Final answer:
Inferential statistical analysis varies by the level of measurement of data: chi-square tests for nominal, Mann-Whitney U for ordinal, and t-tests or ANOVAs for interval and ratio levels, all aiming to make inferences about a population from sample data.
Step-by-step explanation:
The inferential statistical analysis to use with each combination of the research question and level of measurement depends on whether the data is nominal, ordinal, interval, or ratio. For nominal scale level data, which is categorical and not ordered, techniques such as chi-square tests are appropriate. With ordinal scale level data that can be ordered but not quantitatively measured, methods like the Mann-Whitney U test could be suitable. For interval scale level data, where differences can be measured but there's no true zero point, you might conduct a t-test or ANOVA if the data meets certain assumptions. Finally, ratio scale level data, which have a true zero and can be used to compute ratios, can be analyzed using the same techniques as interval data when those techniques assume a true zero, such as t-tests or ANOVAs under specific conditions.
In applying these statistical methods, researchers are attempting to make inferences about populations from samples, estimating population parameters using sample statistics. With inferential statistics, the aim is to determine the likelihood that the observed effects are due to chance or to some meaningful factors. Statistical inference is an essential process in scientific studies as it provides a way to test hypotheses and make conclusions about a population based on sample data.