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 When conducting research, it is important to understand the method used in order to use the proper statistical analysis. When studying the specific measures of an independent variable in a population, a sample of participants can be used to represent the study. Conversely, two different populations may be compared, two different measures may be taken of the same sample.
When there is one independent variable, a simple independent variable t-test can be used to evaluate the statistical significance of the results. When there are two independent samples, either from a between subjects study or a within-subjects design, it is necessary to compare the two samples in relation to the estimated standard error that would be expected between the samples and the population with no treatment effect (Gravetter et al., 2021). The primary difference between these two uses of the hypothesis test is whether to use the data from one sample or incorporate the data of both (or all) of the samples.
One example of a research situation where a single independent variable t-test would be used is when studying a population on a specific characteristic, such as how much people drive their car to work. A population would be sampled on a single variable, and a random sample would be used to represent the population and evaluate the statistics of the mean against the population parameter. On the other hand, studying the number of people who drive their car to work by sampling people 20-30 years old and comparing with adults 40-50 years old presents two different independent sample statistics which have to be compared and then evaluated over the estimated standard error.