parametric alternative to the unpaired t-test.
- Which test is best for assessing the relationship between two normally distributed continuous variables?
a. Spearman rank correlation
b. Chi-square test
c. Pearson correlation coefficient
d. Wilcoxon signed-rank test
Answer: c. Pearson correlation coefficient
Explanation: Pearson correlation assesses the strength and direction of a linear relationship between two continuous normally distributed variables.
- Which test is best for assessing correlation between two ranked variables?
a. Spearman rank correlation
b. Student’s t-test
c. Chi-square test
d. Mann–Whitney U test
Answer: a. Spearman rank correlation
Explanation: Spearman rank correlation is used when the data are ranked, ordinal, or non-parametric. It assesses monotonic association rather than requiring normally distributed continuous data.
- Which of the following is the best non-parametric alternative to the unpaired Student’s t-test?
a. Wilcoxon signed-rank test
b. Mann–Whitney U test
c. Pearson correlation
d. Paired t-test
Answer: b. Mann–Whitney U test
Explanation: The unpaired t-test compares two independent groups when data are normally distributed. If the data are not normally distributed, the Mann–Whitney U test is used instead.
- Which of the following is the best non-parametric alternative to the paired Student’s t-test?
a. Chi-square test
b. Spearman rank correlation
c. Wilcoxon signed-rank test
d. Mann–Whitney U test
Answer: c. Wilcoxon signed-rank test
Explanation: The paired t-test is used for paired normally distributed continuous data. When paired data are non-parametric or ordinal, the Wilcoxon signed-rank test is used.
- A study compares mean haemoglobin between two separate groups of patients. The data are continuous and normally distributed. Which test should be chosen?
a. Chi-square test
b. Spearman rank correlation
c. Unpaired Student’s t-test
d. Wilcoxon signed-rank test
Answer: c. Unpaired Student’s t-test
Explanation: Haemoglobin is continuous measured data. The data are normally distributed and the two groups are independent. This is a classic situation for an unpaired Student’s t-test.
- Which of the following is false?
a. Chi-square test is used for categorical data
b. Mann–Whitney U test compares two independent non-parametric groups
c. Wilcoxon signed-rank test is used for paired non-parametric data
d. Spearman correlation is the best test for comparing two means in normally distributed data
Answer: d. Spearman correlation is the best test for comparing two means in normally distributed data
Explanation: Spearman correlation assesses association between ranked or non-parametric variables. It does not compare two means. Comparing two means in normally distributed data requires Student’s t-test.
- In an exam question, the words “measured variable” and “normal distribution” should make you think first of:
a. Parametric test
b. Non-parametric test
c. Chi-square test
d. Fisher’s exact test
Answer: a. Parametric test
Explanation: Measured continuous data that follow a normal distribution are parametric data. Student’s t-test and Pearson correlation are common parametric tests.
- Which of the following pairings is correct?
a. Chi-square — continuous normally distributed data
b. Student’s t-test — categorical proportions
c. Mann–Whitney U — paired normal data
d. Wilcoxon signed-rank — paired non-parametric data
Answer: d. Wilcoxon signed-rank — paired non-parametric data
Explanation: Wilcoxon signed-rank test is used for paired non-parametric data, such as before-and-after scores in the same patients when the data are not normally distributed.
- A researcher wants to compare median pain scores between two independent treatment groups. The pain scores are ordinal. Which test is most suitable?
a. Student’s paired t-test
b. Mann–Whitney U test
c. Pearson correlation
d. Chi-square test
Answer: b. Mann–Whitney U test
Explanation: Ordinal data are non-parametric. The two groups are independent. Therefore, the Mann–Whitney U test is the most appropriate test.
Summary for quick exam revision
The choice of significance test depends mainly on the type of data, whether the data are normally distributed, and whether the observations are paired or unpaired. Continuous measured data that follow a normal distribution are called parametric data. When comparing means in such data, the Student’s t-test is usually used. If the same patients are measured before and after an intervention, the paired t-test is used. If two separate groups are compared, the unpaired t-test is used. For correlation between two normally distributed continuous variables, Pearson correlation is used. If data are categorical, such as improved/not improved or alive/dead, the chi-square test is used to compare proportions. If data are ordinal or not normally distributed, non-parametric tests are needed. Mann–Whitney U test is used for two independent non-parametric groups. Wilcoxon signed-rank test is used for paired non-parametric data. Spearman rank correlation is used for ranked or non-parametric correlation. In exams, “measured data plus normal distribution” should immediately suggest a parametric test. “Proportions or percentages” should suggest chi-square. “Before and after in the same patient” means paired data. “Two separate groups” means unpaired data. The correct answer here is Student’s t-test because the question describes continuous measured data following a normal distribution.