Final answer:
Pearson's product-moment correlation requires that both variables are ratio or interval data. Bivariate regression also mainly uses continuous variables, while ANOVA and various types of t-tests have different requirements and do not strictly need ratio or interval data.
option d is the correct
Step-by-step explanation:
The question is asking which of the listed techniques requires that both variables involved are either ratio or interval data. Among the options provided, the technique that specifically requires both variables to be ratio or interval data is Pearson's product-moment correlation. This statistical method is used to measure the strength and direction of the association between two continuous variables.
Bivariate regression also generally requires that both the independent and dependent variables are continuous, which includes ratio and interval data. The dependent variable is the outcome of interest, and the independent variable is what you suspect might have an influence on the dependent variable. In bivariate regression, you would draw a scatter plot, use regression to find the line of best fit and the correlation coefficient, and then interpret the significance of the correlation coefficient.
ANOVA (Analysis of Variance) is rather used to compare means from three or more samples and does not strictly require both variables to be ratio or interval. The F Distribution and the F Ratio are critical in computing ANOVA.
The t-test can be of different types, including a test of a single mean, a test of two independent means, and a test of matched pairs. The data requirements for a t-test may vary depending on the specific type of t-test being used, but they can handle both continuous (interval or ratio) and sometimes ordinal data in the case of the ordinal t-test.