Question:
Which of the following assumption(s) are required if an independent t-test is to be used?
A. Samples are drawn from a normally distributed population.
B. Homogeneity of variances (equal variances).
C. The data are either interval or ratio scales.
Which of the following assumption(s) are required if an independent t-test is to be used?
A. Samples are drawn from a normally distributed population.
B. Homogeneity of variances (equal variances).
C. The data are either interval or ratio scales.
A. Samples are drawn from a normally distributed population.
B. Homogeneity of variances (equal variances).
C. The data are either interval or ratio scales.
Show Hint
Before running an independent t-test, use Shapiro-Wilk's test to check the normality assumption and Levene's test to check the homogeneity of variances.
Updated On: Aug 5, 2026
- A, B and C
- A and B only
- C only
- A only
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The independent two-sample t-test is a parametric statistical test used to determine whether there is a statistically significant difference between the means of two independent groups.
Because it is a parametric test, its validity depends on several underlying assumptions about the data structure and distribution.
Step 2: Detailed Explanation:
Let us analyze each of the stated assumptions for the independent t-test:
- Assumption A: Normality.
The t-test assumes that the continuous dependent variable is normally distributed within each of the two comparing groups.
While the test is relatively robust to minor deviations from normality with large sample sizes, severe non-normality can compromise the Type I error rate.
- Assumption B: Homogeneity of Variances.
The test assumes that the variances of the populations from which the two samples are drawn are equal (homoscedasticity).
If this assumption is violated, the standard error calculation can be compromised, requiring the use of Welch's t-test instead.
- Assumption C: Scale of Measurement.
Parametric tests like the t-test require continuous data measured on either an interval scale or a ratio scale.
These scales have constant, meaningful intervals between values, which is necessary to calculate valid means and variances.
For nominal or ordinal data, non-parametric alternatives like the Mann-Whitney U test should be used instead.
Because all three assumptions are required for the standard independent t-test, statement A is correct.
Step 3: Final Answer:
Therefore, the assumptions required are A, B and C.
The independent two-sample t-test is a parametric statistical test used to determine whether there is a statistically significant difference between the means of two independent groups.
Because it is a parametric test, its validity depends on several underlying assumptions about the data structure and distribution.
Step 2: Detailed Explanation:
Let us analyze each of the stated assumptions for the independent t-test:
- Assumption A: Normality.
The t-test assumes that the continuous dependent variable is normally distributed within each of the two comparing groups.
While the test is relatively robust to minor deviations from normality with large sample sizes, severe non-normality can compromise the Type I error rate.
- Assumption B: Homogeneity of Variances.
The test assumes that the variances of the populations from which the two samples are drawn are equal (homoscedasticity).
If this assumption is violated, the standard error calculation can be compromised, requiring the use of Welch's t-test instead.
- Assumption C: Scale of Measurement.
Parametric tests like the t-test require continuous data measured on either an interval scale or a ratio scale.
These scales have constant, meaningful intervals between values, which is necessary to calculate valid means and variances.
For nominal or ordinal data, non-parametric alternatives like the Mann-Whitney U test should be used instead.
Because all three assumptions are required for the standard independent t-test, statement A is correct.
Step 3: Final Answer:
Therefore, the assumptions required are A, B and C.
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