5/16/2023 0 Comments Two sample t test easycalculator![]() In this article, we describe how randomization tests work and demonstrate how to run one using the open-source R programming language. There could be times, however, when UX researchers may need to use a distribution-free method to compare two independent means: a client’s request, a response to criticism for failing to meet the assumptions of the t-test, or to double-check the results of t-tests when analyzing data that may have radically violated multiple assumptions of the t-test. (For details, see Quantifying the User Experience, 2 nd ed.) In our practice, we intend to keep using the t-test as a statistical workhorse, making adjustments to degrees of freedom (when variances are radically different) and using logarithmic transformations (for time data) as needed. We’re not advocating that researchers abandon the t-test when analyzing typical UX data. Of these, the approach that makes the fewest assumptions about underlying distributions is the randomization test, a type of distribution-free nonparametric test. There are different types of nonparametric tests, including rank tests and resampling tests. When that happens, adjusting the degrees of freedom can compensate for the violation.Īnother strategy is to analyze the data with a nonparametric test to see if you get the same result. For some types of data, you can transform the data to enhance normality (e.g., logarithmic transformation of task times).įinally, research has shown that the variance between the two groups needs to be great for the violation of the assumption of homogeneity to affect results. ![]() For most distributions, this will be the case due to the central limit theorem-even for fairly small sample sizes. The assumption of normality is not an assumption that the underlying distribution is normal but rather that the distribution of sample means will be normal. Violation of this assumption does not prevent the t-test from working. These are logical assumptions made whenever you use any method to compare means to generalize results from samples to populations.įor the assumption of continuous data, even if the data themselves are not continuous (e.g., discrete responses to rating scales), the mean becomes more and more continuous as the sample size increases. Unlike the other three assumptions, the assumptions of representativeness and independence have nothing to do with the underlying distribution. Figure 1 shows the assumptions behind the two-sample t-test.įigure 1: Assumptions of the two-sample t-test (* = test is robust against violations of this assumption). One way to respond to this criticism is to cite the large volume of research that shows the t-test to be very robust against violations of its assumptions. ![]() In some cases, researchers report challenges from stakeholders or colleagues to justify their use of t-tests due to concerns about meeting assumptions. In teaching statistical tests to UX researchers over the last decade, we’ve found that the possible violation of assumptions is a common concern about using t-tests. While it’s easy to conduct a two-sample t-test using readily available online calculators and software packages (including Excel, R, and SPSS), it can be hard to remember what the assumptions are and what risks you run by not meeting those assumptions. ![]() The t-test, like most statistical tests, has certain requirements (assumptions) for its use. It can be used to compare two samples of many UX metrics, such as SUS scores, SEQ scores, and task times. The two-sample t-test is one of the most widely used statistical tests, assessing whether mean differences between two samples are statistically significant. ![]()
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