Question

An ecologist must determine whether (i) the means of two independent samples differ, and (ii) there is an association between two continuous variables. Assuming that all samples are normally distributed, which one of the following options represents the most appropriate statistical tests for (i) and (ii), respectively?

• A. Spearman’s correlation; (ii) Shapiro-Wilk test
• B. Wilcoxon’s matched pairs signed rank test; (ii) chi-squared test
• C. t-test; (ii) Pearson’s correlation
• D. Kendall’s test of concordance; (ii) Kolmogorov-Smirnov test

Hint:

To select statistical tests: 1. Use the t-test for mean differences in normally distributed independent samples.
2. Use Pearson’s correlation for associations between continuous variables under normality.
3. Non-parametric alternatives like Spearman’s or Wilcoxon’s tests are used when normality is not assumed.

Answer 1

The Correct Option is C

Step 1: Identify the appropriate test for (i). To determine whether the means of two independent samples differ: - The t-test is appropriate for comparing the means of two independent samples, assuming normal distribution. Step 2: Identify the appropriate test for (ii). To assess the association between two continuous variables: Pearson’s correlation measures the strength and direction of the linear relationship between two continuous variables, assuming normal distribution. Step 3: Evaluate the options. Option (A): Incorrect. Spearman’s correlation is used for non-parametric data, and the Shapiro-Wilk test checks for normality, not mean differences or associations. Option (B): Incorrect. Wilcoxon’s test is a non-parametric alternative for paired samples, not independent samples. The chi-squared test is for categorical data, not continuous variables. Option (C): Correct. The t-test is suitable for comparing means, and Pearson’s correlation is appropriate for continuous variables. Option (D): Incorrect. Kendall’s test is a non-parametric measure of correlation, and the Kolmogorov-Smirnov test is for comparing distributions.